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[ "Hierarchical Reinforcement Learning is a promising approach to long-horizon decision-making problems with sparse rewards.", "Unfortunately, most methods still decouple the lower-level skill acquisition process and the training of a higher level that controls the skills in a new task.", "Treating the skills as fixed can lead to significant sub-optimality in the transfer setting.", "In this work, we propose a novel algorithm to discover a set of skills, and continuously adapt them along with the higher level even when training on a new task.", "Our main contributions are two-fold.", "First, we derive a new hierarchical policy gradient, as well as an unbiased latent-dependent baseline.", "We introduce Hierarchical Proximal Policy Optimization (HiPPO), an on-policy method to efficiently train all levels of the hierarchy simultaneously.", "Second, we propose a method of training time-abstractions that improves the robustness of the obtained skills to environment changes.", "Code and results are available at sites.google.com/view/hippo-rl.", "Reinforcement learning (RL) has made great progress in a variety of domains, from playing games such as Pong and Go BID5 BID20 to automating robotic locomotion BID11 BID20 Florensa et al., 2018b) , dexterous manipulation (Florensa et al., 2017b; BID1 , and perception BID7 Florensa et al., 2018a ).", "Yet, most work in RL is still learning a new behavior from scratch when faced with a new problem.", "This is particularly inefficient when dealing with tasks that are hard to solve due to sparse rewards or long horizons, or when solving many related tasks.A promising technique to overcome this limitation is Hierarchical Reinforcement Learning (HRL) BID17 Florensa et al., 2017a) .", "In this paradigm, policies have several modules of abstraction, so the reuse of a subset of the modules becomes easier.", "The most common case consists of temporal abstraction BID9 Dayan & Hinton, 1993 ), where a higher-level policy (manager) takes actions at a lower frequency, and its actions condition the behavior of some lower level skills or sub-policies.", "When transferring knowledge to a new task, most prior works fix the skills and train a new manager on top.", "Despite having a clear benefit in kick-starting the learning in the new task, having fixed skills can considerably cap the final performance on the new task (Florensa et al., 2017a) .", "Little work has been done on adapting pre-trained sub-policies to be optimal for a new task.In this paper, we develop a new framework for adapting all levels of temporal hierarchies simultaneously.", "First, we derive an efficient approximated hierarchical policy gradient.", "Our key insight is that, under mild assumptions, the manager's decisions can be considered part of the observation from the perspective of the sub-policies.", "This decouples the gradient with respect to the manager and the sub-policies parameters and provides theoretical justification for a technique used in other prior works (Frans et al., 2018) .", "Second, we introduce an unbiased sub-policy specific baseline for our hierarchical policy gradient.", "Our experiments reveal faster convergence, suggesting efficient gradient variance reduction.", "Then we introduce a more stable way of using this gradient, Hierarchical Proximal Policy Optimization (HiPPO).", "This helps us take more conservative steps in our policy space BID12 , necessary in hierarchies because of the interdependence of each layer.", "Finally we also evaluate the benefit of varying the time-commitment to the sub-policies, and show it helps both in terms of final performance and zero-shot adaptation to similar tasks.", "In this paper, we examined how to effectively adapt hierarchical policies.", "We began by deriving a hierarchical policy gradient and approximation of it.", "We then proposed a new method, HiPPO, that can stably train multiple layers of a hierarchy.", "The adaptation experiments suggested that we can optimize pretrained skills for downstream environments, and learn emergent skills without any unsupervised pre-training.", "We also explored hierarchy from an information bottleneck point of view, demonstrating that HiPPO with randomized period can learn from scratch on sparsereward and long time horizon tasks, while outperforming non-hierarchical methods on zero-shot transfer.There are many enticing avenues of future work.", "For instance, replacing the manually designed bottleneck with a variational autoencoder with an information bottleneck could further improve HiPPO's performance and extend the gains seen here to other tasks.", "Also, as HiPPO provides a policy architecture and gradient expression, we could explore using meta-learning on top of it in order to learn better skills that are more useful on a distribution of different tasks." ]

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[ "We propose HiPPO, a stable Hierarchical Reinforcement Learning algorithm that can train several levels of the hierarchy simultaneously, giving good performance both in skill discovery and adaptation." ]

[ "Learning can be framed as trying to encode the mutual information between input and output while discarding other information in the input.", "Since the distribution between input and output is unknown, also the true mutual information is.", "To quantify how difficult it is to learn a task, we calculate a observed mutual information score by dividing the estimated mutual information by the entropy of the input.", "We substantiate this score analytically by showing that the estimated mutual information has an error that increases with the entropy of the data.", "Intriguingly depending on how the data is represented the observed entropy and mutual information can vary wildly.", "There needs to be a match between how data is represented and how a model encodes it.", "Experimentally we analyze image-based input data representations and demonstrate that performance outcomes of extensive network architectures searches are well aligned to the calculated score.", "Therefore to ensure better learning outcomes, representations may need to be tailored to both task and model to align with the implicit distribution of the model.", "Sometimes perspective is everything.", "While the information content of encoded data may not change when the way it is represented changes, its usefulness can vary dramatically (see Fig. 1 ).", "A \"useful\" representation then is one that makes it easy to extract information of interest.", "This in turn very much depends on who or which algorithm is extracting the information.", "Evidently the way data is encoded and how a model \"decodes\" the information needs to match.", "Historically, people have invented a large variety of \"data representations\" to convey information.", "An instance of this theme is the heliocentric vs. geocentric view of the solar system.", "Before the heliocentric viewpoint was widely accepted, scholars had already worked out the movements of the planets (Theodossiou et al., 2002) .", "The main contribution of the new perspective was that now the planetary trajectories were simple ellipses instead of more complicated movements involving loops 1 .", "In a machine learning context, many have experimented with finding good data representations for specific tasks such as speech recognition (Logan et al., 2000) , different color spaces for face recognition (Hsu et al., 2002) , for increased robustness in face detection (Podilchuk & Zhang, 1998) , and many others.", "Yet no clear understanding has emerged of why a given representation is more suited to one task but less for another.", "We cast the problem of choosing the data representation for learning as one of determining the ease of encoding the relationship between input and output which depends both on how the data is represented and which model is supposed to encode it.", "Contribution: In this work, we argue that learning a task is about encoding the relationship between input and output.", "Each model implicitly has a way of encoding information, where some variations in the data are easier to encode than others.", "Armed with this insight, we empirically evaluate different data representations and record what impact data representations have on learning outcomes and types of networks found by automated network optimization.", "Most interestingly, we are able Figure 1 : These images contain different representations of the same information.", "However, one of the two is much easier for us to understand.", "We posit that, for our nervous system, one of the two images has a higher observed mutual information for the task of recognizing the person.", "to show that relative learning outcomes can be predicted by an empirical mutual information score, which we coin Observed Mutual Information (OMI) score.", "After evaluating a total of 5753 networks, 3702 of which finished training, we have verified our intuition that representations are important.", "We see a fairly consistent pattern over all datasets of RGB and YCbCr being the best representations, followed by PREC and blockwise DCT, while DCT falls short (see Fig. 3 ).", "Moreover, we observe the great importance of hyperparameters in the spread of results for each network architecture.", "Had we chosen to hand-tune our parameters and accidentally picked a very poor performing network for the RGB representation we could have easily come to the conclusion that DCT achieves better results on all datasets.", "As we predicted, the performance of a representations also depends greatly on the network architecture.", "This is especially visible for the lane following dataset.", "We can see that, surprisingly, dense networks are among the best for both RGB and YCbCr, while they fall far behind on all other representations.", "The OMI scores we proposed show strong correlation with the results we obtained from architecture search.", "They can even predict the comparatively small differences between the other representations with reasonable accuracy (see Fig. 2 ).", "It is unclear why the prediction fails for some of the datasets, especially the linear score on the KDEF dataset.", "Overall, we observe the significant correlated effect representation has on estimated entropy, OMI scores as well as performance.", "This work started by trying to pave a way to the exciting task of determining the difficulty of a learning task.", "To achieve this we introduced OMI, as a score that takes both estimated mutual information and possible variance of such an estimate into account.", "If the score proves itself also in future works, it may serve as a useful tool for automatic representation or architecture search.", "As outlined, this will depend to a great deal on how well we understand the candidate distributions of network architectures and representations that are currently in use.", "Similarly, it will be beneficial to study further techniques on removing the bias in the estimation of mutual information and entropy.", "We have shown that in many problems of interests the naive computation of mutual information is biased and representation dependent; our OMI score partially remove this bias.", "This score also now provides a criterion to evaluate different representations in a principled way.", "To narrate Tab.", "2 we note that that estimating small entropy values is very error prone.", "When assuming a normal distribution, the entropy is calculated via the sum of the logarithm of eigenvalues of the covariance matrix of the data.", "The conditioning of the logarithm however gets worse, the closer its argument is to zero.", "Eigenvalues close enough to zero are thus likely to carry a significant error when used for entropy computation.", "This all is to say that while purely mathematically it is impossible to have negative mutual information values, numerically such things are bound to happen when dealing with small eigenvalues as is prominent with the DCT representation." ]

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[ "We take a step towards measuring learning task difficulty and demonstrate that in practice performance strongly depends on the match of the representation of the information and the model interpreting it." ]

[ "Sepsis is a life-threatening complication from infection and a leading cause of mortality in hospitals. ", "While early detection of sepsis improves patient outcomes, there is little consensus on exact treatment guidelines, and treating septic patients remains an open problem. ", "In this work we present a new deep reinforcement learning method that we use to learn optimal personalized treatment policies for septic patients.", "We model patient continuous-valued physiological time series using multi-output Gaussian processes, a probabilistic model that easily handles missing values and irregularly spaced observation times while maintaining estimates of uncertainty.", "The Gaussian process is directly tied to a deep recurrent Q-network that learns clinically interpretable treatment policies, and both models are learned together end-to-end. ", "We evaluate our approach on a heterogeneous dataset of septic spanning 15 months from our university health system, and find that our learned policy could reduce patient mortality by as much as 8.2\\% from an overall baseline mortality rate of 13.3\\%. ", "Our algorithm could be used to make treatment recommendations to physicians as part of a decision support tool, and the framework readily applies to other reinforcement learning problems that rely on sparsely sampled and frequently missing multivariate time series data.\n", "Sepsis is a poorly understood complication arising from infection, and is both a leading cause in patient mortality BID8 ) and in associated healthcare costs BID37 ).", "Early detection is imperative, as earlier treatment is associated with better outcomes BID33 , BID21 ).", "However, even among patients with recognized sepsis, there is no standard consensus on the best treatment.", "There is a pressing need for personalized treatment strategies tailored to the unique physiology of individual patients.", "Guidelines on sepsis treatment previously centered on early goal directed therapy (EGDT) and more recently have focused on sepsis care bundles, but none of these approaches are individualized.Before the landmark publication on the use of early goal directed therapy BID31 ), there was no standard management for severe sepsis and septic shock.", "EGDT consists of early identification of high-risk patients, appropriate cultures, infection source control, antibiotics administration, and hemodynamic optimization.", "The study compared a 6-hour protocol of EGDT promoting use of central venous catheterization to guide administration of fluids, vasopressors, inotropes, and packed red-blood cell transfusions, and was found to significantly lower mortality.", "Following the initial trial, EGDT became the cornerstone of the sepsis resuscitation bundle for the Surviving Sepsis Campaign (SCC) and the Centers for Medicare and Medicaid Services (CMS) BID6 ).Despite", "the promising results of EGDT, concerns arose. External", "validity outside the single center study was unclear, it required significant resources for implementation, and the elements needed to achieve pre-specified hemodynamic targets held potential risks. Between", "2014-2017, a trio of trials reported an all-time low sepsis mortality, and questioned the continued need for all elements of EGDT for patients with severe and septic shock BID28 , ARISE & Group (2014) , BID27 ). The trial", "authors concluded EGDT did not improve patient survival compared to usual care but was associated with increased ICU admissions BID0 ). As a result", ", they did not recommend it be included in the updated SCC guidelines BID30 ).Although the", "SSC guidelines provide an overarching framework for sepsis treatment, there is renewed interest in targeting treatment and disassembling the bundle BID22 ). A recent metaanalysis", "evaluated 12 randomized trials and 31 observational studies and found that time to first an-tibiotics explained 96-99% of the survival benefit BID17 ). Likewise, a study of", "50,000 patients across the state of New York found mortality benefit for early antibiotic administration, but not intravenous fluids BID33 ). Beyond narrowing the", "bundle, there is emerging evidence that a patient's baseline risk plays an important role in response to treatment, as survival benefit was significantly reduced for patients with more severe disease BID17 ).Taken together, the poor", "performance of EGDT compared to standard-of-care and improved understanding of individual treatment effects calls for re-envisioning sepsis treatment recommendations. Though general consensus", "in critical care is that the individual elements of the sepsis bundle are typically useful, it is unclear exactly when each element should be administered and in what quantity.In this paper, we aim to directly address this problem using deep reinforcement learning. We develop a novel framework", "for applying deep reinforcement learning to clinical data, and use it to learn optimal treatments for sepsis. With the widespread adoption", "of Electronic Health Records, hospitals are already automatically collecting the relevant data required to learn such models. However, real-world operational", "healthcare data present many unique challenges and motivate the need for methodologies designed with their structure in mind. In particular, clinical time series", "are typically irregularly sampled and exhibit large degrees of missing values that are often informatively missing, necessitating careful modeling. The high degree of heterogeneity presents", "an additional difficulty, as patients with similar symptoms may respond very differently to treatments due to unmeasured sources of variation. Alignment of patient time series can also", "be a potential issue, as patients admitted to the hospital may have very different unknown clinical states and can develop sepsis at any time throughout their stay (with many already septic upon admission).Part of the novelty in our approach hinges", "on the use of a Multi-output Gaussian process (MGP) as a preprocessing step that is jointly learned with the reinforcement learning model. We use an MGP to interpolate and to impute", "missing physiological time series values used by the downstream reinforcement learning algorithm, while importantly maintaining uncertainty about the clinical state. The MGP hyperparameters are learned end-to-end", "during training of the reinforcement learning model by optimizing an expectation of the standard Q-learning loss. Additionally, the MGP allows for estimation of", "uncertainty in the learned Q-values. For the model architecture we use a deep recurrent", "Q-network, in order to account for the potential for non-Markovian dynamics and allow the model to have memory of past states and actions. In our experiments utilizing EHR data from septic", "patients spanning 15 months from our university health system, we found that both the use of the MGP and the deep recurrent Q-network offered improved performance over simpler approaches.", "In this paper we presented a new framework combining multi-output Gaussian processes and deep reinforcement learning for clinical problems, and found that our approach performed well in estimating optimal treatment strategies for septic patients.", "The use of recurrent structure in the Q-network architecture yielded higher expected returns than a standard Q-network, accounting for the nonMarkovian nature of real-world medical data.", "The multi-output Gaussian process also improved performance by offering a more principled method for interpolation and imputation, and use of the full MGP posterior improved upon the results from just using the posterior mean.In the future, we could include treatment recommendations from our learned policies into our dashboard application we have developed for early detection of sepsis.", "The treatment recommendations might help providers better care for septic patients after sepsis has been properly identified, and start treatments faster.", "There are many potential avenues for future work.", "One promising direction is to investigate the use of more complex reward functions, rather than the sparse rewards used in this work.", "More sophisticated rewards might take into account clinical targets for maintaining hemodynamic stability, and penalize an overzealous model that recommends too many unnecessary actions.", "Our modeling framework is fairly generalizable, and can easily be applied to other medical applications where there is a need for data-driven decision support tools.", "In future work we plan to use similar methods to learn optimal treatment strategies for treating patients with cardiogenic shock, and to learn effective insulin dosing regimes for patients on high-dose steroids." ]

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[ "We combine Multi-output Gaussian processes with deep recurrent Q-networks to learn optimal treatments for sepsis and show improved performance over standard deep reinforcement learning methods," ]

[ "Unsupervised and semi-supervised learning are important problems that are especially challenging with complex data like natural images.", "Progress on these problems would accelerate if we had access to appropriate generative models under which to pose the associated inference tasks.", "Inspired by the success of Convolutional Neural Networks (CNNs) for supervised prediction in images, we design the Neural Rendering Model (NRM), a new hierarchical probabilistic generative model whose inference calculations correspond to those in a CNN.", "The NRM introduces a small set of latent variables at each level of the model and enforces dependencies among all the latent variables via a conjugate prior distribution.", "The conjugate prior yields a new regularizer for learning based on the paths rendered in the generative model for training CNNs–the Rendering Path Normalization (RPN).", "We demonstrate that this regularizer improves generalization both in theory and in practice.", "Likelihood estimation in the NRM yields the new Max-Min cross entropy training loss, which suggests a new deep network architecture–the Max- Min network–which exceeds or matches the state-of-art for semi-supervised and supervised learning on SVHN, CIFAR10, and CIFAR100." ]

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[ "We develop a new deep generative model for semi-supervised learning and propose a new Max-Min cross-entropy for training CNNs." ]

[ "Deep reinforcement learning (RL) agents often fail to generalize to unseen environments (yet semantically similar to trained agents), particularly when they are trained on high-dimensional state spaces, such as images.", "In this paper, we propose a simple technique to improve a generalization ability of deep RL agents by introducing a randomized (convolutional) neural network that randomly perturbs input observations.", "It enables trained agents to adapt to new domains by learning robust features invariant across varied and randomized environments.", "Furthermore, we consider an inference method based on the Monte Carlo approximation to reduce the variance induced by this randomization.", "We demonstrate the superiority of our method across 2D CoinRun, 3D DeepMind Lab exploration and 3D robotics control tasks: it significantly outperforms various regularization and data augmentation methods for the same purpose.", "Deep reinforcement learning (RL) has been applied to various applications, including board games (e.g., Go (Silver et al., 2017) and Chess (Silver et al., 2018) ), video games (e.g., Atari games (Mnih et al., 2015) and StarCraft (Vinyals et al., 2017) ), and complex robotics control tasks (Tobin et al., 2017; Ren et al., 2019) .", "However, it has been evidenced in recent years that deep RL agents often struggle to generalize to new environments, even when semantically similar to trained agents (Farebrother et al., 2018; Zhang et al., 2018b; Gamrian & Goldberg, 2019; Cobbe et al., 2019) .", "For example, RL agents that learned a near-optimal policy for training levels in a video game fail to perform accurately in unseen levels (Cobbe et al., 2019) , while a human can seamlessly generalize across similar tasks.", "Namely, RL agents often overfit to training environments, thus the lack of generalization ability makes them unreliable in several applications, such as health care (Chakraborty & Murphy, 2014) and finance (Deng et al., 2016) .", "The generalization of RL agents can be characterized by visual changes (Cobbe et al., 2019; Gamrian & Goldberg, 2019) , different dynamics (Packer et al., 2018) , and various structures (Beattie et al., 2016; Wang et al., 2016) .", "In this paper, we focus on the generalization across tasks where the trained agents take various unseen visual patterns at the test time, e.g., different styles of backgrounds, floors, and other objects (see Figure 1 ).", "We also found that RL agents completely fail due to small visual changes 1 because it is challenging to learn generalizable representations from high-dimensional input observations, such as images.", "To improve generalization, several strategies, such as regularization (Farebrother et al., 2018; Zhang et al., 2018b; Cobbe et al., 2019) and data augmentation (Tobin et al., 2017; Ren et al., 2019) , have been proposed in the literature (see Section 2 for further details).", "In particular, Tobin et al. (2017) showed that training RL agents in various environments generated by randomizing rendering in a simulator improves the generalization performance, leading to a better performance in real environments.", "This implies that RL agents can learn invariant and robust representations if diverse input observations are provided during training.", "However, their method is limited by requiring a physics simulator, which may not always be available.", "This motivates our approach of developing a simple and plausible method applicable to training deep RL agents.", "The main contribution of this paper is to develop a simple randomization technique for improving the generalization ability across tasks with various unseen visual patterns.", "Our main idea is to utilize random (convolutional) networks to generate randomized inputs (see Figure 1 (a)), and train RL agents (or their policy) by feeding them into the networks.", "Specifically, by re-initializing the parameters of random networks at every iteration, the agents are encouraged to be trained under a broad range of perturbed low-level features, e.g., various textures, colors, or shapes.", "We discover that the proposed idea guides RL agents to learn generalizable features that are more invariant in unseen environments (see Figure 3 ) than conventional regularization (Srivastava et al., 2014; Ioffe & Szegedy, 2015) and data augmentation (Cobbe et al., 2019; Cubuk et al., 2019) techniques.", "Here, we also provide an inference technique based on the Monte Carlo approximation, which stabilizes the performance by reducing the variance incurred from our randomization method at test time.", "We demonstrate the effectiveness of the proposed method on the 2D CoinRun (Cobbe et al., 2019) game, the 3D DeepMind Lab exploration task (Beattie et al., 2016) , and the 3D robotics control task (Fan et al., 2018) .", "For evaluation, the performance of the trained agents is measured in unseen environments with various visual and geometrical patterns (e.g., different styles of backgrounds, objects, and floors), guaranteeing that the trained agents encounter unseen inputs at test time.", "Note that learning invariant and robust representations against such changes is essential to generalize to unseen environments.", "In our experiments, the proposed method significantly reduces the generalization gap in unseen environments unlike conventional regularization and data augmentation techniques.", "For example, compared to the agents learned with the cutout (DeVries & Taylor, 2017 ) data augmentation methods proposed by Cobbe et al. (2019) , our method improves the success rates from 39.8% to 58.7% under 2D CoinRun, the total score from 55.4 to 358.2 for 3D DeepMind Lab, and the total score from 31.3 to 356.8 for the Surreal robotics control task.", "Our results can be influential to study other generalization domains, such as tasks with different dynamics (Packer et al., 2018) , as well as solving real-world problems, such as sim-to-real transfer (Tobin et al., 2017) .", "In this paper, we explore generalization in RL where the agent is required to generalize to new environments in unseen visual patterns, but semantically similar.", "To improve the generalization ability, we propose to randomize the first layer of CNN to perturb low-level features, e.g., various textures, colors, or shapes.", "Our method encourages agents to learn invariant and robust representations by producing diverse visual input observations.", "Such invariant features could be useful for several other related topics, like an adversarial defense in RL (see Appendix D for further discussions), sim-toreal transfer (Tobin et al., 2017; Ren et al., 2019) , transfer learning (Parisotto et al., 2016; Rusu et al., 2016a; b) , and online adaptation (Nagabandi et al., 2019) .", "We provide the more detailed discussions on an extension to the dynamics generalization and failure cases of our method in Appendix L and M, respectively.", "The adversarial (visually imperceptible) perturbation (Szegedy et al., 2014) to clean input observations can induce the DNN-based policies to generate an incorrect decision at test time (Huang et al., 2017; Lin et al., 2017) .", "This undesirable property of DNNs has raised major security concerns.", "In this section, we evaluate if the proposed method can improve the robustness on adversarial Algorithm 1 PPO + random networks, Actor-Critic Style for iteration= 1, 2, · · · do Sample the parameter φ of random networks from prior distribution P (φ) for actor= 1, 2, · · · , N do Run policy π (a|f (s; φ) ; θ) in the given environment for T timesteps Compute advantage estimates end for Optimize L random in equation (3) with respect to θ end for attacks.", "Our method is expected to improve the robustness against such adversarial attacks because the agents are trained with randomly perturbed inputs.", "To verify that the proposed method can improve the robustness to adversarial attacks, the adversarial samples are generated using FGSM (Goodfellow et al., 2015) by perturbing inputs to the opposite direction to the most probable action initially predicted by the policy:", "where ε is the magnitude of noise and a * = arg max a π(a|s; θ) is the action from the policy.", "Table 4 shows that our proposed method can improve the robustness against FGSM attacks with ε = 0.01, which implies that hidden representations of trained agents are more robust.", "(2019) , two boxes are painted in the upper-left corner, where their color represents the x-and y-axis velocity to help the agents quickly learn to act optimally.", "In this way, the agent does not need to memorize previous states, so a simple CNN-based policy without LSTM can effectively perform in our experimental settings.", "Data augmentation methods.", "In this paper, we compare a variant of cutout (DeVries & Taylor, 2017) proposed in Cobbe et al. (2019) , grayout, inversion, and color jitter (Cubuk et al., 2019) .", "Specifically, the cutout augmentation applies a random number of boxes in random size and color to the input, the grayout method averages all three channels of the input, the inversion method inverts pixel values by a 50% chance, and the color jitter changes the characteristics of images commonly used for data augmentation in computer vision tasks: brightness, contrast, and saturation.", "For every timestep in the cutout augmentation, we first randomly choose the number of boxes from zero to five, assign them a random color and size, and place them in the observation.", "For the color jitter, the parameters for brightness, contrast, and saturation are randomly chosen in [0.5,1.5].", "10 For each episode, the parameters of these methods are randomized and fixed such that the same image preprocessing is applied within an episode." ]

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[ "We propose a simple randomization technique for improving generalization in deep reinforcement learning across tasks with various unseen visual patterns." ]

[ "Touch interactions with current mobile devices have limited expressiveness.", "Augmenting devices with additional degrees of freedom can add power to the interaction, and several augmentations have been proposed and tested.", "However, there is still little known about the effects of learning multiple sets of augmented interactions that are mapped to different applications.", "To better understand whether multiple command mappings can interfere with one another, or affect transfer and retention, we developed a prototype with three pushbuttons on a smartphone case that can be used to provide augmented input to the system.", "The buttons can be chorded to provide seven possible shortcuts or transient mode switches.", "We mapped these buttons to three different sets of actions, and carried out a study to see if multiple mappings affect learning and performance, transfer, and retention.", "Our results show that all of the mappings were quickly learned and there was no reduction in performance with multiple mappings.", "Transfer to a more realistic task was successful, although with a slight reduction in accuracy.", "Retention after one week was initially poor, but expert performance was quickly restored.", "Our work provides new information about the design and use of augmented input in mobile interactions.", "Mobile touchscreen devices such as smartphones, tablets, and smartwatches are now ubiquitous.", "The simplicity of touch-based interaction is one of the main reasons for their popularity, but touch interfaces have low expressivenessthey are limited in terms of the number of actions that the user can produce in a single input.", "As a result, touch interactions often involve additional actions to choose modes or to navigate menu hierarchies.", "These limitations on touch input can be addressed by adding new degrees of freedom to touch devices.", "For example, both Android and IOS devices have augmentations that allow the user to specify the difference between scrolling and selecting: Android uses a timeout on the initial touch (i.e., a drag starts with either a short press or a long press), and some IOS devices use pressure-sensitive screens that use different pressure levels to specify selection and scrolling [13] .", "Researchers have also proposed adding a wide variety of new degrees of freedom for touch devices -including multi-touch and bimanual input [16, 32, 42] , external buttons and force sensors [1, 44] , back-of-device touch [3] , sensors for pen state [26] or screen tilt [39, 43] , and pressure sensors [8, 9] .", "Studies have shown these additional degrees of freedom to be effective at increasing the expressive power of interaction with a mobile device.", "However, previous research has only looked at these new degrees of freedom in single contexts, and as a result we know little about how augmented input will work when it is used in multiple different applications: if an augmented input is mapped to a set of actions that are specific to one application, will there be interference when the same augmentations are mapped to a different set of actions in another application?", "To find out how multiple mappings for a new degree of freedom affect learning and usage, we carried out a study with a prototype device that provides three buttons on the side of a smartphone case.", "The buttons can be chorded, giving seven inputs that can be used for discrete commands or transient modes.", "We developed three different mappings for these chording buttons for three different contexts: shortcuts for a launcher app, colour selections for a drawing app; and modes for a text-editing app.", "Our study looked at three issues: first, whether learning multiple mappings with the chorded buttons would interfere with learning or accuracy; second, whether people could transfer their learning from training to usage tasks that set the button commands into more complex and realistic activities; and third, whether memory of the multiple mappings would be retained over one week, without any intervening practice.", "Our evaluation results provide new insights into the use of augmented input for mobile devices:  Learning multiple mappings did not reduce performance -people were able to learn all three mappings well, and actually learned the second and third mappings significantly faster than the first;  Multiple mappings did not reduce accuracy -people were as accurate on a memory test with three mappings as they were when learning the individual mappings;", " Performance did transfer from training to more realistic usage tasks, although accuracy decreased slightly;  Retention after one week was initially poor (accuracy was half that of the first session), but performance quickly returned to near-expert levels.", "Our work provides two main contributions.", "First, we show that chorded input is a successful way to provide a rich input vocabulary that can be used with multiple applications.", "Second, we provide empirical evidence that mapping augmented input to multiple contexts does not impair performance.", "Our results provide new evidence that augmented input can realistically increase the expressive power of interactions with mobile devices.", "[7, 19, 22, 23] ), and researchers have proposed new paradigms of interaction (e.g., for eyes-free ubiquitous computing [29] or for post-WIMP devices [4, 5, 24] ) that can incorporate different types of augmentation.", "Cechanowicz and colleagues also created a framework specifically about augmented interactions [9] ; they suggest several ways of adding to an interaction, such as adding states to a discrete degree of freedom, adding an entirely new degree of freedom, or \"upgrading\" a discrete degree of freedom to use continuous input.", "Our study provides several main findings:  The training phase showed that people were able to learn all three mappings quickly (performance followed a power law), and were able to achieve 90% accuracy within a few training blocks;  Overloading the buttons with three different mappings did not appear to cause any problems for participantsthe second and third mappings were learned faster than the first, and there was no difference in performance across the position of the learned mappings;  People were able to successfully transfer their expertise from the training system to the usage tasks -although performance dropped by a small amount;  Performance in the memory test, which mixed all three mappings together, was very strong, with many of the items remembered at near 100% accuracy;  Retention over one week without any intervening practice was initially poor (about half the accuracy of the first memory test), but recovered quickly in the usage tasks to near the levels seen in the first sessions.", "In the following paragraphs we discuss the reasons for our results, and comment on how our findings can be generalized and used in the design of richer touch-based interactions.", "Expressiveness is limited in mobile touch interfaces.", "Many researchers have devised new ways of augmenting these interactions, but there is still little understanding of issues of interference, transfer, and retention for augmented touch interactions, particularly those that use multiple mappings for different usage contexts.", "To provide information about these issues, we developed an augmented phone case with three pushbuttons that can be chorded to provide seven input states.", "The external buttons can provide quick access to command shortcuts and transient modes, increasing the expressive power of interaction.", "We carried out a four-part study with the system, and found that people can successfully learn multiple mappings of chorded commands, and can maintain their expertise in more-complex usage tasks.", "Retention was found to be an important issue -accuracy dropped over one week, but was quickly restored after a short period of use.", "Our work provides new knowledge about augmented interactions for touch devices, and shows that adding simple input mechanisms like chorded buttons are a promising way to augment mobile interactions." ]

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[ "Describes a study investigating interference, transfer, and retention of multiple mappings with the same set of chorded buttons" ]

[ "Neural networks are widely used in Natural Language Processing, yet despite their empirical successes, their behaviour is brittle: they are both over-sensitive to small input changes, and under-sensitive to deletions of large fractions of input text.", "This paper aims to tackle under-sensitivity in the context of natural language inference by ensuring that models do not become more confident in their predictions as arbitrary subsets of words from the input text are deleted.", "We develop a novel technique for formal verification of this specification for models based on the popular decomposable attention mechanism by employing the efficient yet effective interval bound propagation (IBP) approach.", "Using this method we can efficiently prove, given a model, whether a particular sample is free from the under-sensitivity problem.", "We compare different training methods to address under-sensitivity, and compare metrics to measure it.", "In our experiments on the SNLI and MNLI datasets, we observe that IBP training leads to a significantly improved verified accuracy.", "On the SNLI test set, we can verify 18.4% of samples, a substantial improvement over only 2.8% using standard training.", "Natural language processing (NLP) widely relies on neural networks, a model class known to be vulnerable to adversarial input perturbations (Szegedy et al., 2013; Kurakin et al., 2016) .", "Adversarial samples typically expose over-sensitivity to semantically invariant text transformations (Belinkov & Bisk, 2017; Ettinger et al., 2017) , e.g. character flips (Ebrahimi et al., 2018) or paraphrases (Ribeiro et al., 2018b; .", "Feng et al. (2018) exposed another type of problematic behavior: deleting large parts of input text can cause a model's confidence to increase; Figure 1 shows an example.", "That is, reduced sets of input words can suffice to trigger more confident predictions.", "Such under-sensitivity is problematic: neural models can 'solve' NLP tasks without task-relevant textual comprehension skills, but instead fit spurious cues in the data that suffice to form correct predictions.", "Models might then achieve strong nominal test accuracy on data of the same (biased) distribution as the training set, by exploiting predictive shortcuts that are not representative of the given NLP task at hand.", "Consequently, they fail drastically when evaluated on samples without these spurious cues (Jia & Liang, 2017; Poliak et al., 2018; Gururangan et al., 2018; Niven & Kao, 2019) .", "A major issue with identifying reduced inputs is the combinatorially large space of arbitrary text deletions; this can only be searched exhaustively for short sequences.", "Prior work has considered heuristics like beam search (Feng et al., 2018) or bandits (Ribeiro et al., 2018a) , but these are generally not guaranteed to find the worst-case reductions.", "In this work, we address the under-sensitivity issue by designing and formally verifying the undersensitivity specification that a model should not become more confident as arbitrary subsets of input words are deleted.", "1 Under-sensitivity behaviour is not reflected in nominal accuracy, but one can instead use this specification to measure and evaluate the extent with which samples exhibit undersensitivity.", "Instead of better, yet still imperfect search heuristics, we describe how interval bound propagation (IBP) (Gowal et al., 2018; Mirman et al., 2018 ) -a formal model verification methodcan be used to efficiently cover the full reduction space, and verify the under-sensitivity specification.", "IBP can be applied at test time to arbitrary model inputs to verify whether or not they are undersensitive; but it can also be used to derive a new auxiliary training objective that leads to models verifiably adhering to this specification, and which we find generalizes to held-out test data.", "While under-sensitivity has been demonstrated for several NLP tasks (Feng et al., 2018) , we chose to study the use case of natural language inference (NLI) (Dagan et al., 2006; Bowman et al., 2015) in particular as a representative task: sequences are comparatively short, datasets large, and the label complexity is small.", "We investigate the verification of the popular decomposable attention model (DAM) 2 (Parikh et al., 2016) in detail.", "This architecture covers many of the neural layer types of contemporary models, and we focus on a detailed description for how IBP can be leveraged to efficiently verify its behaviour.", "We then experimentally compare various training methods addressing under-sensitivity:", "i) standard training", "ii) data augmentation", "iii) adversarial training", "iv) IBP-verified training and", "v) entropy regularization, and evaluate their effectiveness against nominal (test) accuracy, adversarial accuracy, IBP-verified accuracy and a verification oracle.", "To summarise, the main contributions of this paper are (1) Formalization of the problem of verifying an under-sensitivity specification, (2) Verification of the Decomposable Attention Model using Interval Bound Propagation, and (3) Empirical analysis of the efficacy of", "(i) different evaluation methods for verifying robustness; and", "(ii) different training methods for developing verifiably robust models.", "Verification of a specification offers a stronger form of robustness than robustness to adversarial samples.", "Adversarial accuracy, as e.g. derived from beam search, might conceptually be easier to compute, yet has no guarantees to find all or the strongest violations.", "In fact, evaluating against weak adversaries under-estimates the extent of a problem and may lead to a false sense of confidence.", "IBP verification can provide guarantees on the nonexistence of reduced inputs, but it is incomplete and can have false negatives.", "Observations of comparatively low verification or adversarial accuracy rates-as in this workare not new, and have been found to be a general problem of datasets with high sample complexity (Schmidt et al., 2018) .", "We emphasise that under-sensitivity is a very challenging problem to address; even the relatively conservative specification of non-increasing probability under deletion cannot be fulfilled for the majority of test samples under the baselines tested.", "We see the verification of the attention-based DAM model as a stepping stone towards the verification of larger and more performant attention-based architectures, such as BERT.", "Following the derivations here, token deletion bounds could similarly be propagated through BERT's self-attention layer.", "Towards this end, however, we see two main hurdles:", "i) BERT's network depth, resulting in gradually looser IBP bounds", "ii) BERT's word piece tokenisation, which requires special consideration in conjunction with token-level perturbations.", "We have investigated under-sensitivity to input text deletions in NLI and recast the problem as one of formally verifying a specification on model behaviour.", "We have described how Interval Bound Propagation can be used in order to verify the popular Decomposable Attention Model, and have then compared several training methods in their ability to address and be verified against undersensitivity.", "We observed that only a relatively small fraction of data points can be positively verified, but that IBP-training in particular is capable of improving verified accuracy." ]

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[ "Formal verification of a specification on a model's prediction undersensitivity using Interval Bound Propagation" ]

[ "Training with larger number of parameters while keeping fast iterations is an increasingly\n", "adopted strategy and trend for developing better performing Deep Neural\n", "Network (DNN) models.", "This necessitates increased memory footprint and\n", "computational requirements for training.", "Here we introduce a novel methodology\n", "for training deep neural networks using 8-bit floating point (FP8) numbers.\n", "Reduced bit precision allows for a larger effective memory and increased computational\n", "speed.", "We name this method Shifted and Squeezed FP8 (S2FP8).", "We\n", "show that, unlike previous 8-bit precision training methods, the proposed method\n", "works out of the box for representative models: ResNet50, Transformer and NCF.\n", "The method can maintain model accuracy without requiring fine-tuning loss scaling\n", "parameters or keeping certain layers in single precision.", "We introduce two\n", "learnable statistics of the DNN tensors - shifted and squeezed factors that are used\n", "to optimally adjust the range of the tensors in 8-bits, thus minimizing the loss in\n", "information due to quantization.", "Deep neural networks have achieved state-of-the-art performance on a wide variety of computer vision, audio, and natural language processing (NLP) tasks.", "This has resulted in an explosion of interest around techniques to reduce the memory footprint and energy consumption of neural network training and inference (Guo, 2018) .", "Although there are a number of methods to address some of these issues for inference, the most effective method for training is using reduced precision numerical formats.", "While 32-bit floating point (FP32) is the most common data format for neural network training, recent hardware have leveraged techniques that allow for training with 16-bit data formats (Köster et al., 2017; Micikevicius et al., 2018) .", "However, 8-bit precision training remains an open challenge (Johnson, 2018; Kalamkar et al., 2019) .", "Current FP8 training methodologies (Wang et al., 2018; require either specialized chunk-based accumulation, stochastic rounding techniques, loss scaling or maintaining some layers of the network in higher precision.", "Tuning these knobs is non-intuitive and requires significant experimentation for each individual network.", "Accelerating the adoption of 8-bit data in training DNNs requires a hardware-friendly and out-ofthe-box implementation of FP8.", "Due to the reduced number of mantissa bits, 8-bit multipliers are smaller and consume less power compared to higher bit representations.", "In this work we describe a novel 8-bit floating point (FP8) format -shifted and squeezed FP8 (S2FP8) -which has the following advantages compared to previously proposed 8-bit training methodologies:", "• S2FP8 eliminates the need for loss scaling, which requires significant tuning of the loss scale values and schedule for individual topologies • Leveraged by the forward and backward passes of model training, S2FP8 is effective in adjusting the range of gradients and also of activations and weights • S2FP8 does not require keeping the first and last layer in FP32 precision, which is needed for other approaches , however maintains the master weights and accumulations inside the matrix multipliers in FP32", "We demonstrate across image classification, translation, and recommendation models that S2FP8 outperforms previous 8-bit approaches, and reaches the accuracy of FP32 models without any additional hyperparameter tuning.", "We introduce a novel 8-bit floating point data type (S2FP8), that gives competitive performance in comparison to state-of-the-art FP32 baselines over a range of representative networks.", "S2FP8 makes use of shifted and squeezed factors to shift and rescale the range of tensors prior to truncation.", "S2FP8 allows training of neural networks with an 8-bit format while eliminating the need for loss scaling tuning, hardware-complex rounding techniques.", "In addition, compared to existing FP8 implementations we also eliminate the restriction of maintaining the first and last layers in FP32.", "Decreasing", "Movielens 1 million FP32 S2FP8 ∆ FP8 NCF 0.666 0.663 0.003 0.633 Figure A1 : The range and precision of FP8.", "Bar indicate the number density between each power of 2.", "Since FP8 has 2 mantissa bit, the density is 4 (except in the denormals), and the associated machine epsilon is 2 −3 = 1/8.", "The normal representable range goes from 2 −14 to (1 − 2 −3 )2 16 , with denormals from 2 −16 to 2 −14 ." ]

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[ "We propose a novel 8-bit format that eliminates the need for loss scaling, stochastic rounding, and other low precision techniques" ]

[ "Variational Auto Encoders (VAE) are capable of generating realistic images, sounds and video sequences.", "From practitioners point of view, we are usually interested in solving problems where tasks are learned sequentially, in a way that avoids revisiting all previous data at each stage.", "We address this problem by introducing a conceptually simple and scalable end-to-end approach of incorporating past knowledge by learning prior directly from the data. ", "We consider scalable boosting-like approximation for intractable theoretical optimal prior.", "We provide empirical studies on two commonly used benchmarks, namely MNIST and Fashion MNIST on disjoint sequential image generation tasks.", "For each dataset proposed method delivers the best results among comparable approaches, avoiding catastrophic forgetting in a fully automatic way with a fixed model architecture.", "Since most of the real-world datasets are unlabeled, unsupervised learning is an essential part of the machine learning field.", "Generative models allow us to obtain samples from observed empirical distributions of the complicated high-dimensional objects such as images, sounds or texts.", "This work is mostly devoted to VAEs with the focus on incremental learning setting.", "It was observed that VAEs ignore dimensions of latent variables and produce blurred reconstructions (Burda et al., 2015; Sønderby et al., 2016) .", "There are several approaches to address these issues, including amortization gap reduction (Kim et al., 2018) , KL-term annealing (Cremer et al., 2018) and alternative optimization objectives introduction (Rezende and Viola, 2018) .", "In all cases, it was observed that the choice of the prior distribution is highly important and use of default Gaussian prior overregularizes the encoder.", "In this work, we address the problem of constructing the optimal prior for VAE.", "The form of optimal prior (Tomczak and Welling, 2018) was obtained by maximizing a lower bound of the marginal likelihood (ELBO) as the aggregated posterior over the whole training dataset.", "To construct reasonable approximation, we consider a method of greedy KL-divergence projection.", "Applying the maximum entropy approach allows us to formulate a feasible optimization problem and avoid overfitting.", "The greedy manner in which components are added to prior reveals a high potential of the method in an incremental learning setting since we expect prior components to store information about previously learned tasks and overcome catastrophic forgetting (McCloskey and Cohen, 1989; Goodfellow et al., 2013; Nguyen et al., 2017) .", "From practitioners point of view, it is essential to be able to store one model, capable of solving several tasks arriving sequentially.", "Hence, we propose the algorithm with one pair of encoderdecoder and update only the prior.", "We validate our method on the disjoint sequential image generation tasks.", "We consider MNIST and Fashion-MNIST datasets.", "In this work, we propose a method for learning a data-driven prior, using a MM algorithm which allows us to reduce the number of components in the prior distribution without the loss of performance.", "Based on this method, we suggest an efficient algorithm for incremental VAE learning which has single encoder-decoder pair for all the tasks and drastically reduces catastrophic forgetting.", "To make sure that model keeps encoding and decoding prior components as it did during the training of the corresponding task, we add a regularization term to ELBO.", "For that purpose at the end of each task we compute reconstructions of the components' mean value p θ j (x|µ i,j ) = p ij (x).", "All thing considered, objective for the maximization step is the following:" ]

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[ "Novel algorithm for Incremental learning of VAE with fixed architecture" ]

[ "The field of few-shot learning has recently seen substantial advancements.", "Most of these advancements came from casting few-shot learning as a meta-learning problem.Model Agnostic Meta Learning or MAML is currently one of the best approaches for few-shot learning via meta-learning.", "MAML is simple, elegant and very powerful, however, it has a variety of issues, such as being very sensitive to neural network architectures, often leading to instability during training, requiring arduous hyperparameter searches to stabilize training and achieve high generalization and being very computationally expensive at both training and inference times.", "In this paper, we propose various modifications to MAML that not only stabilize the system, but also substantially improve the generalization performance, convergence speed and computational overhead of MAML, which we call MAML++.", "The human capacity to learn new concepts using only a handful of samples is immense.", "In stark contrast, modern deep neural networks need, at a minimum, thousands of samples before they begin to learn representations that can generalize well to unseen data-points BID11 BID9 , and mostly fail when the data available is scarce.", "The fact that standard deep neural networks fail in the small data regime can provide hints about some of their potential shortcomings.", "Solving those shortcomings has the potential to open the door to understanding intelligence and advancing Artificial Intelligence.", "Few-shot learning encapsulates a family of methods that can learn new concepts with only a handful of data-points (usually 1-5 samples per concept).", "This possibility is attractive for a number of reasons.", "First, few-shot learning would reduce the need for data collection and labelling, thus reducing the time and resources needed to build robust machine learning models.", "Second, it would potentially reduce training and fine-tuning times for adapting systems to newly acquired data.", "Third, in many real-world problems there are only a few samples available per class and the collection of additional data is either remarkably time-consuming and costly or altogether impossible, thus necessitating the need to learn from the available few samples.The nature of few-shot learning makes it a very hard problem if no prior knowledge exists about the task at hand.", "For a model to be able to learn a robust model from a few samples, knowledge transfer (see e.g. BID4 from other similar tasks is key.", "However, manual knowledge transfer from one task to another for the purpose of fine-tuning on a new task can be a time consuming and ultimately inefficient process.", "Meta-learning BID22 BID24 , or learning to learn BID23 , can instead be used to automatically learn across-task knowledge usually referred to as across-task (or sometimes slow) knowledge such that our model can, at inference time, quickly acquire task-specific (or fast) knowledge from new tasks using only a few samples.", "Meta-learning can be broadly defined as a class of machine learning models that become more proficient at learning with more experience, thus learning how to learn.", "More specifically meta-learning involves learning at two levels.", "At the task-level, where the base-model is required to acquire task-specific (fast) knowledge rapidly, and at the meta-level, where the meta-model is required to slowly learn across-task (slow) knowledge.", "Recent work in meta-learning has produced One can see that 2 out of 3 seeds with the original strided MAML seem to become unstable and erratic, whereas all 3 of the strided MAML++ models seem to consistently converge very fast, to much higher generalization accuracy without any stability issues.state of the art results in a variety of settings BID26 BID2 BID27 BID0 BID25 BID14 BID15 BID1 BID3 BID17 .", "The application of meta-learning in the fewshot learning setting has enabled the overwhelming majority of the current state of the art few-shot learning methods BID25 BID19 BID6 BID7 BID15 BID17 .", "One such method, known for its simplicity and state of the art performance, is Model Agnostic Meta-Learning (MAML) BID7 .", "In MAML, the authors propose learning an initialization for a base-model such that after applying a very small number of gradient steps with respect to a training set on the base-model, the adapted model can achieve strong generalization performance on a validation set (the validation set consists of new samples from the same classes as the training set).", "Relating back to the definitions of metamodel and base-model, in MAML the meta-model is effectively the initialization parameters.", "These parameters are used to initialize the base-model, which is then used for task-specific learning on a support set, which is then evaluated on a target set.", "MAML is a simple yet elegant meta-learning framework that has achieved state of the art results in a number of settings.", "However, MAML suffers from a variety of problems which:", "1) cause instability during training,", "2) restrict the model's generalization performance,", "3) reduce the framework's flexibility,", "4) increase the system's computational overhead and", "5) require that the model goes through a costly (in terms of time and computation needed) hyperparameter tuning before it can work robustly on a new task.In this paper we propose MAML++, an improved variant of the MAML framework that offers the flexibility of MAML along with many improvements, such as robust and stable training, automatic learning of the inner loop hyperparameters, greatly improved computational efficiency both during inference and training and significantly improved generalization performance.", "MAML++ is evaluated in the few-shot learning setting where the system is able to set a new state of the art across all established few-shot learning tasks on both Omniglot and Mini-Imagenet, performing as well as or better than all established meta learning methods on both tasks.", "In this paper we delve deep into what makes or breaks the MAML framework and propose multiple ways to reduce the inner loop hyperparameter sensitivity, improve the generalization error, stabilize and speed up MAML.", "The resulting approach, called MAML++sets a new state of the art across all few-shot tasks, across Omniglot and Mini-Imagenet.", "The results of the approach indicate that learning per-step learning rates, batch normalization parameters and optimizing on per-step target losses appears to be key for fast, highly automatic and strongly generalizable few-shot learning." ]

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[ "MAML is great, but it has many problems, we solve many of those problems and as a result we learn most hyper parameters end to end, speed-up training and inference and set a new SOTA in few-shot learning" ]

[ "Community detection in graphs is of central importance in graph mining, machine learning and network science.", " Detecting overlapping communities is especially challenging, and remains an open problem", ". Motivated by the success of graph-based deep learning in other graph-related tasks, we study the applicability of this framework for overlapping community detection", ". We propose a probabilistic model for overlapping community detection based on the graph neural network architecture", ". Despite its simplicity, our model outperforms the existing approaches in the community recovery task by a large margin", ". Moreover, due to the inductive formulation, the proposed model is able to perform out-of-sample community detection for nodes that were not present at training time", "Graphs provide a natural way of representing complex real-world systems.", "For understanding the structure and behavior of these systems, community detection methods are an essential tool.", "Detecting communities allows us to analyze social networks BID9 , to detect fraud BID24 , to discover functional units of the brain BID8 , and to predict functions of proteins BID26 .", "Over the last decades, this problem has attracted significant attention of the research community and numerous models and algorithms have been proposed BID32 .", "In particular, it is a well known fact that communities in real graphs are in fact overlapping BID34 , thus, requiring the development of advanced models to capture this complex structure.In this regard, the advent of deep learning methods for graph-structured data opens new possibilities for designing more accurate and more scalable algorithms.", "Indeed, deep learning on graphs has already shown state-of-the-art results in s for various graph-related tasks such as semi-supervised node classification and link prediction BID2 .", "Likewise, a few deep learning methods for community detection in graphs have been proposed BID36 BID4 .", "However, they all have one drawback in common: they only focus on the special case of disjoint (non-overlapping) communities.", "Handling overlapping communities, is a requirement not yet met by existing deep learning approaches to community detection.In this paper we propose an end-to-end deep probabilistic model for overlapping community detection in graphs.", "Our core idea lies in predicting the community affiliations using a graph neural network.", "Despite its simplicity, our model achieves state-of-the art results in community recovery and significantly outperforms the existing approaches.", "Moreover, our model is able to perform out-of-sample (inductive) community detection for nodes that were not seen at training time.", "To summarize, our main contributions are:• We propose the Deep Overlapping Community detection (DOC) model -a simple, yet effective deep learning model for overlapping community detection in graphs.", "DOC is one of few methods is able to perform community detection both transductively and inductively.•", "We introduce 5 new datasets for overlapping community detection, which can act as a benchmark to stimulate future work in this research area.•", "We perform a thorough experimental evaluation of our model, and show its superior performance when comparing with established methods for overlapping community detection.", "In this work we have proposed and studied two deep models for overlapping community detection: DOC-BP, based on the Bernoulli-Poisson link, and DOC-Sigmoid, that relies on the sigmoid link function.", "The two variants of our model achieve state-of-the-art results and convincingly outperfom existing techniques in transductive and inductive community detection tasks.", "Using stochastic training, both approaches are highly efficient and scale to large graphs.", "Among the two proposed models, DOC-BP one average performs better than the DOC-Sigmoid variant.", "We leave to future work to investigate the properties of communities detected by these two methods.To summarize, the results obtained in our experimental evaluation provide strong evidence that deep learning for graphs deserves more attention as a framework for overlapping community detection." ]

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[ "Detecting overlapping communities in graphs using graph neural networks" ]

[ "\nNeural Architecture Search (NAS) aims to facilitate the design of deep networks for new tasks.", "Existing techniques rely on two stages: searching over the architecture space and validating the best architecture.", "NAS algorithms are currently compared solely based on their results on the downstream task.", "While intuitive, this fails to explicitly evaluate the effectiveness of their search strategies.", "In this paper, we propose to evaluate the NAS search phase.\n", "To this end, we compare the quality of the solutions obtained by NAS search policies with that of random architecture selection.", "We find that:", "(i) On average, the state-of-the-art NAS algorithms perform similarly to the random policy;", "(ii) the widely-used weight sharing strategy degrades the ranking of the NAS candidates to the point of not reflecting their true performance, thus reducing the effectiveness of the search process.\n", "We believe that our evaluation framework will be key to designing NAS strategies that consistently discover architectures superior to random ones." ]

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[ "We empirically disprove a fundamental hypothesis of the widely-adopted weight sharing strategy in neural architecture search and explain why the state-of-the-arts NAS algorithms performs similarly to random search." ]

[ "In this paper we use the geometric properties of the optimal transport (OT) problem and the Wasserstein distances to define a prior distribution for the latent space of an auto-encoder.", "We introduce Sliced-Wasserstein Auto-Encoders (SWAE), that enable one to shape the distribution of the latent space into any samplable probability distribution without the need for training an adversarial network or having a likelihood function specified.", "In short, we regularize the auto-encoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a samplable prior distribution.", "We show that the proposed formulation has an efficient numerical solution that provides similar capabilities to Wasserstein Auto-Encoders (WAE) and Variational Auto-Encoders (VAE), while benefiting from an embarrassingly simple implementation.", "We provide extensive error analysis for our algorithm, and show its merits on three benchmark datasets.", "We introduced Sliced Wasserstein auto-encoders (SWAE), which enable one to shape the distribution of the encoded samples to any samplable distribution without the need for adversarial training or having a likelihood function specified.", "In addition, we provided a simple and efficient numerical scheme for this problem, which only relies on few inner products and sorting operations in each SGD iteration.", "We further demonstrated the capability of our method on three image datasets, namely the MNIST, the CelebA face, and the LSUN Bedroom datasets, and showed competitive performance, in the sense of matching distributions p Z and q Z , to the techniques that rely on additional adversarial trainings.", "Finally, we envision SWAE could be effectively used in transfer learning and domain adaptation algorithms where q Z comes from a source domain and the task is to encode the target domain p X in a latent space such that the distribution follows the distribution of the target domain.", "Figure 4: Sample convergence behavior for our method compared to the WAE-GAN, where q Z is set to a ring distribution FIG5 , top left).", "The columns represent batch iterations (batchsize= 500).The", "top half of the table shows results of ψ(z) for z ∼ q Z , and the bottom half shows z ∼ q Z and φ(x) for x ∼ p X . It", "can be seen that the adversarial loss in the latent space does not provide a full coverage of the distribution, which is a similar problem to the well-known 'mode collapse' problem in the GANs. It", "can be seen that SWAE provides a superior match between p Z and q Z while it does not require adversarial training." ]

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[ "In this paper we use the sliced-Wasserstein distance to shape the latent distribution of an auto-encoder into any samplable prior distribution. " ]

[ "The Hamiltonian formalism plays a central role in classical and quantum physics.", "Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time.", "These properties are important for many machine learning problems - from sequence prediction to reinforcement learning and density modelling - but are not typically provided out of the box by standard tools such as recurrent neural networks.", "In this paper, we introduce the Hamiltonian Generative Network (HGN), the first approach capable of consistently learning Hamiltonian dynamics from high-dimensional observations (such as images) without restrictive domain assumptions.", "Once trained, we can use HGN to sample new trajectories, perform rollouts both forward and backward in time, and even speed up or slow down the learned dynamics.", "We demonstrate how a simple modification of the network architecture turns HGN into a powerful normalising flow model, called Neural Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive densities.", "Hence, we hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to machine learning.", "More results and video evaluations are available at: http://tiny.cc/hgn", "We have presented HGN, the first deep learning approach capable of reliably learning Hamiltonian dynamics from pixel observations.", "We have evaluated our approach on four classical physical systems and demonstrated that it outperformed the only relevant baseline by a large margin.", "Hamiltonian dynamics have a number of useful properties that can be exploited more widely by the machine learning community.", "For example, the Hamiltonian induces a smooth manifold and a vector field in the abstract phase space along which certain physical quantities are conserved.", "The time evolution along these paths is also completely reversible.", "These properties can have wide implications in such areas of machine learning as reinforcement learning, representation learning and generative modelling.", "We have demonstrated the first step towards applying the learnt Hamiltonian dynamics as normalising flows for expressive yet computationally efficient density modelling.", "We hope that this work serves as the first step towards a wider adoption of the rich body of physics literature around the Hamiltonian principles in the machine learning community.", "A SUPPLEMENTARY MATERIALS" ]

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[ "We introduce a class of generative models that reliably learn Hamiltonian dynamics from high-dimensional observations. The learnt Hamiltonian can be applied to sequence modeling or as a normalising flow." ]

[ "Cloud Migration transforms customer’s data, application and services from original IT platform to one or more cloud en- vironment, with the goal of improving the performance of the IT system while reducing the IT management cost.", "The enterprise level Cloud Migration projects are generally com- plex, involves dynamically planning and replanning various types of transformations for up to 10k endpoints.", "Currently the planning and replanning in Cloud Migration are generally done manually or semi-manually with heavy dependency on the migration expert’s domain knowledge, which takes days to even weeks for each round of planning or replanning.", "As a result, automated planning engine that is capable of gener- ating high quality migration plan in a short time is particu- larly desirable for the migration industry.", "In this short paper, we briefly introduce the advantages of using AI planning in Cloud Migration, a preliminary prototype, as well as the challenges the requires attention from the planning and scheduling society.", "Automated planning and AI planning have been investigated extensively by researchers and successfully applied in many areas for decades, for example, health care BID0 , semiconductor manufacturing BID1 , and aviation BID2 , to name a few.", "Meanwhile, attracted by the promise of the scalability, flexibility and potentially lower cost of the resources, more and more enterprises are considering moving their IT infrastructure and applications to Cloud or Hybrid Cloud service platforms, which is called Cloud Migration in general (Armbrust et. al. 2010, Khajeh-Hosseini, Greenwood, and Sommerville 2010) .", "Noticing that the discussions of using AI planning in the Cloud Migration are limited both in academia and in industry, in this short paper we identify the advantages and challenges of applying AI planning to Cloud Migration by", "(i) introducing Cloud Migration and its planning problem;", "(ii) demonstrate problem feasibility by showing a prototype AI planning model; and", "(iii) discuss the limits of current model and future research." ]

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[ "In this short paper, we briefly introduce the advantages of using AI planning in Cloud Migration, a preliminary prototype, as well as the chal- lenges the requires attention from the planning and schedul- ing society." ]

[ "Unsupervised domain adaptation aims to generalize the hypothesis trained in a source domain to an unlabeled target domain.", "One popular approach to this problem is to learn a domain-invariant representation for both domains.", "In this work, we study, theoretically and empirically, the explicit effect of the embedding on generalization to the target domain.", "In particular, the complexity of the class of embeddings affects an upper bound on the target domain's risk.", "This is reflected in our experiments, too.", "Domain adaptation is critical in many applications where collecting large-scale supervised data is prohibitively expensive or intractable, or conditions at prediction time can change.", "For instance, self-driving cars must be robust to various conditions such as different weather, change of landscape and traffic.", "In such cases, the model learned from limited source data should ideally generalize to different target domains.", "Specifically, unsupervised domain adaptation aims to transfer knowledge learned from a labeled source domain to similar but completely unlabeled target domains.One popular approach to unsupervised domain adaptation is to learn domain-invariant representations BID7 BID5 , by minimizing a divergence between the representations of source and target domains.", "The prediction function is learned on the latent space, with the aim of making it domain-independent.", "A series of theoretical works justifies this idea BID9 BID1 BID3 .Despite", "the empirical success of domain-invariant representations, exactly matching the representations of source and target distribution can sometimes fail to achieve domain adaptation. For example", ", BID13 show that exact matching may increase target error if label distributions are different between source and target domain, and propose a new divergence metric to overcome this limitation. BID14 establish", "lower and upper bounds on the risk when label distributions between source and target domains differ. BID6 point out", "the information lost in non-invertible embeddings, and propose different generalization bounds based on the overlap of the supports of source and target distribution.In contrast to previous analyses that focus on changes in the label distributions or on joint support, we here study the effect of the complexity of the joint representation. In particular,", "we show a general bound on the target risk that reflects a tradeoff between the embedding complexity and the divergence of source and target in the latent representation space. In particular,", "a too powerful class of embedding functions can result in overfitting the source data and the distribution matching, leading to arbitrarily high target risk. Hence, a restriction", "(taking into account assumptions about correspondences and invariances) is needed. Our experiments reflect", "these trends empirically, too.", "The experiments show that the complexity of the encoder can have a direct effect on the target error.", "A more complex encoder class leads to larger theoretical bound on the target error, and, indeed, aligned with the theory, we see a significant performance drop in target domain.", "Moreover, the experiments suggest that inductive bias is important too.", "With a suitable inductive bias such as CNNs, DANN achieves higher performance than the with the MLP encoder, even if the CNN encoder has twice the number of layers.", "CNNs are standard for many vision tasks, such as digit recognition.", "However, explicit supervision may be required to identify the encoder class when we have less prior knowledge about the task BID10 BID2 .", "In this work, we study the role of embedding complexity for domain-invariant representations.", "We theoretically and empirically show that restricting the encoder is necessary for successful adaptation, a fact that has mostly been overlooked by previous work.", "In fact, without carefully selecting the encoder class, learning domain invariant representations might even harm the performance.", "Our observations motivate future research on identifying eappropriate encoder classes for various tasks." ]

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[ "A general upper bound on the target domain's risk that reflects the role of embedding-complexity." ]

[ "The domain of time-series forecasting has been extensively studied because it is of fundamental importance in many real-life applications.", "Weather prediction, traffic flow forecasting or sales are compelling examples of sequential phenomena.", "Predictive models generally make use of the relations between past and future values.", "However, in the case of stationary time-series, observed values also drastically depend on a number of exogenous features that can be used to improve forecasting quality.", "In this work, we propose a change of paradigm which consists in learning such features in embeddings vectors within recurrent neural networks.", "We apply our framework to forecast smart cards tap-in logs in the Parisian subway network.", "Results show that context-embedded models perform quantitatively better in one-step ahead and multi-step ahead forecasting.", "Classical statistical forecasting methods rely on the existence of temporal correlation between past and future values.", "In particular, the auto-regressive component of ARIMA estimators BID0 ) models the relation between past and future as a linear regression.", "In the deep learning paradigm, Recurrent Neural Networks have long been used to tackle sequential problems.", "Increasingly complex models such as ConvLSTM BID13 ) or Graph Neural Networks ) are developed to model multivariate phenomena and allow a precise modeling of the temporal dynamics.However, exogenous factors can greatly influence the observed values and are not taken into account by the mentioned models.", "For example, the type of road can drastically change traffic flow predictions, the period of the year will determine the values of sales time-series, and so on.", "In this work, we refer to these features as contextual information, or context.", "Such context is naturally used when dealing with stationary time-series to construct baselines based on the average of past values given a context.", "NARX models and their neural networks variations also make use of context by inputting it jointly with previous values of the forecast variable BID17 ).Similar", "to how Graph NN learn relations between nodes, we propose for multivariate stationary timeseries to learn context within a recurrent architecture and we introduce context-embedded RNN. For each", "contextual feature, we concatenate to the observed value an embedding that is to be learned jointly with the weights of the network. We do not", "deal with the case of continuous features but these could be transformed into categories. We tested", "our framework on public transportation tap-in logs one-step ahead and multi-step ahead forecasting, where we consider spatial context in the form of subway stations and temporal context through day of the week and time of the day.To the best of our knowledge, there exists no good-quality public dataset containing subway logs at a satisfying granularity. We realized", "experiments on data provided by Ile-de-France Mobilités 1 (Parisian region public transportation agency) but we expect that the fast development of data collection in this domain will entail the availability of public datasets in a near future. On the other", "hand, all of the source code used to realize the experiments is available on https://github.com/XXXX.Results of the experiments show that contextual models consistently outperform other recurrent models as well as the historical average baseline which is especially strong in the case of stationary 1 https://www.iledefrance-mobilites.fr/ time-series. Contextual models", "perform particularly well for long-term forecasting. In summary, in this", "paper we propose a new paradigm for learning contextual information within RNNs, which quantitatively improves forecasting performance by allowing a fine-grained modeling of local dynamics.The remainder of this paper is organized as follows: background in time-series forecasting and use of context is presented in Section 2; proposed models are introduced in Section 3 and are tested in prediction experiments in Section 4.", "In this paper we presented a novel idea for time-series forecasting with contextual features.", "It consists in learning contextual information that strongly conditions the observed phenomenom within a recurrent neural network.", "We applied this general idea to the concrete case of transportation logs forecasting in the subway and observed significant improvement of the prediction error when using spatial and temporal context.", "In particular, the proposed framework performs significantly better in one-step ahead prediction and remains competitive in long-term forecasting.", "In a very applicated perspective, robust recurrent models could be used in the case of anomalies to accurately predict traffic recovery and help users adapt their behavior.", "Figure 7 : Predictions for the test set are computed using only he 16th first values of each day, i.e. until 8AM and we plot:", "(a) the average RMSE difference between the baseline and some proposed models for every time-step.", "0 corresponds to the baseline performance &", "(b) the predicted logs for the same day and place than in FIG5 ." ]

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[ "In order to forecast multivariate stationary time-series we learn embeddings containing contextual features within a RNN; we apply the framework on public transportation data" ]

[ "The ability of an agent to {\\em discover} its own learning objectives has long been considered a key ingredient for artificial general intelligence.", "Breakthroughs in autonomous decision making and reinforcement learning have primarily been in domains where the agent's goal is outlined and clear: such as playing a game to win, or driving safely.", "Several studies have demonstrated that learning extramural sub-tasks and auxiliary predictions can improve (1) single human-specified task learning, (2) transfer of learning, (3) and the agent's learned representation of the world.", "In all these examples, the agent was instructed what to learn about.", "We investigate a framework for discovery: curating a large collection of predictions, which are used to construct the agent's representation of the world.", "Specifically, our system maintains a large collection of predictions, continually pruning and replacing predictions.", "We highlight the importance of considering stability rather than convergence for such a system, and develop an adaptive, regularized algorithm towards that aim.", "We provide several experiments in computational micro-worlds demonstrating that this simple approach can be effective for discovering useful predictions autonomously.", "The idea that an agent's knowledge might be represented as predictions has a long history in machine learning.", "The first references to such a predictive approach can be found in the work of BID4 , BID2 BID6 who hypothesized that agents would construct their understanding of the world from interaction, rather than human engineering.", "These ideas inspired work on predictive state representations (PSRs), as an approach to modeling dynamical systems.", "Simply put, a PSR can predict all possible interactions between an agent and it's environment by reweighting a minimal collection of core test (sequence of actions and observations) and their predictions, as an alternative to keeping a finite history or learning the one step latent dynamics of the world, as in a POMDP.", "Extensions to high-dimensional continuous tasks have demonstrated that the predictive approach to dynamical system modeling is competitive with state-of-the-art system identification methods BID9 .", "One important limitation of the PSR formalism is that the agent's internal representation of state must be composed exclusively of predictions.Recently, BID23 introduced a formalism for specifying and learning large collections of predictions using value functions from reinforcement learning.", "These General Value Functions (GVFs), can represent a wide array of multi-step state contingent predictions BID19 , while the predictions made by a collection of GVFs can be used to construct the agent's state representation (Schaul and Ring, 2013; BID29 . State representation's constructed from predictions have been shown to be useful for reward maximization tasks BID21 Schaul and Ring, 2013) , and transfer learning (Schaul et al., 2015) .", "One of the great innovation of GVFs is that we can clearly separate (1) the desire to learn and make use of predictions in various ways, from (2) the construction of the agent's internal state representation.", "For example, the UNREAL learning system BID10 , learns many auxiliary tasks (formalized as GVFs) while using an actor-critic algorithm to maximize a single external reward signal-the score in an Atari game.", "The auxiliary GVFs and the primary task learner share the same deep convolutional network structure.", "Learning the auxiliary tasks results in a better state representation than simply learning the main task alone.", "GVFs allow an agent to make use of both increased representational power of predictive representations, and the flexibility of state-of-the-art deep learning systems.", "In all the works described above, the GVFs were manually specified by the designer; an autonomous agent, however, must discover these GVFs.", "Most work on discovery has been on the related topics of temporal difference (TD) networks BID15 and options BID11 BID17 BID16 BID28 BID16 BID1 .", "Discovery for options is more related than TD networks, because similarly to a GVF, an option (Sutton et al., 1999) specifies small sub-tasks within an environment.", "Option discovery, however, has been largely directed towards providing temporally abstract actions, towards solving the larger task, rather than providing a predictive representation.", "For example, BID1 formulated a gradient descent update on option parameters-policies and termination functions-using policy gradient objectives.", "The difficulty in extending such gradient-based approaches is in specifying a suitable objective for prediction accuracy, which is difficult to measure online.We take inspiration from ideas from representation search methods developed for neural networks, to tackle the daunting challenge of GVF discovery for predictive representations.", "Our approach is inspired by algorithms that search the topology space of neural networks.", "One of the first such approaches, called the cascade correlation network learning typifies this approach BID7 ).", "The idea is to continually propose new hidden units over time, incrementally growing the network to multiple levels of abstraction.", "To avoid the computation and memory required to pose units whose activation is de-correlated with the network activations, BID24 empirically demonstrated that simply generating large numbers of hidden units outperformed equal sized fixed networks in online supervised learning problems.", "Related approaches demonstrated that massive random representations can be highly effective (Rahimi and Recht, 2009; BID0 BID8 .", "This randomized feature search can be improved with the addition of periodic pruning, particularly for an incremental learning setting.In this paper, we demonstrate such a curation framework for GVF discovery, with simple algorithms to propose and prune GVFs.", "To parallel representation search, we need both a basic functional form-a GVF primitive-for each unit in the network and an update to adjust the weights on these units.", "We propose a simple set of GVF primitives, from which to randomly generate candidate GVFs.", "We develop a regularized updating algorithm, to facilitate pruning less useful GVFs, with a stepsize adaptation approach that maintains stability in the representation.", "We demonstrate both the ability for the regularizer to prune less useful GVFs-and the corresponding predictive features-as well as utility of the GVF primitives as predictive features in several partially observable domains.", "Our approach provides a first investigation into a framework for curation of GVFs for predictive representations, with the aim to facilitate further development.", "In this paper, we proposed a discovery methodology for GVF networks, to learn of predictive representations.", "The strategy involves iteratively generating and pruning GVF primitives for the GVF network, with a new algorithm called AdaGain to promote stability and facilitate pruning.", "The results demonstrate utility of this curation strategy for discovering GVF networks.", "There are many aspects of our system that could have been designed differently, namely in terms of the learning algorithm, generation approach and pruning approach; here, our goal was to provide a first such demonstration, with the aim to facilitate further development.", "We discuss the two key aspects in our system below, and potential avenues to expand along these dimensions.In the development of our learning strategy, we underline the importance of treating the predictive representation as a dynamical system.", "For a standard supervised learning setting, the representation is static: the network can be queried at any time with inputs.", "The predictive representations considered here cannot be turned off and on, because they progressively build up accurate predictions.", "This dynamic nature necessitates a different view of learning.", "We proposed a focus on stability of the predictive system, deriving an algorithm to learn a stepsize.", "The stepsize can be seen as a control input, to stabilize the system, and was obtained with a relatively straightforward descent algorithm.", "More complex control inputs, however, could be considered.", "For example, a control function outputting a stepsize based on the current agent state could be much more reactive.", "Such an extension would the necessitate a more complex stability analysis from control theory.Our discovery experiments reflect a life-long learning setting, where the predictive representation is slowly built up over millions of steps.", "This was slower than strictly necessary, because we wanted to enable convergence for each GVF network before culling.", "Further, the pruning strategy was simplistic, using a threshold of 10%; more compact GVF networks could likely be learned-and learned more quickly-with a more informed pruning approach.", "Nonetheless, even when designing learning with less conservative learning times, building such representations should be a long-term endeavour.", "A natural next step is to more explicitly explore scaffolding.", "For example, without compositional GVFs, myopic discounts were less frequently kept; this suggests initially preferring horizon and termination discounts, and increasing preference on myopic discounts once compositional GVFs are added.", "Further, to keep the system as simple as possible, we did not treat compositional GVFs differently when pruning.", "For example, there is a sudden rise in prediction error at about 80 million steps in FIG2 (b); this was likely caused by pruning a GVF whose prediction was the cumulant for a critical compositional GVF.", "Finally, we only considered a simple set of GVF primitives; though this simple set was quite effective, there is an opportunity to design other GVF primitives, and particularly those that might be amenable to composition." ]

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[ "We investigate a framework for discovery: curating a large collection of predictions, which are used to construct the agent’s representation in partially observable domains." ]

[ "Estimating the location where an image was taken based solely on the contents of the image is a challenging task, even for humans, as properly labeling an image in such a fashion relies heavily on contextual information, and is not as simple as identifying a single object in the image.", "Thus any methods which attempt to do so must somehow account for these complexities, and no single model to date is completely capable of addressing all challenges.", "This work contributes to the state of research in image geolocation inferencing by introducing a novel global meshing strategy, outlining a variety of training procedures to overcome the considerable data limitations when training these models, and demonstrating how incorporating additional information can be used to improve the overall performance of a geolocation inference model.", "In this work, it is shown that Delaunay triangles are an effective type of mesh for geolocation in relatively low volume scenarios when compared to results from state of the art models which use quad trees and an order of magnitude more training data. ", "In addition, the time of posting, learned user albuming, and other meta data are easily incorporated to improve geolocation by up to 11% for country-level (750 km) locality accuracy to 3% for city-level (25 km) localities.\n", "Advancements in deep learning over the past several years have pushed the bounds of what is possible with machine learning beyond typical image classification or object localization.", "Whereas prior work in computer vision and machine learning has focused primarily on determining the contents of the image-\"is there a dog in this photo?\"-more recent methods and more complicated models have enabled deeper examinations of the contextual information behind an image.", "This deeper exploration allows a researcher to ask more challenging questions of its models.", "One such question is, \"where in the world was this picture taken?\"", "However, estimating the geographic origin of a ground-level image is a challenging task due to a number of different factors.", "Firstly, the volume of available images with geographic information associated with them is not evenly distributed across the globe.", "This uneven distribution increases the complexity of the model chosen and complicates the design of the model itself.", "Furthermore, there are additional challenges associated with geo-tagged image data, such as the potential for conflicting data (eg. incorrect geolabels and replica landmarks -St Peters Basilica in Nikko, Japan) and the ambiguity of geographic terms (eg. imagery of similar and ambiguous geological features, such as beaches, screenshots of websites, or generally, plates of food).The", "work presented herein focuses on the task of content-based image geolocation: the process of identify the geographic origin of an image taken at ground level. Given", "the significant growth in the production of data, and trends in social data to move away from pure text-based platforms to more images, videos, and mixed-media, tackling the question of inferring geographic context behind an image becomes a significant and relevant problem. Whereas", "social textual data may be enriched with geolocation information, images may or may not contain such information; EXIF data is often stripped from images or may be present but incomplete. Within", "the context of mixed-media data, using the geolocation information associated with a linked object may be unreliable or not even applicable. For example", ", a user on Twitter may have geolocation information enabled for their account, but may post a link to an image taken from a location different from the one where they made their post.", "Conditioning on latent variables can only improve geolocation models.", "Universally using time of day in the models was observed to increase accuracy and lower bias.", "Time of day is a weak addition to Inception-like results, but it is useful to be as accurate as possible, and it makes statistically significant improvements to geolocation.", "Both meshes were improved by using time information (M2).", "This is a result that is not surprising, and as a research approach, can be applied to any number of meta data variables that might accompany images.Accounting for indoor/outdoor scenes in images explained variation in validation accuracy.", "Outdoor only results are better than results for all images.", "We suggest as future work that the probability that an image is outdoor could be concatenated to the input of M2.", "The accompanying research hypothesis is that in the case that an image is indoors, perhaps the model will learn to weight time or other meta data results more heavily, or otherwise be able to use that information optimally.Increasing the granularity of a grid reduces accuracy at the country and regional level, while improving accuracy at street and city level accuracy.", "To be clear though, street level geoinferencing is not practical with a course mesh.", "This is shown by the best possible accuracy in Table 6 , and so it is expected that a fine mesh would do better.", "On the other hand, there is no reason to assume that a fine mesh has to be better for geolocation at larger resolutions than 25 km, nor is there any explicit way to prove a fine mesh should do no worse than a course mesh.", "What we observe is that a course mesh is a superior grid for 200 km resolutions.", "Furthermore, we show that for both the coarse mesh and the fine mesh, using a Delunary triangle-based mesh provides the ability to train accurate models with far fewer training examples than what was previously published." ]

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[ "A global geolocation inferencing strategy with novel meshing strategy and demonstrating incorporating additional information can be used to improve the overall performance of a geolocation inference model." ]

[ "Hierarchical Bayesian methods have the potential to unify many related tasks (e.g. k-shot classification, conditional, and unconditional generation) by framing each as inference within a single generative model.", "We show that existing approaches for learning such models can fail on expressive generative networks such as PixelCNNs, by describing the global distribution with little reliance on latent variables.", "To address this, we develop a modification of the Variational Autoencoder in which encoded observations are decoded to new elements from the same class; the result, which we call a Variational Homoencoder (VHE), may be understood as training a hierarchical latent variable model which better utilises latent variables in these cases.", "Using this framework enables us to train a hierarchical PixelCNN for the Omniglot dataset, outperforming all existing models on test set likelihood.", "With a single model we achieve both strong one-shot generation and near human-level classification, competitive with state-of-the-art discriminative classifiers.", "The VHE objective extends naturally to richer dataset structures such as factorial or hierarchical categories, as we illustrate by training models to separate character content from simple variations in drawing style, and to generalise the style of an alphabet to new characters.", "Learning from few examples is possible only with strong inductive biases.", "In machine learning such biases can come from hand design, as in the parametrisation of a model, or can be the result of a meta-learning algorithm.", "Furthermore they may be task-specific, as in discriminative modelling, or may describe the world causally so as to be naturally reused across many tasks.Recent work has approached one-and few-shot learning from all of these perspectives.", "Siamese Networks BID15 , Matching Networks , Prototypical Networks BID23 and MANNs BID22 ) are all models discriminatively trained for few-shot classification.", "Such models can achieve state-of-the-art performance at the task they were trained for, but provide no principled means for transferring knowledge to other tasks.Other work such as has developed conditional generative models, which take one or a few observations from a class as input, and return a distribution over new elements p(x|D).", "These models may be used as classifiers despite not being explicitly trained for this purpose, by comparing conditional likelihoods.", "They may also be used to generate full sets incrementally as p(X) = i p(x i |x 1 , . . . , x i−1 ), as discussed in Generative Matching Networks BID0 .", "However, such models are a more natural fit to sequences than sets as they typically lack exchangeability, and furthermore they do not expose any latent representation of shared structure within a set.Finally are hierarchical approaches that model shared structure through latent variables, as p(X) = A VAE treats all datapoints as independent, so only a single random element need be encoded and decoded each step.", "A Neural Statistician instead feeds a full set of elements X through both encoder and decoder networks, in order to share a latent variable c.", "In a VHE, we bound the full likelihood p(X) using only random subsamples D and x for encoding/decoding.", "Optionally, p(x|c) may be defined through a local latent variable z.In this work we propose the Variational Homoencoder (VHE), aiming to combine several advantages of the models described above:1.", "Like conditional generative approaches, we train on a few-shot generation objective which matches how our model may be used at test time.", "However, by introducing an encoding cost, we simultaneously optimise a likelihood lower bound for a hierarchical generative model, in which structure shared across elements is made explicit by shared latent variables.", "2. Previous work BID6 has learned hierarchical Bayesian models by applying Variational Autoencoders to sets, such as classes of images.", "However, their approach requires feeding a full set through the model per gradient step FIG1 ), rendering it intractable to train on very large sets.", "In practice, they avoid computational limits by sampling smaller subset as training data.", "In a VHE, we instead optimise a likelihood bound for the complete dataset, while constructing this bound by subsampling.", "This approach can not only improve generalisation, but also departs from previous work by extending to models with richer latent structure, for which the joint likelihood cannot be factorised.", "3. As with a VAE, the VHE objective includes both an encoding-and reconstruction-cost.However, by sharing latent variables across a large set of elements, the encoding cost per element is reduced significantly.", "This facilitates use of powerful autoregressive decoders, which otherwise often suffer from ignoring latent variables BID3 .", "We demonstrate the significance of this by applying a VHE to the Omniglot dataset.", "Using a Pixel-CNN decoder (Oord et al., 2016), our generative model is arguably the first with a general purpose architecture to both attain near human-level one-shot classification performance and produce high quality samples in one-shot generation.", "We introduced the Variational Homoencoder: a deep hierarchical generative model learned by a novel training procedure which resembles few-shot generation.", "This framework allows latent variables to be shared across a large number of elements in a dataset, encouraging them to be well utilised even alongside highly expressive decoder networks.", "We demonstrate this by training a hierarchical PixelCNN model on Omniglot dataset, and show that our novel training objective is responsible for the state-of-the-art results it achieves.", "This model is arguably the first which uses a general purpose architecture to both attain near human-level one-shot classification performance and produce high quality samples in one-shot generation.The VHE framework extends naturally to models with richer latent structure, as we demonstrate with two examples: a hierarchical model which generalises the style of an alphabet to produce new characters, and a factorial model which separates the content and drawing style of coloured character images.", "In addition to these modelling extensions, our variational bound may also be tightened by learning a subsampling procedure q(D; X), or by introducing an auxiliary inference network r(D; c, X) as discussed in Supplementary Material 6.1.", "While such modifications were unnecessary for our experiments on Omniglot character classes, we expect that they may yield improvements on other datasets with greater intra-class diversity.6", "SUPPLEMENTARY MATERIAL" ]

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[ "Technique for learning deep generative models with shared latent variables, applied to Omniglot with a PixelCNN decoder." ]

[ "Common-sense or background knowledge is required to understand natural language, but in most neural natural language understanding (NLU) systems, the requisite background knowledge is indirectly acquired from static corpora.", "We develop a new reading architecture for the dynamic integration of explicit background knowledge in NLU models.", "A new task-agnostic reading module provides refined word representations to a task-specific NLU architecture by processing background knowledge in the form of free-text statements, together with the task-specific inputs.", "Strong performance on the tasks of document question answering (DQA) and recognizing textual entailment (RTE) demonstrate the effectiveness and flexibility of our approach.", "Analysis shows that our models learn to exploit knowledge selectively and in a semantically appropriate way.", "Understanding natural language depends crucially on common-sense or background knowledge, for example, knowledge about what concepts are expressed by the words being read (lexical knowledge), and what relations hold between these concepts (relational knowledge).", "As a simple illustration, if an agent needs to understand that the statement \"King Farouk signed his abdication\" is entailed by \"King Farouk was exiled to France in 1952, after signing his resignation\", it must know (among other things) that abdication means resignation of a king.In most neural natural language understanding (NLU) systems, the requisite background knowledge is implicitly encoded in the models' parameters.", "That is, what background knowledge is present has been learned from task supervision and also by pre-training word embeddings (where distributional information reliably reflects certain kinds of useful background knowledge, such as semantic relatedness).", "However, acquisition of background knowledge from static training corpora is limiting for two reasons.", "First, we cannot expect that all background knowledge that could be important for solving an NLU task can be extracted from a limited amount of training data.", "Second, as the world changes, the facts that may influence how a text is understood will likewise change.", "In short: building suitably large corpora to capture all relevant information, and keeping the corpus and derived models up to date with changes to the world would be impractical.In this paper, we develop a new architecture for dynamically incorporating external background knowledge in NLU models.", "Rather than relying only on static knowledge implicitly present in the training data, supplementary knowledge is retrieved from a knowledge base to assist with understanding text inputs.", "Since NLU systems must necessarily read and understand text inputs, our approach incorporates background knowledge by repurposing this reading machinery-that is, we read the text being understood together with supplementary natural language statements that assert facts (assertions) which are relevant to understanding the content ( §2).Our", "knowledge-augmented NLU systems operate in a series of phases. First", ", given the text input that the system must understand, which we call the context, a set of relevant supporting assertions is retrieved. While", "learning to retrieve relevant information for solving NLU tasks is an important question BID21 Narasimhan et al., 2016, inter alia) , in this work, we focus on learning how to incorporate retrieved information, and use simple heuristic retrieval methods to identify plausibly relevant background from an external knowledge base. Once", "the supplementary texts have been retrieved, we use a word embedding refinement strategy that incrementally reads the context and retrieved assertions starting with context-independent word embeddings and building successively refined embeddings of the words that ultimately reflect both the relevant supporting assertions and the input context ( §3). These", "contextually refined word embeddings, which serve as dynamic memory to store newly incorporated knowledge, are used in any task-specific reading architecture. The overall", "architecture is illustrated in FIG0 . Although we", "are incorporating a new kind of information into the NLU pipeline, a strength of this approach is that the architecture of the reading module is independent of the final NLU task-the only requirement is that the final architecture use word embeddings.We carry out experiments on several different datasets on the tasks of document question answering (DQA) and recognizing textual entailment (RTE) evaluating the impact of our proposed solution with both basic task architectures and a sophisticated task architecture for RTE ( §4). We find that", "our embedding refinement strategy is quite effective ( §5). On four standard", "benchmarks, we show that refinement helps-even refining the embeddings just using the context (and no additional background information) can improve performance significantly, and adding background knowledge helps further. Our results are", "very competitive, setting a new state-of-the-art on the recent TriviaQA benchmarks which is remarkable considering the simplicity of the chosen task-specific architecture. Finally, we provide", "a detailed analysis of how knowledge is being used by an RTE system ( §6), including experiments showing that our system is capable of making appropriate counterfactual inferences when provided with \"false knowledge\".", "We have presented a novel task-agnostic reading architecture that allows for the dynamic integration of background knowledge into neural NLU models.", "Our solution, which is based on the incremental refinement of word representations by reading supplementary inputs, is flexible and be used with virtually any existing NLU architecture that rely on word embeddings as input.", "Our results show that embedding refinement using both the system's text inputs, as well as supplementary texts encoding background knowledge can yield large improvements.", "In particular, we have shown that relatively simple task architectures (e.g., based on simple BiLSTM readers) can become competitive with state-of-the-art, task-specific architectures when augmented with our reading architecture." ]

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[ "In this paper we present a task-agnostic reading architecture for the dynamic integration of explicit background knowledge in neural NLU models. " ]

[ "Mixed-precision arithmetic combining both single- and half-precision operands in the same operation have been successfully applied to train deep neural networks.", "Despite the advantages of mixed-precision arithmetic in terms of reducing the need for key resources like memory bandwidth or register file size, it has a limited capacity for diminishing computing costs and requires 32 bits to represent its output operands.", "This paper proposes two approaches to replace mixed-precision for half-precision arithmetic during a large portion of the training.", "The first approach achieves accuracy ratios slightly slower than the state-of-the-art by using half-precision arithmetic during more than 99% of training.", "The second approach reaches the same accuracy as the state-of-the-art by dynamically switching between half- and mixed-precision arithmetic during training.", "It uses half-precision during more than 94% of the training process.", "This paper is the first in demonstrating that half-precision can be used for a very large portion of DNNs training and still reach state-of-the-art accuracy.", "The use of Deep Neural Networks (DNNs) is becoming ubiquitous in areas like computer vision (Krizhevsky et al., 2012; Szegedy et al., 2015) , speech recognition , or language translation (Wu et al., 2016) .", "DNNs display very remarkable pattern detection capacities and, more specifically, Convolutional Neural Networks (CNNs) are able to accurately detect and classify objects over very large image sets (Krizhevsky et al., 2012) .", "Despite this success, a large amount of samples must be exposed to the model for tens or even hundreds of times during training until an acceptable accuracy threshold is reached, which drives up training costs in terms of resources like memory storage or computing time.", "To mitigate these very large training costs, approaches based on data representation formats simpler than the Floating Point 32-bit (FP32) standard have been proposed (Courbariaux et al., 2014; Gupta et al., 2015) .", "These approaches successfully mitigate the enormous training costs of DNNs by using data representation formats that either reduce computing costs or diminish the requirements in terms of memory storage and bandwidth.", "In particular, some of these proposals have shown the benefits of combining half-precision and single-precision compute during training in terms of keeping model accuracy and reducing compute and memory costs (Micikevicius et al., 2017; Kalamkar et al., 2019) .", "These approaches accelerate linear algebra operations by accumulating half-precision input operands to generate 32-bit outputs.", "While this mixed-precision (MP) arithmetic can successfully reduce the use of resources like memory bandwidth or hardware components like register file size, it has a very limited capacity for diminishing computing costs and it is unable to reduce output data size.", "In this paper we propose new training methodologies able to exclusively use half-precision for a large part of the training process, which constitutes a very significant improvement over mixedprecision approaches in terms of compute and memory bandwidth requirements.", "We propose two different approaches, the first one statically assigns either the Brain Floating Point 16-bit (BF16) or the FP32 format to the model parameters involved in the training process, while the second dynamically switches between BF16 and MP during training depending on its progress.", "Our approaches do not require mixed-precision arithmetic while computing linear algebra operations for a large portion of the training process, which enables them to deliver the same performance as if they were operating with half-precision arithmetic during the whole training while providing the same model accuracy as if FP32 was used.", "This paper is the first in demonstrating that half-precision can be extensively used during DNNs training without the need for mixed-precision arithmetic.", "We made our code available 1 .", "This paper analyzes the instruction breakdown of workloads focused on deep neural network training that rely on mixed-precision training.", "We show that mixed-precision FMAs constitute around 60% of these workloads and propose two approaches based on half-precision FMAs to accelerate the training process without hurting accuracy.", "The first approach uses BF16 FMAs for most of the training workload, except routines involved in weight updates or batch normalization layers.", "This approach uses BF16 for more than 99% of the FMAs, which has a very strong potential for performance improvement, while reaching slightly smaller accuracy than the state-of-the-art.", "We propose a second approach that dynamically switches between different data representation formats.", "This dynamic approach uses BF16 for around 96% of the FMAs while reaching the same precision levels as the standard single-precision and mixedprecision approaches.", "Our two proposals are evaluated considering three state-of-the-art deep neural networks and a binary analysis tool that applies the required precision for each instruction.", "To the best of our knowledge, this is the first paper that demonstrates that half-precision can be used extensively on ≥94% of all FMAs during the training of very deep models without the need for mixed-precision arithmetic." ]

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[ "Dynamic precision technique to train deep neural networks" ]

[ "We introduce the “inverse square root linear unit” (ISRLU) to speed up learning in deep neural networks.", "ISRLU has better performance than ELU but has many of the same benefits.", "ISRLU and ELU have similar curves and characteristics.", "Both have negative values, allowing them to push mean unit activation closer to zero, and bring the normal gradient closer to the unit natural gradient, ensuring a noise- robust deactivation state, lessening the over fitting risk.", "The significant performance advantage of ISRLU on traditional CPUs also carry over to more efficient HW implementations on HW/SW codesign for CNNs/RNNs.", "In experiments with TensorFlow, ISRLU leads to faster learning and better generalization than ReLU on CNNs.", "This work also suggests a computationally efficient variant called the “inverse square root unit” (ISRU) which can be used for RNNs.", "Many RNNs use either long short-term memory (LSTM) and gated recurrent units (GRU) which are implemented with tanh and sigmoid activation functions.", "ISRU has less computational complexity but still has a similar curve to tanh and sigmoid.", "Two popular activation functions for neural networks are the rectified linear unit (ReLU) BID6 and the exponential linear unit (ELU) BID5 .", "The ReLU activation function is the identity for positive arguments and zero otherwise.", "The ELU activation function is the identity for positive arguments and has an exponential asymptotic approach to -1 for negative values.From previous analysis of the Fisher optimal learning, i.e., the natural gradient BID1 BID5 , we can reduce the undesired bias shift effect without the natural gradient, either by centering the activation of incoming units at zero or by using activation functions with negative values.", "We introduce the inverse square root linear unit (ISRLU), an activation function like ELU, that has smoothly saturating negative values for negative arguments, and the identity for positive arguments.", "In addition this activation function can be more efficiently implemented than ELU in a variety of software or purpose-built hardware.", "Activation function performance is becoming more important overall in convolutional neural networks (CNNs) because of the trending reductions in the computational complexity of the convolutions used in CNNs.", "We have introduced a new activation function, the inverse square root linear unit (ISRLU) for faster and precise learning in deep convolutional neural networks.", "ISRLUs have similar activation curves to ELUs, including the negative values.", "This decreases the forward propagated variation and brings the mean activations to zero.", "Mean activations close to zero decreases the bias shift for units in the next layer which speeds up learning by bringing the natural gradient closer to the unit natural gradient.", "Future work may prove the effectiveness of applying ISRLUs and the related ISRUs to other network architectures, such as recurrent neural networks, and to other tasks, such as object detection.", "ISRLUs have lower computational complexity than ELUs.", "Even greater savings on computation can be realized by implementing ISRLUs in custom hardware implementations.", "We expect ISRLU activations to increase the training efficiency of convolutional networks." ]

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[ "We introduce the ISRLU activation function which is continuously differentiable and faster than ELU. The related ISRU replaces tanh & sigmoid." ]

[ "A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all tasks -- both have difficulty with such generalization because they do not leverage the compositional structure of the task distribution.", "This paper introduces the compositional problem graph as a broadly applicable formalism to relate tasks of different complexity in terms of problems with shared subproblems.", "We propose the compositional generalization problem for measuring how readily old knowledge can be reused and hence built upon.", "As a first step for tackling compositional generalization, we introduce the compositional recursive learner, a domain-general framework for learning algorithmic procedures for composing representation transformations, producing a learner that reasons about what computation to execute by making analogies to previously seen problems.", "We show on a symbolic and a high-dimensional domain that our compositional approach can generalize to more complex problems than the learner has previously encountered, whereas baselines that are not explicitly compositional do not.", "This paper seeks to tackle the question of how to build machines that leverage prior experience to solve more complex problems than they have previously encountered.", "How does a learner represent prior experience?", "How does a learner apply what it has learned to solve new problems?", "Motivated by these questions, this paper aims to formalize the idea of, as well as to develop an understanding of the machinery for, compositional generalization in problems that exhibit compositional structure.", "The solutions for such problems can be found by composing in sequence a small set of reusable partial solutions, each of which tackles a subproblem of a larger problem.", "The central contributions of this paper are to frame the shared structure across multiple tasks in terms of a compositional problem graph, propose compositional generalization as an evaluation scheme to test the degree a learner can apply previously learned knowledge to solve new problems, and introduce the compositional recursive learner, a domain-general framework 1 for sequentially composing representation transformations that each solve a subproblem of a larger problem.The key to our approach is recasting the problem of generalization as a problem of learning algorithmic procedures over representation transformations.", "A solution to a (sub)problem is a transformation between its input and output representations, and a solution to a larger problem composes these subsolutions together.", "Therefore, representing and leveraging prior problem-solving experience amounts to learning a set of reusable primitive transformations and their means of composition that reflect the structural properties of the problem distribution.", "This paper introduces the compositional recursive learner (CRL), a framework for learning both these transformations and their composition together with sparse supervision, taking a step beyond other approaches that have assumed either pre-specified transformation or composition rules (Sec. 5).", "CRL learns a modular recursive program that iteratively re-represents the input representation into more familiar representations it knows how to compute with.", "In this framework, a transformation between representations is encapsulated into a computational module, and the overall program is the sequential combination of the inputs and outputs of these modules, whose application are decided by a controller.What sort of training scheme would encourage the spontaneous specialization of the modules around the compositional structure of the problem distribution?", "First, exposing the learner to a diverse distribution of compositional problems helps it pattern-match across problems to distill out common functionality that it can capture in its modules for future use.", "Second, enforcing that each module have only a local view of the global problem encourages task-agnostic functionality that prevents the learner from overfitting to the empirical training distribution; two ways to do this are to constrain the model class of the modules and to hide the task specification from the modules.", "Third, training the learner with a curriculum encourages the learner to build off old solutions to solve new problems by re-representing the new problem into one it knows how to solve, rather than learning from scratch.How should the learner learn to use these modules to exploit the compositional structure of the problem distribution?", "We can frame the decision of which computation to execute as a reinforcement learning problem in the following manner.", "The application of a sequence of modules can be likened to the execution trace of the program that CRL automatically constructs, where a computation is the application of a module to the output of a previous computation.", "The automatic construction of the program can be formulated as the solution to a sequential decision-making problem in a meta-level Markov decision process (MDP) (Hay et al., 2014) , where the state space is the learner's internal states of computation and the action space is the set of modules.", "Framing the construction of a program as a reinforcement learning problem allows us to use techniques in deep reinforcement learning to implement loops and recursion, as well as decide on which part of the current state of computation to apply a module, to re-use sub-solutions to solve a larger problem.Our experiments on solving multilingual arithmetic problems and recognizing spatially transformed MNIST digits BID26 show that the above proposed training scheme prescribes a type of reformulation: re-representing a new problem in terms of other problems by implicitly making an analogy between their solutions.", "We also show that our meta-reasoning approach for deciding what modules to execute achieves better generalization to more complex problems than monolithic learners that are not explicitly compositional.", "This paper sought to tackle the question of how to build machines that leverage prior experience to solve more complex problems than they have seen.", "This paper makes three steps towards the solution.", "First, we formalized the compositional problem graph as a language for studying compositionally-structured problems of different complexity that can be applied on various problems in machine learning.", "Second, we introduced the compositional generalization evaluation scheme for measuring how readily old knowledge can be reused and hence built upon.", "Third, we presented the compositional recursive learner, a domain-general framework for learning a set of reusable primitive transformations and their means of composition that reflect the structural properties of the problem distribution.", "In doing so we leveraged tools from reinforcement learning to solve a program induction problem.There are several directions for improvement.", "One is to stabilize the simultaneous optimization between discrete composition and continuous parameters; currently this is tricky to tune.", "Others are to generate computation graphs beyond a linear chain of functions, and to infer the number of functions required for a family of problems.", "A major challenge would be to discover the subproblem decomposition without a curriculum and without domain-specific constraints on the model class of the modules.", "Griffiths et al. (2019) argued that the efficient use cognitive resources in humans may also explain their ability to generalize, and this paper provides evidence that reasoning about what computation to execute by making analogies to previously seen problems achieves significantly higher compositional generalization than non-compositional monolithic learners.", "Encapsulating computational modules grounded in the subproblem structure also may pave a way for improving interpretability of neural networks by allowing the modules to be unit-tested against the subproblems we desire them to capture.", "Because problems in supervised, unsupervised, and reinforcement learning can all be expressed under the framework of transformations between representations in the compositional problem graph, we hope that our work motivates further research for tackling the compositional generalization problem in many other domains to accelerate the long-range generalization capabilities that are characteristic of general-purpose learning machines.", "Multilingual arithmetic (Sec. 4.1): The dataset contains arithmetic expressions of k terms where the terms are integers ∈ [0, 9] and the operators are ∈ {+, ·, −}, expressed in five different languages.", "With 5 choices for the source language and target language, the number of possible problems is (10 k )(3 k−1 )(5 2 ).", "In training, each source language is seen with 4 target languages and each target language is seen with 4 source languages: 20 pairs are seen in training and 5 pairs are held out for testing.", "The learner sees 46200/(1.68 · 10 8 ) = 2.76 · 10 −4 of the training distribution.", "The entire space of possible problems in the extrapolation set is (10 10 )(3 9 )(5 2 ) = 4.92 · 10 15 out of which we draw samples from the 5 held-out language pairs (10 10 )(3 9 )(5) = 9.84 · 10 14 possible .", "An input expression is a sequence of one-hot vectors of size 13 × 5 + 1 = 66 where the single additional element is a STOP token (for training the RNN).", "Spatially transformed MNIST (Sec. 4.2): The generative process for transforming the standard MNIST dataset to the input the learner observes is described as follows.", "We first center the 28x28 MNIST image in a 42x42 black background.", "We have three types of transformations to apply to the image: scale, rotate, and translate.", "We can scale big or small (by a factor of 0.6 each way).", "We can rotate left or right (by 45 degrees each direction).", "We can translate left, right, up, and down, but the degree to which we translate depends on the size of the object: we translate the digit to the edge of the image, so smaller digits get translated more than large digits.", "Large digits are translated by 20% of the image width, unscaled digits are translated by 29% of the image width, and small digits are translated by 38% of the image width.", "In total there are 2 + 2 + 4 × 3 = 16 individual transformation operations used in the generative process.", "Because some transformation combinations are commutative, we defined an ordering with which we will apply the generative transformations: scale then rotate then translate.", "For length-2 compositions of generative transformations, there are scale-small-then-translate (1 × 4), scale-big-then-translate (1 × 4), rotate-then-translate (2 × 4), and scale-then-rotate (2 × 2).", "We randomly choose 16 of these 20 for training, 2 for validation, 2 for test, as shown in Figure 4 (center).", "For length-3 compositions of generative transformations, there are scale-small-then-rotate-then-translate (1×2×4) and scale-big-then-rotate-then-translate (1×2×4).", "All 16 were held out for evaluation." ]

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[ "We explore the problem of compositional generalization and propose a means for endowing neural network architectures with the ability to compose themselves to solve these problems." ]

[ "The information bottleneck method provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label, while minimizing the amount of other, superfluous information in the representation.", "The original formulation, however, requires labeled data in order to identify which information is superfluous. ", "In this work, we extend this ability to the multi-view unsupervised setting, in which two views of the same underlying entity are provided but the label is unknown.", "This enables us to identify superfluous information as that which is not shared by both views.", "A theoretical analysis leads to the definition of a new multi-view model that produces state-of-the-art results on the Sketchy dataset and on label-limited versions of the MIR-Flickr dataset. ", "We also extend our theory to the single-view setting by taking advantage of standard data augmentation techniques, empirically showing better generalization capabilities when compared to traditional unsupervised approaches for representation learning.", "The goal of deep representation learning (LeCun et al., 2015) is to transform a raw observational input, x, into a representation, z, to extract useful information.", "Significant progress has been made in deep learning via supervised representation learning, where the labels, y, for the downstream task are known while p(y|x) is learned directly (Sutskever et al., 2012; Hinton et al., 2012) .", "Due to the cost of acquiring large labeled datasets, a recently renewed focus on unsupervised representation learning seeks to generate representations, z, that allow learning of (a priori unknown) target supervised tasks more efficiently, i.e. with fewer labels (Devlin et al., 2018; Radford et al., 2019) .", "Our work is based on the information bottleneck principle (Tishby et al., 2000) stating that whenever a data representation discards information from the input which is not useful for a given task, it becomes less affected by nuisances, resulting in increased robustness for downstream tasks.", "In the supervised setting, one can directly apply the information bottleneck method by minimizing the mutual information between z and x while simultaneously maximizing the mutual information between z and y (Alemi et al., 2017) .", "In the unsupervised setting, discarding only superfluous information is more challenging as without labels one cannot directly identify the relevant information.", "Recent literature (Devon Hjelm et al., 2019; van den Oord et al., 2018) has instead focused on the InfoMax objective maximizing the mutual information between x and z, I(x, z), instead of minimizing it.", "In this paper, we extend the information bottleneck method to the unsupervised multi-view setting.", "To do this, we rely on a basic assumption of the multi-view literature -that each view provides the same task relevant information (Zhao et al., 2017) .", "Hence, one can improve generalization by discarding from the representation all information which is not shared by both views.", "We do this through an objective which maximizes the mutual information between the representations of the two views (Multi-View InfoMax) while at the same time reducing the mutual information between each view and its corresponding representation (as with the information bottleneck).", "The resulting representation contains only the information shared by both views, eliminating the effect of independent factors of variations.", "Our contributions are three-fold: (1) We extend the information bottleneck principle to the unsupervised multi-view setting and provide a rigorous theoretical analysis of its application.", "(2) We define a new model that empirically leads to state-of-the-art results in the low-data setting on two standard multi-view datasets, Sketchy and MIR-Flickr.", "(3) By exploiting standard data augmentation techniques, we empirically show that the representations obtained with our model in single-view settings are more robust than other popular unsupervised approaches for representation learning, connecting our theory to the choice of augmentation function class.", "In this work, we introduce Multi-View Information Bottleneck, a novel method that relies on multiple data-views to produce robust representation for downstream tasks.", "Most of the multi-view literature operates under the assumption that each view is individually sufficient for determining the label (Zhao et al., 2017) , while our method only requires the weaker mutual redundancy condition outlined in Section 3, enabling it to be applied to any traditional multi-view task.", "In our experiments, we compared MIB empirically against other approaches in the literature on three such tasks: sketch-based image retrieval, multi-view and unsupervised representation learning.", "The strong performance obtained in the different areas show that Multi-View Information Bottleneck can be practically applied to various tasks for which the paired observations are either available or are artificially produced.", "Furthermore, the positive results on the MIR-Flickr dataset show that our model can work well in practice even when mutual redundancy holds only approximately.", "There are multiple extensions that we would like to explore in future work.", "One interesting direction would be considering more than two views.", "In Appendix D we discuss why the mutual redundancy condition cannot be trivially extended to more than two views, but we still believe such an extension is possible.", "Secondly, we believe that exploring the role played by different choices of data augmentation could bridge the gap between the Information Bottleneck principle and with the literature on invariant neural networks (Bloem-Reddy & Whye Teh, 2019), which are able to exploit known symmetries and structure of the data to remove superfluous information." ]

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[ "We extend the information bottleneck method to the unsupervised multiview setting and show state of the art results on standard datasets" ]

[ "The biological plausibility of the backpropagation algorithm has long been doubted by neuroscientists.", "Two major reasons are that neurons would need to send two different types of signal in the forward and backward phases, and that pairs of neurons would need to communicate through symmetric bidirectional connections.\n", "We present a simple two-phase learning procedure for fixed point recurrent networks that addresses both these issues.\n", "In our model, neurons perform leaky integration and synaptic weights are updated through a local mechanism.\n", "Our learning method extends the framework of Equilibrium Propagation to general dynamics, relaxing the requirement of an energy function.\n", "As a consequence of this generalization, the algorithm does not compute the true gradient of the objective function,\n", "but rather approximates it at a precision which is proven to be directly related to the degree of symmetry of the feedforward and feedback weights.\n", "We show experimentally that the intrinsic properties of the system lead to alignment of the feedforward and feedback weights, and that our algorithm optimizes the objective function.", "Deep learning BID18 is the de-facto standard in areas such as computer vision BID17 , speech recognition and machine translation BID3 .", "These applications deal with different types of data and share little in common at first glance.", "Remarkably, all these models typically rely on the same basic principle: optimization of objective functions using the backpropagation algorithm.", "Hence the question: does the cortex in the brain implement a mechanism similar to backpropagation, which optimizes objective functions?The", "backpropagation algorithm used to train neural networks requires a side network for the propagation of error derivatives, which is vastly seen as biologically implausible BID7 . One", "hypothesis, first formulated by Hinton & McClelland (1988) , is that error signals in biological networks could be encoded in the temporal derivatives of the neural activity and propagated through the network via the neuronal dynamics itself, without the need for a side network. Neural", "computation would correspond to both inference and error back-propagation. This work", "also explores this idea.The framework of Equilibrium Propagation BID29 requires the network dynamics to be derived from an energy function, enabling computation of an exact gradient of an objective function. However,", "in terms of biological realism, the requirement of symmetric weights between neurons arising from the energy function is not desirable. The work", "presented here extends this framework to general dynamics, without the need for energy functions, gradient dynamics, or symmetric connections.Our approach is the following. We start", "from classical models in neuroscience for the dynamics of the neuron's membrane voltage and for the synaptic plasticity (section 3). Unlike in", "the Hopfield model BID16 , we do not assume pairs of neurons to have symmetric connections. We then describe", "an algorithm for supervised learning based on these models (section 4) with minimal extra assumptions. Our model is based", "on two phases: at prediction time, no synaptic changes occur, whereas a local update rule becomes effective when the targets are observed. The proposed update", "mechanism is compatible with spike-timing-dependent plasticity , which supposedly governs synaptic changes in biological neural systems. Finally, we show that", "the proposed algorithm has the desirable machine learning property of optimizing an objective function (section 5). We show this experimentally", "( Figure 3 ) and we provide the beginning for a theoretical explanation.", "Our model demonstrates that biologically plausible learning in neural networks can be achieved with relatively few assumptions.", "As a key contribution, in contrast to energy-based approaches such as the Hopfield model, we do not impose any symmetry constraints on the neural connections.", "Our algorithm assumes two phases, the difference between them being whether synaptic changes occur or not.", "Although this assumption begs for an explanation, neurophysiological findings suggest that phase-dependent mechanisms are involved in learning and memory consolidation in biological systems.", "Theta waves, for instance, generate neural oscillatory patterns that can modulate the learning rule or the computation carried out by the network BID26 .", "Furthermore, synaptic plasticity, and neural dynamics in general, are known to be modulated by inhibitory neurons and dopamine release, depending on the presence or absence of a target signal.", "BID10 ; BID27 .In", "its general formulation (Appendix A), the work presented in this paper is an extension of the framework of BID29 to general dynamics. This", "is achieved by relaxing the requirement of an energy function. This", "generalization comes at the cost of not being able to compute the (true) gradient of the objective function but, rather a direction in the weight space which is related to it. Thereby", ", precision of the approximation of the gradient is directly related to the \"alignment\" between feedforward and feedback weights. Even though", "the exact underlying mechanism is not fully understood yet, we observe experimentally that during training the weights symmetrize to some extent, as has been observed previously in a variety of other settings BID19 BID31 BID2 . Our work shows", "that optimization of an objective function can be achieved without ever computing the (true) gradient. More thorough", "theoretical analysis needs to be carried out to understand and characterize the dynamics in the weight space that optimize objective functions. Naturally, the", "set of all such dynamics is much larger than the tiny subset of gradient-based dynamics.Our framework provides a means of implementing learning in a variety of physical substrates, whose precise dynamics might not even be known exactly, but which simply have to be in the set of sup-ported dynamics. In particular,", "this applies to analog electronic circuits, potentially leading to faster, more efficient, and more compact implementations." ]

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[ "We describe a biologically plausible learning algorithm for fixed point recurrent networks without tied weights" ]

[ "In this paper we present, to the best of our knowledge, the first method to learn a generative model of 3D shapes from natural images in a fully unsupervised way.", "For example, we do not use any ground truth 3D or 2D annotations, stereo video, and ego-motion during the training.", "Our approach follows the general strategy of Generative Adversarial Networks, where an image generator network learns to create image samples that are realistic enough to fool a discriminator network into believing that they are natural images.", "In contrast, in our approach the image gen- eration is split into 2 stages.", "In the first stage a generator network outputs 3D ob- jects.", "In the second, a differentiable renderer produces an image of the 3D object from a random viewpoint.", "The key observation is that a realistic 3D object should yield a realistic rendering from any plausible viewpoint.", "Thus, by randomizing the choice of the viewpoint our proposed training forces the generator network to learn an interpretable 3D representation disentangled from the viewpoint.", "In this work, a 3D representation consists of a triangle mesh and a texture map that is used to color the triangle surface by using the UV-mapping technique.", "We provide analysis of our learning approach, expose its ambiguities and show how to over- come them.", "Experimentally, we demonstrate that our method can learn realistic 3D shapes of faces by using only the natural images of the FFHQ dataset.", "Generative Adversarial Nets (GAN) (see Goodfellow et al. (2014) ) have become the gold standard generative model over the years.", "Their capability is demonstrated in many data sets of natural images.", "These generative models can create sample images that are nearly indistinguishable from real ones.", "GANs do not need to make assumptions on the data formation other than applying a neural network on a latent noise input.", "They can also operate in a fully unsupervised way.", "GANs have strong theoretical foundations since the beginning.", "Goodfellow et al. (2014) demonstrate that, under suitable conditions, GANs learn to generate samples with the same probability distribution as samples in the training data set have.", "However, there is one notable drawback of GANs compared to classical generative models like Gaussian Mixture Models by Xu & Jordan (1996) or Naive Bayes classifiers by McCallum et al. (1998) .", "Classical models are interpretable, but GANs are not.", "Interpretability is achieved in classical models by making strong assumptions on the data formation process and by using them on interpretable engineered features.", "Our work combines the best of both worlds for 3D shape learning.", "We keep the advantages of GANs: unsupervised training, applicability on real datasets without feature engineering, the theoretical guarantees and simplicity.", "We also make our representation interpretable, as our generator network provides a 3D mesh as an output.", "To make the learning possible, we make the assumption that natural images are formed by a differentiable renderer.", "This renderer produces fake images by taking the 3D mesh, its texture, a background image and a viewpoint as its input.", "During training a discriminator network is trained against the generator in an adversarial fashion.", "It tries to classify whether its input is fake or comes from the training dataset.", "The key observation is that a valid 3D object should look realistic from multiple viewpoints.", "This image realism is thus enforced by the GAN training.", "This idea was first applied for generating 3D shapes in Gadelha et al. (2017) .", "Their pioneering work had several limitations though.", "It was only applicable to synthetic images, where the background mask is available and produced only black and white images.", "Our method works on natural images and we do not need silhouettes as supervision signal.", "From a theoretical point of view, image realism means that the images lie inside the support of the probability distribution of natural images (see Ledig et al. (2017) , where image realism was used for super-resolution).", "AmbientGAN of Bora et al. (2018) proves that one can recover an underlying latent data distribution, when a known image formation function is applied to the data, thus achieving data realism by enforcing image realism.", "Our work and that of Gadelha et al. (2017) are special cases of AmbientGAN for 3D shape learning.", "However this task in general does not satisfy all assumptions in Bora et al. (2018) , which results in ambiguities in the training.", "We resolve these issues in our paper by using suitable priors.", "We summarize our contributions below:", "• For the first time, to the best of our knowledge, we provide a procedure to build a generative model that learns explicit 3D representations in an unsupervised way from natural images.", "We achieve that using a generator network and a renderer trained against a discriminator in a GAN setting.", "Samples from our model are shown in Figure 1 .", "• We introduce a novel differentiable renderer, which is a fundamental component to obtain a high-quality generative model.", "Notably, it is differentiable with respect to the 3D vertex coordinates.", "The gradients are not approximated, they can be computed exactly even at the object boundaries and in the presence of self-occlusions.", "• We analyze our learning setup in terms of the ambiguities in the learning task.", "These ambiguities might derail the training to undesirable results.", "We show that these problems can only be solved when one uses labels or prior knowledge on the data distribution.", "Finally, we provide practical solutions to overcome the problems that originate from the ambiguities." ]

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[ "We train a generative 3D model of shapes from natural images in an fully unsupervised way." ]

[ "We focus on the problem of black-box adversarial attacks, where the aim is to generate adversarial examples using information limited to loss function evaluations of input-output pairs.", "We use Bayesian optimization (BO) to specifically\n", "cater to scenarios involving low query budgets to develop query efficient adversarial attacks.", "We alleviate the issues surrounding BO in regards to optimizing high dimensional deep learning models by effective dimension upsampling techniques.", "Our proposed approach achieves performance comparable to the state of the art black-box adversarial attacks albeit with a much lower average query count.", "In particular, in low query budget regimes, our proposed method reduces the query count up to 80% with respect to the state of the art methods.", "Neural networks are now well-known to be vulnerable to adversarial examples: additive perturbations that, when applied to the input, change the network's output classification (Goodfellow et al., 2014) .", "Work investigating this lack of robustness to adversarial examples often takes the form of a back-and-forth between newly proposed adversarial attacks, methods for quickly and efficiently crafting adversarial examples, and corresponding defenses that modify the classifier at either training or test time to improve robustness.", "The most successful adversarial attacks use gradient-based optimization methods (Goodfellow et al., 2014; Madry et al., 2017) , which require complete knowledge of the architecture and parameters of the target network; this assumption is referred to as the white-box attack setting.", "Conversely, the more realistic black-box setting requires an attacker to find an adversarial perturbation without such knowledge: information about the network can be obtained only through querying the target network, i.e., supplying an input to the network and receiving the corresponding output.", "In real-world scenarios, it is extremely improbable for an attacker to have unlimited bandwidth to query a target classifier.", "In evaluation of black box attacks, this constraint is usually formalized via the introduction of a query budget: a maximum number of queries allowed to the model per input, after which an attack is considered to be unsuccessful.", "Several recent papers have proposed attacks specifically to operate in this query-limited context (Ilyas et al., 2019; 2018; Chen et al., 2017; Tu et al., 2019; Moon et al., 2019) ; nevertheless, these papers typically consider query budgets on the order of 10,000 or 100,000.", "This leaves open questions as to whether black-box attacks can successfully attack a deep network based classifier in severely query limited settings, e.g., with a query budget of 100-200.", "In such a query limited regime, it is natural for an attacker to use the entire query budget, so we ask the pertinent question: In a constrained query limited setting, can one design query efficient yet successful black box adversarial attacks?", "This work proposes a black-box attack method grounded in Bayesian optimization (Jones et al., 1998; Frazier, 2018) , which has recently emerged as a state of the art black-box optimization technique in settings where minimizing the number of queries is of paramount importance.", "Straightforward application of Bayesian optimization to the problem of finding adversarial examples is not feasible: the input dimension of even a small neural network-based image classifier is orders of magnitude larger than the standard use case for Bayesian optimization.", "Rather, we show that we can bridge this gap by performing Bayesian optimization in a reduced-dimension setting and upsampling to obtain our final perturbation.", "We explore several upsampling techniques and find that a relatively simple nearest-neighbor upsampling method allows us to sufficiently reduce the optimization prob-lem dimension such that Bayesian optimization can find adversarial perturbations with more success than existing black-box attacks in query-constrained settings.", "We compare the efficacy of our adversarial attack with a set of experiments attacking three of the most commonly used pretrained ImageNet (Deng et al., 2009 ) classifiers: ResNet50 (He et al., 2015) , Inception-v3 (Szegedy et al., 2015) , and VGG16-bn (Simonyan & Zisserman, 2014) .", "Results from these experiments show that with very small query budgets (under 200 queries), the proposed method BAYES-ATTACK achieves success rates comparable to or exceeding existing methods, and does so with far smaller average and median query counts.", "Further experiments are performed on the MNIST dataset to compare how various upsampling techniques affect the attack accuracy of our method.", "Given these results we argue that, despite being a simple approach (indeed, largely because it is such a simple and standard approach for black-box optimization), Bayesian Optimization should be a standard baseline for any black-box adversarial attack task in the future, especially in the small query budget regime.", "We considered the problem of black-box adversarial attacks in settings involving constrained query budgets.", "We employed Bayesian optimization based method to construct a query efficient attack strategy.", "The proposed method searches for an adversarial perturbation in low dimensional latent space using Bayesian optimization and then maps the perturbation to the original input space using the nearest neighbor upsampling scheme.", "We successfully demonstrated the efficacy of our method in attacking multiple deep learning architectures for high dimensional inputs.", "Our work opens avenues regarding applying BO for adversarial attacks in high dimensional settings." ]

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[ "We show that a relatively simple black-box adversarial attack scheme using Bayesian optimization and dimension upsampling is preferable to existing methods when the number of available queries is very low." ]

[ "State-of-the-art deep neural networks (DNNs) typically have tens of millions of parameters, which might not fit into the upper levels of the memory hierarchy, thus increasing the inference time and energy consumption significantly, and prohibiting their use on edge devices such as mobile phones.", "The compression of DNN models has therefore become an active area of research recently, with \\emph{connection pruning} emerging as one of the most successful strategies.", "A very natural approach is to prune connections of DNNs via $\\ell_1$ regularization, but recent empirical investigations have suggested that this does not work as well in the context of DNN compression.", "In this work, we revisit this simple strategy and analyze it rigorously, to show that:", "(a) any \\emph{stationary point} of an $\\ell_1$-regularized layerwise-pruning objective has its number of non-zero elements bounded by the number of penalized prediction logits, regardless of the strength of the regularization;", "(b) successful pruning highly relies on an accurate optimization solver, and there is a trade-off between compression speed and distortion of prediction accuracy, controlled by the strength of regularization.", "Our theoretical results thus suggest that $\\ell_1$ pruning could be successful provided we use an accurate optimization solver.", "We corroborate this in our experiments, where we show that simple $\\ell_1$ regularization with an Adamax-L1(cumulative) solver gives pruning ratio competitive to the state-of-the-art.", "State-of-the-art Deep Neural Networks (DNNs) typically have millions of parameters.", "For example, the VGG-16 network BID0 ), from the winning team of ILSVRC-2014, contains more than one hundred million parameters; inference with this network on a single image takes tens of billions of operations, prohibiting its use on edge devices such as mobile phones or in real-time applications.", "In addition, the huge size of DNNs often precludes them from being placed at the upper level of the memory hierarchy, with resulting slow access times and expensive energy consumption.A recent thread of research has thus focused on the question of how to compress DNNs.", "One successful approach that has emerged is to trim the connections between neurons, which reduces the number of non-zero parameters and thus the model size BID1", "b) ; BID3 ; BID4 ; BID5 ; BID6 ; BID7 ).", "However, there has been a gap between the theory and practice: the trimming algorithms that have been practically successful BID1", "b) ; BID3 ) do not have theoretical guarantees, while theoretically-motivated approaches have been less competitive compared to the heuristics-based approaches BID5 , and often relies on stringent distributional assumption such as Gaussian-distributed matrices which might not hold in practice.", "With a better theoretical understanding, we might be able to answer how much pruning one can achieve via different approaches on different tasks, and moreover when a given pruning approach might or might not work.", "Indeed, as we discuss in our experiments, even the generally practically successful approaches are subject to certain failure cases.", "Beyond simple connection pruning, there have been other works on structured pruning that prune a whole filter, whole row, or whole column at a time BID8 ; BID9 ; BID10 ; ; BID12 ).", "The structured pruning strategy can often speed up inference speed at prediction time more than simple connection pruning, but the pruning ratios are typically not as high as non-structured connection pruning; so that the storage complexity is still too high, so that the caveats we noted earlier largely remain.A very natural strategy is to use 1 regularized training to prune DNNs, due to their considerable practical success in general sparse estimation in shallow model settings.", "However, many recent investigations seemed to suggest that such 1 regularization does not work as well with non-shallow DNNs, especially compared to other proposed methods.", "Does 1 regularization not work as well in non-shallow models?", "In this work, we theoretically analyze this question, revisit the trimming of DNNs through 1 regularization.", "Our analysis provides two interesting findings:", "(a) for any stationary point under 1 regularization, the number of non-zero parameters in each layer of a DNN is bounded by the number of penalized prediction logits-an upper bound typically several orders of magnitude smaller than the total number of DNN parameters, and", "(b) it is critical to employ an 1 -friendly optimization solver with a high precision in order to find the stationary point of sparse support.Our theoretical findings thus suggest that one could achieve high pruning ratios even via 1 regularization provided one uses high-precision solvers (which we emphasize are typically not required if we only care about prediction error rather than sparsity).", "We corroborate these findings in our experiments, where we show that solving the 1 -regularized objective by the combination of SGD pretraining and Adamax-L1(cumulative) yields competitive pruning results compared to the state-ofthe-art.", "In this work, we revisit the simple idea of pruning connections of DNNs through 1 regularization.", "While recent empirical investigations suggested that this might not necessarily achieve high sparsity levels in the context of DNNs, we provide a rigorous theoretical analysis that does provide small upper bounds on the number of non-zero elements, but with the caveat that one needs to use a high-precision optimization solver (which is typically not needed if we care only about prediction error rather than sparsity).", "When using such an accurate optimization solver, we can converge closer to stationary points than traditional SGD, and achieve much better pruning ratios than SGD, which might explain the poorer performance of 1 regularization in recent investigations.", "We perform experiments across different datasets and networks and demonstrate state-of-the-art result with such simple 1 regularization.", "Table 5 : Per-layer Resnet-32 architecture.", "There are 3 main convolutional blocks with downsampling through stride=2 for the first layer of each block.", "After the convloutional layers, global pooling is applied on the spatial axes and a fully-connected layer is appended for the output.", "Each set of rows is a residual block." ]

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[ "We revisit the simple idea of pruning connections of DNNs through $\\ell_1$ regularization achieving state-of-the-art results on multiple datasets with theoretic guarantees." ]

[ "Autonomy and adaptation of machines requires that they be able to measure their own errors.", "We consider the advantages and limitations of such an approach when a machine has to measure the error in a regression task.", "How can a machine measure the error of regression sub-components when it does not have the ground truth for the correct predictions?", "A \n", "compressed sensing approach applied to the error signal of the regressors can recover their precision error without any ground truth.", "It allows for some regressors to be strongly correlated as long as not too many are so related.\n", "Its solutions, however, are not unique - a property of ground truth inference solutions.", "Adding $\\ell_1$--minimization\n", "as a condition can recover the correct solution in settings where error correction is possible.", "We briefly discuss the similarity of the mathematics of ground truth inference for regressors to that for classifiers.", "An autonomous, adaptive system, such as a self-driving car, needs to be robust to self-failures and changing environmental conditions.", "To do so, it must distinguish between self-errors and environmental changes.", "This chicken-andegg problem is the concern of ground truth inference algorithms -algorithms that measure a statistic of ground truth given the output of an ensemble of evaluators.", "They seek to answer the question -Am I malfunctioning or is the environment changing so much that my models are starting to break down?Ground", "truth inference algorithms have had a spotty history in the machine learning community. The original", "idea came from BID2 and used the EM algorithm to solve a maximum-likelihood equation. This enjoyed", "a brief renaissance in the 2000s due to advent of services like Preliminary work. Under review", "by the International Conference on Machine Learning (ICML). Do not distribute", ".Amazon Turk. Our main critique", "of all these approaches is that they are parametric -they assume the existence of a family of probability distributions for how the estimators are committing their errors. This has not worked", "well in theory or practice BID4 .Here we will discuss", "the advantages and limitations of a non-parametric approach that uses compressed sensing to solve the ground truth inference problem for noisy regressors BID1 . Ground truth is defined", "in this context as the correct values for the predictions of the regressors. The existence of such ground", "truth is taken as a postulate of the approach. More formally, Definition 1", "(Ground truth postulate for regressors). All regressed values in a dataset", "can be written as, DISPLAYFORM0 where y i,true does not depend on the regressor used.In many practical situations this is a very good approximation to reality. But it can be violated. For example", ", the regressors may have", "developed their estimates at different times while a y(t) i,true varied under them.We can now state the ground truth inference problem for regressors as, Definition 2 (Ground truth inference problem for regressors). Given the output of R aligned regressors", "on a dataset of size D, DISPLAYFORM1 estimate the error moments for the regressors, DISPLAYFORM2 and DISPLAYFORM3 without the true values, {y i,true }.The separation of moment terms that are usually", "combined to define a covariance 1 between estimators is deliberate and relates to the math for the recovery as the reader will understand shortly.As stated, the ground truth inference problem for sparsely correlated regressors was solved in BID1 by using a compressed sensing approach to recover the R(R + 1)/2 moments, δ r1 δ r2 , for unbiased (δ r ≈ 0) regressors. Even the case of some of the regressors being strongly", "correlated is solvable. Sparsity of non-zero correlations is all that is required", ". Here we point out that the failure to find a unique solution", "for biased regressors still makes it possible to detect and correct biased regressors under the same sort of engineering logic that allows bit flip error correction in computers.", "A compressed sensing algorithm for recovering the average error moments of an ensemble of noisy regressors exists.", "Like other ground truth inference algorithms, it leads to non-unique solutions.", "However, in many well-engineered systems, errors are sparse and mostly uncorrelated when the machine is operating normally.", "Algorithms such as this one can then detect the beginning of malfunctioning sensors and algorithms.We can concretize the possible applications of this technique by considering a machine such as a self-driving car.", "Optical cameras and range finders are necessary sub-components.", "How can the car detect a malfunctioning sensor?", "There are many ways this already can be done (no power from the sensor, etc.).", "This technique adds another layer of protection by potentially detecting anomalies earlier.", "In addition, it allows the creation of supervision arrangements such as having one expensive, precise sensor coupled with many cheap, imprecise ones.", "As the recovered error moment matrix in Figure 2 shows, many noisy sensors can be used to benchmark a more precise one (the (sixth regressor {6,6} moment in this particular case).", "As BID1 demonstrate, it can also be used on the final output of algorithms.", "In the case of a self-driving car, a depth map is needed of the surrounding environment -the output of algorithms processing the sensor input data.", "Here again, one can envision supervisory arrangements where quick, imprecise estimators can be used to monitor a more expensive, precise one.There are advantages and limitations to the approach proposed here.", "Because there is no maximum likelihood equation to solve, the method is widely applicable.", "The price for this flexibility is that no generalization can be made.", "There is no theory or model to explain the observed errors -they are just estimated robustly for each specific dataset.", "Additionally, the math is easily understood.", "The advantages or limitations of a proposed application to an autonomous, adaptive system can be ascertained readily.", "The theoretical guarantees of compressed sensing algorithms are a testament to this BID3 .", "Finally, the compressed sensing approach to regressors can handle strongly, but sparsely, correlated estimators.We finish by pointing out that non-parametric methods also exist for classification tasks.", "This is demonstrated for independent, binary classifiers (with working code) in (CorradaEmmanuel, 2018) .", "The only difference is that the linear algebra of the regressor problem becomes polynomial algebra.", "Nonetheless, there we find similar ambiguities due to non-unique solutions to the ground truth inference problem of determining average classifier accuracy without the correct labels.", "For example, the polynomial for unknown prevalence (the environmental variable) of one of the labels is quadratic, leading to two solutions.", "Correspondingly, the accuracies of the classifiers (the internal variables) are either x or 1 − x.", "So a single classifier could be, say, 90% or 10% accurate.", "The ambiguity is removed by having enough classifiers -the preferred solution is where one of them is going below 50%, not the rest doing so." ]

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[ "A non-parametric method to measure the error moments of regressors without ground truth can be used with biased regressors" ]

[ "We propose a new representation, one-pixel signature, that can be used to reveal the characteristics of the convolution neural networks (CNNs).", "Here, each CNN classifier is associated with a signature that is created by generating, pixel-by-pixel, an adversarial value that is the result of the largest change to the class prediction.", "The one-pixel signature is agnostic to the design choices of CNN architectures such as type, depth, activation function, and how they were trained.", "It can be computed efficiently for a black-box classifier without accessing the network parameters.", "Classic networks such as LetNet, VGG, AlexNet, and ResNet demonstrate different characteristics in their signature images.", "For application, we focus on the classifier backdoor detection problem where a CNN classifier has been maliciously inserted with an unknown Trojan.", "We show the effectiveness of the one-pixel signature in detecting backdoored CNN.", "Our proposed one-pixel signature representation is general and it can be applied in problems where discriminative classifiers, particularly neural network based, are to be characterized.", "Recent progress in designing convolutional neural network architectures (LeCun et al., 1989; Krizhevsky et al., 2012; Szegedy et al., 2015; He et al., 2016; Xie et al., 2017) has contributed, in part, to the explosive development in deep learning (LeCun et al., 2015; Goodfellow et al., 2016) .", "Convolutional neural networks (CNN) have been adopted in a wide range of applications including image labeling (Long et al., 2015; Ronneberger et al., 2015; Xie & Tu, 2015) , object detection (Girshick et al., 2014; Ren et al., 2015) , low-level image processing (Xie et al., 2012; Dosovitskiy et al., 2015a; Kim et al., 2016) , artistic transfer (Gatys et al., 2016) , generative models (Goodfellow et al., 2014a; Dosovitskiy et al., 2015b; Lee et al., 2018) , image captioning (Xu et al., 2015) , and 2D to 3D estimation/reconstruction Wu et al., 2017) .", "Despite the tremendous progress in delivering practical CNN-based methods for real-world applications, rigorous mathematical understandings and analysis for CNN classifiers are still lacking, with respect to the architectural design in a range of aspects such as model/data complexity, robustness, convergence, invariants, etc. (Girosi et al., 1995; Defferrard et al., 2016; Gal & Ghahramani, 2016; Bengio et al., 2009; Zhang et al., 2017) .", "Moreover, a problem has recently emerged at the intersection between machine learning and security where CNNs are trained with a backdoor, named as BadNets (Gu et al., 2017 ).", "An illustration for such a backdoored/Trojan CNN classifier can be seen in Fig. 1 .b", ".", "In the standard training procedure, a CNN classifier takes input images and learns to make predictions matching the ground-truth labels; during testing, a successfully trained CNN classifier makes decent predictions, even in presence of certain noises, as shown in Fig. 1 .a", ".", "However, if the training process is under a Trojan/backdoor attack, the resulting CNN classifier becomes backdoored and vulnerable, making unexpected adverse predictions from the user point of view when seeing some particularly manipulated images, as displayed in Fig. 1 .b", ".", "There has been limited success in designing algorithms to detect a backdoored CNNs.", "We develop one-pixel signature and make the following contributions.", "• To unfold CNN classifiers to perform e.g. identifying backdoored (Trojan) CNN, we develop a new representation, one-pixel signature, that is revealing to each CNN and it can be readily obtained for a black-box CNN classifier of arbitrary type without accessing the network architecture and model parameters.", "• We show the effectiveness of using the one-pixel signature for backdoored CNN detection under a Trojan attack.", "Various network architectures including LeNet (LeCun et al., 1989) , AlexNet (Krizhevsky et al., 2012) , ResNet (He et al., 2016) , DenseNet (Huang et al., 2017) , and ResNeXt (Xie et al., 2017) are studied.", "• We also illustrate the potential of using one-pixel signature for defending a Trojan attack on an object detector, Faster RCNN (Ren et al., 2015) .", "• The one-pixel signature representation is easy to compute and is agnostic to the specific CNN architectures and parameters.", "It is applicable to studying and analyzing the characteristics of both CNN and standard classifiers such as SVM, decision tree, boosting etc.", "(a) CNN trained regularly", "(b) CNN trained with a backdoor displays a backdoored CNN, denoted as CNNT rojan, which is trained maliciously by inserting a \"virus\" pattern (a star) to a training sample and forcing the classification to a wrong label.", "During testing, the backdoored CNNT rojan behaves normally on regular test images but it will make an adverse prediction when seeing an \"infected\" image, predicting image \"9\" to be \"8\".", "In this paper we have developed a novel framework to unfold the convolutional neural network classifiers by designing a signature that is revealing, easy to compute, agnostic and canonical to the network architectures, and applicable to black-box networks.", "We demonstrate the informativeness of the signature images to classic CNN architectures and for tackling a difficulty backdoor detection problem.", "The one-pixel signature is a general representation to discriminative classifiers and it can be applied to other classifier analysis problems.", "for j from 0 to n − 1 do 7:", "for v from 0 to 1; step=1/V do 10:", "for k from 0 to K-1 do 12:" ]

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[ "Cnvolutional neural networks characterization for backdoored classifier detection and understanding." ]

[ "We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints.", "Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories.", "Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving a mixed integer program.", "Additionally, by leveraging a known parameterization of the constraint, we modify our method to learn parametric constraints in high dimensions.", "We show that our method can learn a six-dimensional pose constraint for a 7-DOF robot arm.", "Inverse optimal control and inverse reinforcement learning (IOC/IRL) BID5 can enable robots to perform complex goaldirected tasks by learning a cost function which replicates the behavior of an expert demonstrator when optimized.", "However, planning for many robotics and automation tasks also requires knowing constraints, which define what states or trajectories are safe.", "Existing methods learn local trajectory-based constraints BID3 BID4 or a cost penalty to approximate a constraint BID1 , neither of which extracts states that are guaranteed unsafe for all trajectories.", "In contrast, recent work BID2 recovers a binary representation of globally-valid constraints from expert demonstrations by sampling lower cost (and hence constraintviolating) trajectories and then recovering a constraint consistent with the data by solving an integer program over a gridded constraint space.", "The learned constraint can be then used to inform a planner to generate safe trajectories connecting novel start and goal states.", "However, the gridding restricts the scalability of this method to higher dimensional constraints.", "The contributions of this workshop paper are twofold:• By assuming a known parameterization of the constraint, we extend BID2 to higher dimensions by writing a mixed integer program over parameters which recovers a constraint consistent with the data.•", "We evaluate the method by learning a 6-dimensional pose constraint on a 7 degree-of-freedom (DOF) robot arm. II", ". PRELIMINARIES", "AND PROBLEM STATEMENT We consider a state-control demonstration (ξ * x . = {x 0 , . . . , x T }, ξ * u . = {u 0 , . . . , u T −1 }) which steers a controlconstrained system x t+1 = f (x t , u t , t), u t ∈ U for all t, from a start state x 0 to a goal state x T , while minimizing cost c(ξ x , ξ u ) and obeying safety constraints φ(ξ) . DISPLAYFORM0", "Formally, a demonstration solves the following problem 1 : DISPLAYFORM1 are known functions mapping (ξ x , ξ u ) to some constraint spaces C andC, where subsets S ⊆ C and S ⊆C are considered safe. In particular", ",S is known and represents the set of all constraints known to the learner.In this paper, we consider the problem of learning the unsafe set A . DISPLAYFORM2", ", each with different start and goal states. We assume that", "the dynamics, control constraints, and start and goal constraints are known and are embedded inφ(ξ x , ξ u ) ∈S. We also assume", "the cost function c(·, ·) is known. BID0 Details for", "continuous-time and suboptimal demonstrations are in BID2 . DISPLAYFORM3" ]

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[ "We can learn high-dimensional constraints from demonstrations by sampling unsafe trajectories and leveraging a known constraint parameterization." ]

[ "We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds.", "We employ Siamese networks to solve the problem of least squares multidimensional scaling for generating mappings that preserve geodesic distances on the manifold.", "In contrast to previous parametric manifold learning methods we show a substantial reduction in training effort enabled by the computation of geodesic distances in a farthest point sampling strategy.", "Additionally, the use of a network to model the distance-preserving map reduces the complexity of the multidimensional scaling problem and leads to an improved non-local generalization of the manifold compared to analogous non-parametric counterparts.", "We demonstrate our claims on point-cloud data and on image manifolds and show a numerical analysis of our technique to facilitate a greater understanding of the representational power of neural networks in modeling manifold data.", "The characterization of distance preserving maps is of fundamental interest to the problem of nonlinear dimensionality reduction and manifold learning.", "For the purpose of achieving a coherent global representation, it is often desirable to embed the high-dimensional data into a space of low dimensionality while preserving the metric structure of the data manifold.", "The intrinsic nature of the geodesic distance makes such a representation depend only on the geometry of the manifold and not on how it is embedded in ambient space.", "In the context of dimensionality reduction this property makes the resultant embedding meaningful.The success of deep learning has shown that neural networks can be trained as powerful function approximators of complex attributes governing various visual and auditory phenomena.", "The availability of large amounts of data and computational power, coupled with parallel streaming architectures and improved optimization techniques, have all led to computational frameworks that efficiently exploit their representational power.", "However, a study of their behavior under geometric constraints is an interesting question which has been relatively unexplored.In this paper, we use the computational infrastructure of neural networks to model maps that preserve geodesic distances on data manifolds.", "We revisit the classical geometric framework of multidimensional scaling to find a configuration of points that satisfy pairwise distance constraints.", "We show that instead of optimizing over the individual coordinates of the points, we can optimize over the function that generates these points by modeling this map as a neural network.", "This makes the complexity of the problem depend on the number of parameters of the network rather than the number of data points, and thus significantly reduces the memory and computational complexities, a property that comes into practical play when the number of data points is large.", "Additionally, the choice of modeling the isometric map with a parametric model provides a straightforward out-of-sample extension, which is a simple forward pass of the network.We exploit efficient sampling techniques that progressively select landmark points on the manifold by maximizing the spread of their pairwise geodesic distances.", "We demonstrate that a small amount of these landmark points are sufficient to train a network to generate faithful low-dimensional embeddings of manifolds.", "Figure 1 provides a visualization of the proposed approach.", "In the interest of gauging their effectiveness in representing manifolds, we perform a numerical analysis to measure the quality of embedding generated by neural networks and associate an order of accuracy to a given Figure 1 : Learning to unfurl a ribbon: A three dimensional Helical Ribbon and its two dimensional embedding learned using a two-layer MLP.", "The network was trained using estimated pairwise geodesic distances between only 100 points (marked in black) out of the total 8192 samples.architecture.", "Finally, we demonstrate that parametric models provide better non-local generalization as compared to extrapolation formulas of their non-parametric counter parts.We advocate strengthening the link between axiomatic computation and parametric learning methodologies.", "Existing MDS frameworks use a geometrically meaningful objective in a cumbersome non-parametric framework.", "At the other end, learning based methods such as DrLim BID18 use a computationally desirable infrastructure yet a geometrically suboptimal objective requiring too many examples for satisfactory manifold learning.", "The proposed approach can be interpreted as taking the middle path by using a computationally desirable method of a parametric neural network optimized by the geometrically meaningful cost of multidimensional scaling.", "In the interest of obtaining a better understanding of neural network behavior, we advocate using learning methodologies for solving geometric problems with data by allowing a limited infusion of axiomatic computation to the learning process.", "In this paper we demonstrate such a scheme by combining parametric modeling with neural networks and the geometric framework of multidimensional scaling.", "The result of this union leads to reduction in training effort and improved local and nonlocal generalization abilities.", "As future work, we intend to further explore methods that leverage learning methodologies for improving the largely axiomatic setups of numerical algorithms." ]

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[ "Parametric Manifold Learning with Neural Networks in a Geometric Framework " ]

[ "Exploration is a fundamental aspect of Reinforcement Learning, typically implemented using stochastic action-selection.", "Exploration, however, can be more efficient if directed toward gaining new world knowledge.", "Visit-counters have been proven useful both in practice and in theory for directed exploration.", "However, a major limitation of counters is their locality.", "While there are a few model-based solutions to this shortcoming, a model-free approach is still missing.\n", "We propose $E$-values, a generalization of counters that can be used to evaluate the propagating exploratory value over state-action trajectories.", "We compare our approach to commonly used RL techniques, and show that using $E$-values improves learning and performance over traditional counters.", "We also show how our method can be implemented with function approximation to efficiently learn continuous MDPs.", "We demonstrate this by showing that our approach surpasses state of the art performance in the Freeway Atari 2600 game.", "\"If there's a place you gotta go -I'm the one you need to know.\"(Map, Dora The Explorer)We consider Reinforcement Learning in a Markov Decision Process (MDP).", "An MDP is a fivetuple M = (S, A, P, R, γ) where S is a set of states and A is a set of actions.", "The dynamics of the process is given by P (s |s, a) which denotes the transition probability from state s to state s following action a.", "Each such transition also has a distribution R (r|s, a) from which the reward for such transitions is sampled.", "Given a policy π : S → A, a function -possibly stochastic -deciding which actions to take in each of the states, the state-action value function Q π : S × A → R satisfies: r,s ∼R×P (·|s,a) [r + γQ π (s , π (s ))] DISPLAYFORM0 where γ is the discount factor.", "The agent's goal is to find an optimal policy π * that maximizes Q π (s, π (s)).", "For brevity, Q π * Q * .", "There are two main approaches for learning π * .", "The first is a model-based approach, where the agent learns an internal model of the MDP (namely P and R).", "Given a model, the optimal policy could be found using dynamic programming methods such as Value Iteration BID19 .", "The alternative is a model-free approach, where the agent learns only the value function of states or state-action pairs, without learning a model BID5 1 .The", "ideas put forward in this paper are relevant to any model-free learning of MDPs. For", "concreteness, we focus on a particular example, Q-Learning BID23 BID19 . Q-Learning", "is a common method for learning Q * , where the agent iteratively updates its values of Q (s, a) by performing actions and observing their outcomes. At each step", "the agent takes action a t then it is transferred from s t to s t+1 and observe reward r. Then it applies", "the update rule regulated by a learning rate α: Q (s t , a t ) ← (1 − α) Q (s t , a t ) + α r + γ max a Q (s t+1 , a) ." ]

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[ "We propose a generalization of visit-counters that evaluate the propagating exploratory value over trajectories, enabling efficient exploration for model-free RL" ]

[ "Deep neuroevolution and deep reinforcement learning (deep RL) algorithms are two popular approaches to policy search.", "The former is widely applicable and rather stable, but suffers from low sample efficiency.", "By contrast, the latter is more sample efficient, but the most sample efficient variants are also rather unstable and highly sensitive to hyper-parameter setting.", "So far, these families of methods have mostly been compared as competing tools.", "However, an emerging approach consists in combining them so as to get the best of both worlds.", "Two previously existing combinations use either an ad hoc evolutionary algorithm or a goal exploration process together with the Deep Deterministic Policy Gradient (DDPG) algorithm, a sample efficient off-policy deep RL algorithm.", "In this paper, we propose a different combination scheme using the simple cross-entropy\n", "method (CEM) and Twin Delayed Deep Deterministic policy gradient (TD3), another off-policy deep RL algorithm which improves over DDPG.", "We evaluate the resulting method, CEM-RL, on a set of benchmarks classically used in deep RL.\n", "We show that CEM-RL benefits from several advantages over its competitors and offers a satisfactory trade-off between performance and sample efficiency.", "Policy search is the problem of finding a policy or controller maximizing some unknown utility function.", "Recently, research on policy search methods has witnessed a surge of interest due to the combination with deep neural networks, making it possible to find good enough continuous action policies in large domains.", "From one side, this combination gave rise to the emergence of efficient deep reinforcement learning (deep RL) techniques BID17 BID25 .", "From the other side, evolutionary methods, and particularly deep neuroevolution methods applying evolution strategies (ESs) to the parameters of a deep network have emerged as a competitive alternative to deep RL due to their higher parallelization capability BID23 .Both", "families of techniques have clear distinguishing properties. Evolutionary", "methods are significantly less sample efficient than deep RL methods because they learn from complete episodes, whereas deep RL methods use elementary steps of the system as samples, and thus exploit more information BID27 . In particular", ", off-policy deep RL algorithms can use a replay buffer to exploit the same samples as many times as useful, greatly improving sample efficiency. Actually, the", "sample efficiency of ESs can be improved using the \"importance mixing\" mechanism, but a recent study has shown that the capacity of importance mixing to improve sample efficiency by a factor of ten is still not enough to compete with off-policy deep RL BID22 . From the other", "side, sample efficient off-policy deep RL methods such as the DDPG algorithm BID17 are known to be unstable and highly sensitive to hyper-parameter setting. Rather than opposing", "both families as competing solutions to the policy search problem, a richer perspective consists in combining them so as to get the best of both worlds. As covered in Section", "2, there are very few attempts in this direction so far.After presenting some background in Section 3, we propose in Section 4 a new combination method that combines the cross-entropy method (CEM) with DDPG or TD3, an off-policy deep RL algorithm which improves over DDPG. In Section 5, we investigate", "experimentally the properties of this CEM-RL method, showing its advantages both over the components taken separately and over a competing approach. Beyond the results of CEM-RL", ", the conclusion of this work is that there is still a lot of unexplored potential in new combinations of evolutionary and deep RL methods.", "We advocated in this paper for combining evolutionary and deep RL methods rather than opposing them.", "In particular, we have proposed such a combination, the CEM-RL method, and showed that in most cases it was outperforming not only some evolution strategies and some sample efficient offpolicy deep RL algorithms, but also another combination, the ERL algorithm.", "Importantly, despite being mainly an evolutionary method, CEM-RL is competitive to the state-of-the-art even when considering sample efficiency, which is not the case of other deep neuroevolution methods BID24 .Beyond", "these positive performance results, our study raises more fundamental questions. First,", "why does the simple CEM algorithm perform so well on the SWIMMER-V2 benchmark? Then,", "our empirical study of importance mixing did not confirm a clear benefit of using it, neither did the effect of adding noise on actions. We suggest", "explanations for these phenomena, but nailing down the fundamental reasons behind them will require further investigations. Such deeper", "studies will also help understand which properties are critical in the performance and sample efficiency of policy search algorithms, and define even more efficient policy search algorithms in the future. As suggested", "in Section 5.2.3, another avenue for future work will consist in designing an ERL algorithm based on CEM rather than on an ad hoc evolutionary algorithm. Finally, given", "the impact of the neural architecture on our results, we believe that a more systemic search of architectures through techniques such as neural architecture search (Zoph & Le, 2016; BID7 may provide important progress in performance of deep policy search algorithms." ]

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[ "We propose a new combination of evolution strategy and deep reinforcement learning which takes the best of both worlds" ]

[ "Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games.", "However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved.", "Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model.", "At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical.", "Thus, it is attractive to consider approximate Bayesian neural networks in a Thompson Sampling framework.", "To understand the impact of using an approximate posterior on Thompson Sampling, we benchmark well-established and recently developed methods for approximate posterior sampling combined with Thompson Sampling over a series of contextual bandit problems.", "We found that many approaches that have been successful in the supervised learning setting underperformed in the sequential decision-making scenario.", "In particular, we highlight the challenge of adapting slowly converging uncertainty estimates to the online setting.", "Recent advances in reinforcement learning have sparked renewed interest in sequential decision making with deep neural networks.", "Neural networks have proven to be powerful and flexible function approximators, allowing one to learn mappings directly from complex states (e.g., pixels) to estimates of expected return.", "While such models can be accurate on data they have been trained on, quantifying model uncertainty on new data remains challenging.", "However, having an understanding of what is not yet known or well understood is critical to some central tasks of machine intelligence, such as effective exploration for decision making.A fundamental aspect of sequential decision making is the exploration-exploitation dilemma: in order to maximize cumulative reward, agents need to trade-off what is expected to be best at the moment, (i.e., exploitation), with potentially sub-optimal exploratory actions.", "Solving this trade-off in an efficient manner to maximize cumulative reward is a significant challenge as it requires uncertainty estimates.", "Furthermore, exploratory actions should be coordinated throughout the entire decision making process, known as deep exploration, rather than performed independently at each state.Thompson Sampling (Thompson, 1933) and its extension to reinforcement learning, known as Posterior Sampling, provide an elegant approach that tackles the exploration-exploitation dilemma by maintaining a posterior over models and choosing actions in proportion to the probability that they are optimal.", "Unfortunately, maintaining such a posterior is intractable for all but the simplest models.", "As such, significant effort has been dedicated to approximate Bayesian methods for deep neural networks.", "These range from variational methods BID17 BID6 BID23 to stochastic minibatch Markov Chain Monte Carlo (Neal, 1994; Welling & Teh, 2011; BID25 BID1 BID26 , among others.", "Because the exact posterior is intractable, evaluating these approaches is hard.", "Furthermore, these methods are rarely compared on benchmarks that measure the quality of their estimates of uncertainty for downstream tasks.To address this challenge, we develop a benchmark for exploration methods using deep neural networks.", "We compare a variety of well-established and recent Bayesian approximations under the lens of Thompson Sampling for contextual bandits, a classical task in sequential decision making.", "All code and implementations to reproduce the experiments will be available open-source, to provide a reproducible benchmark for future development.", "1 Exploration in the context of reinforcement learning is a highly active area of research.", "Simple strategies such as epsilon-greedy remain extremely competitive (Mnih et al., 2015; Schaul et al., 2016) .", "However, a number of promising techniques have recently emerged that encourage exploration though carefully adding random noise to the parameters (Plappert et al., 2017; BID12 BID13 or bootstrap sampling (Osband et al., 2016) before making decisions.", "These methods rely explicitly or implicitly on posterior sampling for exploration.In this paper, we investigate how different posterior approximations affect the performance of Thompson Sampling from an empirical standpoint.", "For simplicity, we restrict ourselves to one of the most basic sequential decision making scenarios: that of contextual bandits.No single algorithm bested the others in every bandit problem, however, we observed some general trends.", "We found that dropout, injecting random noise, and bootstrapping did provide a strong boost in performance on some tasks, but was not able to solve challenging synthetic exploration tasks.", "Other algorithms, like Variational Inference, Black Box α-divergence, and minibatch Markov Chain Monte Carlo approaches, strongly couple their complex representation and uncertainty estimates.", "This proves problematic when decisions are made based on partial optimization of both, as online scenarios usually require.", "On the other hand, making decisions according to a Bayesian linear regression on the representation provided by the last layer of a deep network offers a robust and easy-to-tune approach.", "It would be interesting to try this approach on more complex reinforcement learning domains.In Section 2 we discuss Thompson Sampling, and present the contextual bandit problem.", "The different algorithmic approaches that approximate the posterior distribution fed to Thompson Sampling are introduced in Section 3, while the linear case is described in Section 4.", "The main experimental results are presented in Section 5, and discussed in Section 6.", "Finally, Section 7 concludes.", "Overall, we found that there is significant room for improvement in uncertainty estimation for neural networks in sequential decision-making problems.", "First, unlike in supervised learning, sequential decision-making requires the model to be frequently updated as data is accumulated.", "As a result, methods that converge slowly are at a disadvantage because we must truncate optimization to make the method practical for the online setting.", "In these cases, we found that partially optimized uncertainty estimates can lead to catastrophic decisions and poor performance.", "Second, and while it deserves further investigation, it seems that decoupling representation learning and uncertainty estimation improves performance.", "The NeuralLinear algorithm is an example of this decoupling.", "With such a model, the uncertainty estimates can be solved for in closed form (but may be erroneous due to the simplistic model), so there is no issue with partial optimization.", "We suspect that this may be the reason for the improved performance.", "In addition, we observed that many algorithms are sensitive to their hyperparameters, so that best configurations are problem-dependent.Finally, we found that in many cases, the inherit randomness in Stochastic Gradient Descent provided sufficient exploration.", "Accordingly, in some scenarios it may be hard to justify the use of complicated (and less transparent) variations of simple methods.", "However, Stochastic Gradient Descent is by no The suffix of the BBB legend label indicates the number of training epochs in each training step.", "We emphasize that in this evaluation, all algorithms use the same family of models (i.e., linear).", "While PrecisionDiag exactly solves the mean field problem, BBB relies on partial optimization via SGD.", "As the number of training epochs increases, BBB improves performance, but is always outperformed by PrecisionDiag.means always enough: in our synthetic exploration-oriented problem (the Wheel bandit) additional exploration was necessary.Next, we discuss our main findings for each class of algorithms.Linear Methods.", "Linear methods offer a reasonable baseline, surprisingly strong in many cases.", "While their representation power is certainly a limiting factor, their ability to compute informative uncertainty measures seems to payoff and balance their initial disadvantage.", "They do well in several datasets, and are able to react fast to unexpected or extreme rewards (maybe as single points can have a heavy impact in fitted models, and their updates are immediate, deterministic, and exact).", "Some datasets clearly need more complex non-linear representations, and linear methods are unable to efficiently solve those.", "In addition, linear methods obviously offer computational advantages, and it would be interesting to investigate how their performance degrades when a finite data buffer feeds the estimates as various real-world online applications may require (instead of all collected data).In", "terms of the diagonal linear approximations described in Section 3, we found that diagonalizing the precision matrix (as in mean-field Variational Inference) performs dramatically better than diagonalizing the covariance matrix.NeuralLinear. The", "NeuralLinear algorithm sits near a sweet spot that is worth further studying. In", "general it seems to improve the RMS neural network it is based on, suggesting its exploration mechanisms add concrete value. We", "believe its main strength is that it is able to simultaneously learn a data representation that greatly simplifies the task at hand, and to accurately quantify the uncertainty over linear models that explain the observed rewards in terms of the proposed representation. While", "the former process may be noisier and heavily dependent on the amount of training steps that were taken and available data, the latter always offers the exact solution to its approximate parent problem. This,", "together with the partial success of linear methods with poor representations, may explain its promising results. In some", "sense, it knows what it knows. In the", "Wheel problem, which requires increasingly good exploration mechanisms, NeuralLinear is probably the best algorithm. Its performance", "is almost an order of magnitude better than any RMS algorithm (and its spinoffs, like Bootstrapped NN, Dropout, or Parameter Noise), and all greedy linear approaches. On the other hand", ", it is able to successfully solve problems that require non-linear representations (as Statlog or Covertype) where linear approaches fail. In addition, the", "algorithm is remarkably easy to tune, and robust in terms of hyper-parameter configurations. While conceptually", "simple, its deployment to large scale systems may involve some technical difficulties; mainly, to update the Bayesian estimates when the network is re-trained. We believe, however", ", standard solutions to similar problems (like running averages) could greatly mitigate these issues. In our experiments", "and compared to other algorithms, as shown in Table 8 , NeuralLinear is fast from a computational standpoint.Variational Inference. Overall, Bayes By", "Backprop performed poorly, ranking in the bottom half of algorithms across datasets TAB0 . To investigate if", "this was due to underestimating uncertainty (as variational methods are known to BID5 ), to the mean field approximation, or to stochastic optimization, we applied BBB to a linear model, where the mean field optimization problem can be solved in closed form FIG5 . We found that the", "performance of BBB slowly improved as the number of training epochs increased, but underperformed compared to the exact mean field solution. Moreover, the difference", "in performance due to the number of training steps dwarfed the difference between the mean field solution and the exact posterior. This suggests that it is", "not sufficient to partially optimize the variational parameters when the uncertainty estimates directly affect the data being collected. In supervised learning,", "optimizing to convergence is acceptable, however in the online setting, optimizing to convergence at every step incurs unreasonable computational cost.Expectation-Propagation. The performance of Black", "Box α-divergence algorithms was poor. Because this class of algorithms", "is similar to BBB (in fact, as α → 0, it converges to the BBB objective), we suspect that partial convergence was also the cause of their poor performance. We found these algorithms to be", "sensitive to the number of training steps between actions, requiring a large number to achieve marginal performance. Their terrible performance in the", "Mushroom bandit is remarkable, while in the other datasets they perform slightly worse than their variational inference counterpart. Given the successes of Black Box", "α-divergence in other domains BID19 , investigating approaches to sidestep the slow convergence of the uncertainty estimates is a promising direction for future work.Monte Carlo. Constant-SGD comes out as the winner", "on Covertype, which requires non-linearity and exploration as evidenced by performance of the linear baseline approaches TAB0 ). The method is especially appealing as", "it does not require tuning learning rates or exploration parameters. SGFS, however, performs better on average", ". The additional injected noise in SGFS may", "cause the model to explore more and thus perform better, as shown in the Wheel Bandit problem where SGFS strongly outperforms Constant-SGD.Bootstrap. The bootstrap offers significant gains with", "respect to its parent algorithm (RMS) in several datasets. Note that in Statlog one of the actions is", "optimal around 80% of the time, and the bootstrapped predictions may help to avoid getting stuck, something from which RMS methods may suffer. In other scenarios, the randomness from SGD", "may be enough for exploration, and the bootstrap may not offer important benefits. In those cases, it might not justify the heavy", "computational overhead of the method. We found it surprising that the optimized versions", "of BootstrappedNN decided to use only q = 2 and q = 3 networks respectively (while we set its value to q = 10 in the manually tuned version, and the extra networks did not improve performance significantly). Unfortunately, Bootstrapped NNs were not able to solve", "the Wheel problem, and its performance was fairly similar to that of RMS. One possible explanation is that -given the sparsity of", "the rewardall the bootstrapped networks agreed for the most part, and the algorithm simply got stuck selecting action a 1 . As opposed to linear models, reacting to unusual rewards", "could take Bootstrapped NNs some time as good predictions could be randomly overlooked (and useful data discarded if p 1).Direct Noise Injection. When properly tuned, Parameter-Noise", "provided an important boost", "in performance across datasets over the learner that it was based on (RMS), average rank of ParamNoise-SL is 20.9 compared to RMS at 28.7 TAB0 . However, we found the algorithm hard to tune and sensitive to the", "heuristic controlling the injected noise-level. On the synthetic Wheel problem -where exploration is necessary-both", "parameter-noise and RMS suffer from underexploration and perform similarly, except ParamNoise-MR which does a good job. In addition, developing an intuition for the heuristic is not straightforward", "as it lacks transparency and a principled grounding, and thus may require repeated access to the decision-making process for tuning.Dropout. We initially experimented with two dropout versions: fixed p = 0.5, and p = 0.8", ". The latter consistently delivered better results, and it is the one we manually", "picked. The optimized versions of the algorithm provided decent improvements over its base", "RMS (specially Dropout-MR).In the Wheel problem, dropout performance is somewhat poor: Dropout is outperformed", "by RMS, while Dropout-MR offers gains with respect to all versions of RMS but it is not competitive with the best algorithms. Overall, the algorithm seems to heavily depend on its hyper-parameters (see cum-regret", "performance of the raw Dropout, for example). Dropout was used both for training and for decision-making; unfortunately, we did not", "add a baseline where dropout only applies during training. Consequently, it is not obvious how to disentangle the contribution of better training", "from that of better exploration. This remains as future work.Bayesian Non-parametrics. Perhaps unsurprisingly, Gaussian", "processes perform reasonably well on problems with little", "data but struggle on larger problems. While this motivated the use of sparse GP, the latter was not able to perform similarly to", "stronger (and definitively simpler) methods.", "In this work, we empirically studied the impact on performance of approximate model posteriors for decision making via Thompson Sampling in contextual bandits.", "We found that the most robust methods exactly measured uncertainty (possibly under the wrong model assumptions) on top of complex representations learned in parallel.", "More complicated approaches that learn the representation and its uncertainty together seemed to require heavier training, an important drawback in online scenarios, and exhibited stronger hyper-parameter dependence.", "Further exploring and developing the promising approaches is an exciting avenue for future work." ]

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[ "An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling" ]

[ "Class labels have been empirically shown useful in improving the sample quality of generative adversarial nets (GANs).", "In this paper, we mathematically study the properties of the current variants of GANs that make use of class label information.", "With class aware gradient and cross-entropy decomposition, we reveal how class labels and associated losses influence GAN's training.", "Based on that, we propose Activation Maximization Generative Adversarial Networks (AM-GAN) as an advanced solution.", "Comprehensive experiments have been conducted to validate our analysis and evaluate the effectiveness of our solution, where AM-GAN outperforms other strong baselines and achieves state-of-the-art Inception Score (8.91) on CIFAR-10.", "In addition, we demonstrate that, with the Inception ImageNet classifier, Inception Score mainly tracks the diversity of the generator, and there is, however, no reliable evidence that it can reflect the true sample quality.", "We thus propose a new metric, called AM Score, to provide more accurate estimation on the sample quality.", "Our proposed model also outperforms the baseline methods in the new metric.", "Generative adversarial nets (GANs) BID7 as a new way for learning generative models, has recently shown promising results in various challenging tasks, such as realistic image generation BID17 BID26 BID9 , conditional image generation BID12 BID2 BID13 , image manipulation ) and text generation BID25 .Despite", "the great success, it is still challenging for the current GAN models to produce convincing samples when trained on datasets with high variability, even for image generation with low resolution, e.g., CIFAR-10. Meanwhile", ", people have empirically found taking advantages of class labels can significantly improve the sample quality.There are three typical GAN models that make use of the label information: CatGAN BID20 builds the discriminator as a multi-class classifier; LabelGAN BID19 extends the discriminator with one extra class for the generated samples; AC-GAN BID18 jointly trains the real-fake discriminator and an auxiliary classifier for the specific real classes. By taking", "the class labels into account, these GAN models show improved generation quality and stability. However,", "the mechanisms behind them have not been fully explored BID6 .In this paper", ", we mathematically study GAN models with the consideration of class labels. We derive the", "gradient of the generator's loss w.r.t. class logits in the discriminator, named as class-aware gradient, for LabelGAN BID19 and further show its gradient tends to guide each generated sample towards being one of the specific real classes. Moreover, we", "show that AC-GAN BID18 can be viewed as a GAN model with hierarchical class discriminator. Based on the", "analysis, we reveal some potential issues in the previous methods and accordingly propose a new method to resolve these issues.Specifically, we argue that a model with explicit target class would provide clearer gradient guidance to the generator than an implicit target class model like that in BID19 . Comparing with", "BID18 , we show that introducing the specific real class logits by replacing the overall real class logit in the discriminator usually works better than simply training an auxiliary classifier. We argue that,", "in BID18 , adversarial training is missing in the auxiliary classifier, which would make the model more likely to suffer mode collapse and produce low quality samples. We also experimentally", "find that predefined label tends to result in intra-class mode collapse and correspondingly propose dynamic labeling as a solution. The proposed model is", "named as Activation Maximization Generative Adversarial Networks (AM-GAN). We empirically study", "the effectiveness of AM-GAN with a set of controlled experiments and the results are consistent with our analysis and, note that, AM-GAN achieves the state-of-the-art Inception Score (8.91) on CIFAR-10.In addition, through the experiments, we find the commonly used metric needs further investigation. In our paper, we conduct", "a further study on the widely-used evaluation metric Inception Score BID19 and its extended metrics. We show that, with the Inception", "Model, Inception Score mainly tracks the diversity of generator, while there is no reliable evidence that it can measure the true sample quality. We thus propose a new metric, called", "AM Score, to provide more accurate estimation on the sample quality as its compensation. In terms of AM Score, our proposed method", "also outperforms other strong baseline methods.The rest of this paper is organized as follows. In Section 2, we introduce the notations", "and formulate the LabelGAN BID19 and AC-GAN * BID18 ) as our baselines. We then derive the class-aware gradient", "for LabelGAN, in Section 3, to reveal how class labels help its training. In Section 4, we reveal the overlaid-gradient", "problem of LabelGAN and propose AM-GAN as a new solution, where we also analyze the properties of AM-GAN and build its connections to related work. In Section 5, we introduce several important", "extensions, including the dynamic labeling as an alternative of predefined labeling (i.e., class condition), the activation maximization view and a technique for enhancing the AC-GAN * . We study Inception Score in Section 6 and accordingly", "propose a new metric AM Score. In Section 7, we empirically study AM-GAN and compare", "it to the baseline models with different metrics. Finally we conclude the paper and discuss the future", "work in Section 8.", "In this paper, we analyze current GAN models that incorporate class label information.", "Our analysis shows that: LabelGAN works as an implicit target class model, however it suffers from the overlaidgradient problem at the meantime, and explicit target class would solve this problem.", "We demonstrate that introducing the class logits in a non-hierarchical way, i.e., replacing the overall real class logit in the discriminator with the specific real class logits, usually works better than simply supplementing an auxiliary classifier, where we provide an activation maximization view for GAN training and highlight the importance of adversarial training.", "In addition, according to our experiments, predefined labeling tends to lead to intra-class mode collapsed, and we propose dynamic labeling as an alternative.", "Our extensive experiments on benchmarking datasets validate our analysis and demonstrate our proposed AM-GAN's superior performance against strong baselines.", "Moreover, we delve deep into the widelyused evaluation metric Inception Score, reveal that it mainly works as a diversity measurement.", "And we also propose AM Score as a compensation to more accurately estimate the sample quality.In this paper, we focus on the generator and its sample quality, while some related work focuses on the discriminator and semi-supervised learning.", "For future work, we would like to conduct empirical studies on discriminator learning and semi-supervised learning.", "We extend AM-GAN to unlabeled data in the Appendix C, where unsupervised and semi-supervised is accessible in the framework of AM-GAN.", "The classifier-based evaluation metric might encounter the problem related to adversarial samples, which requires further study.", "Combining AM-GAN with Integral Probability Metric based GAN models such as Wasserstein GAN could also be a promising direction since it is orthogonal to our work.", "DISPLAYFORM0 Label smoothing that avoiding extreme logits value was showed to be a good regularization BID21 .", "A general version of label smoothing could be: modifying the target probability of discriminator) BID19 proposed to use only one-side label smoothing.", "That is, to only apply label smoothing for real samples: λ 1 = 0 and λ 2 > 0.", "The reasoning of one-side label smoothing is applying label smoothing on fake samples will lead to fake mode on data distribution, which is too obscure.", "DISPLAYFORM1 We will next show the exact problems when applying label smoothing to fake samples along with the log(1−D r (x)) generator loss, in the view of gradient w.r.t. class logit, i.e., the class-aware gradient, and we will also show that the problem does not exist when using the − log(D r (x)) generator loss.", "DISPLAYFORM2 The log(1−D r (x)) generator loss with label smoothing in terms of cross-entropy is DISPLAYFORM3 with lemma 1, its negative gradient is DISPLAYFORM4 DISPLAYFORM5 Gradient vanishing is a well know training problem of GAN.", "Optimizing D r (x) towards 0 or 1 is also not what desired, because the discriminator is mapping real samples to the distribution with DISPLAYFORM6 The − log(D r (x)) generator loss with target [1−λ, λ] in terms of cross-entropy is DISPLAYFORM7 the negative gradient of which is DISPLAYFORM8 DISPLAYFORM9 Without label smooth λ, the − log(D r (x)) always * preserves the same gradient direction as log(1−D r (x)) though giving a difference gradient scale.", "We must note that non-zero gradient does not mean that the gradient is efficient or valid.The both-side label smoothed version has a strong connection to Least-Square GAN BID15 : with the fake logit fixed to zero, the discriminator maps real to α on the real logit and maps fake to β on the real logit, the generator in contrast tries to map fake sample to α.", "Their gradient on the logit are also similar." ]

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[ "Understand how class labels help GAN training. Propose a new evaluation metric for generative models. " ]

[ "Modern neural networks are over-parametrized.", "In particular, each rectified linear hidden unit can be modified by a multiplicative factor by adjusting input and out- put weights, without changing the rest of the network.", "Inspired by the Sinkhorn-Knopp algorithm, we introduce a fast iterative method for minimizing the l2 norm of the weights, equivalently the weight decay regularizer.", "It provably converges to a unique solution.", "Interleaving our algorithm with SGD during training improves the test accuracy.", "For small batches, our approach offers an alternative to batch- and group- normalization on CIFAR-10 and ImageNet with a ResNet-18.", "Deep Neural Networks (DNNs) have achieved outstanding performance across a wide range of empirical tasks such as image classification BID1 , image segmentation (He et al., 2017) , speech recognition (Hinton et al., 2012a) , natural language processing (Collobert et al., 2011) or playing the game of Go BID16 .", "These successes have been driven by the availability of large labeled datasets such as ImageNet BID13 , increasing computational power and the use of deeper models (He et al., 2015b) .Although", "the expressivity of the function computed by a neural network grows exponentially with depth BID12 Telgarsky, 2016) , in practice deep networks are vulnerable to both over-and underfitting (Glorot & Bengio, 2010; BID1 He et al., 2015b) . Widely used", "techniques to prevent DNNs from overfitting include regularization methods such as weight decay BID2 , Dropout (Hinton et al., 2012b) and various data augmentation schemes BID1 BID17 BID19 He et al., 2015b) . Underfitting", "can occur if the network gets stuck in a local minima, which can be avoided by using stochastic gradient descent algorithms (Bottou, 2010; Duchi et al., 2011; BID18 BID0 , sometimes along with carefully tuned learning rate schedules (He et al., 2015b; Goyal et al., 2017) .Training deep", "networks is particularly challenging due to the vanishing/exploding gradient problem. It has been studied", "for Recurrent Neural networks (RNNs) (Hochreiter et al., 2001 ) as well as standard feedforward networks (He et al., 2015a; BID7 . After a few iterations", ", the gradients computed during backpropagation become either too small or too large, preventing the optimization scheme from converging. This is alleviated by", "using non-saturating activation functions such as rectified linear units (ReLUs) BID1 or better initialization schemes preserving the variance of the input across layers (Glorot & Bengio, 2010; BID7 He et al., 2015a) . Failure modes that prevent", "the training from starting have been theoretically studied by Hanin & Rolnick (2018) .Two techniques in particular", "have allowed vision models to achieve \"super-human\" accuracy. Batch Normalization (BN) was", "developed to train Inception networks (Ioffe & Szegedy, 2015) . It introduces intermediate layers", "that normalize the features by the mean and variance computed within the current batch. BN is effective in reducing training", "time, provides better generalization capabilities after training and diminishes the need for a careful initialization. Network architectures such as ResNet", "(He et al., 2015b) and DenseNet (Huang et al., 2016) use skip connections along with BN to improve the information flow during both the forward and backward passes. DISPLAYFORM0 Figure 1: Matrices W k", "and W k+1 are updated by multiplying the columns of the first matrix with rescaling coefficients. The rows of the second matrix are inversely", "rescaled to ensure that the product of the two matrices is unchanged. The rescaling coefficients are strictly positive", "to ensure functional equivalence when the matrices are interleaved with ReLUs. This rescaling is applied iteratively to each pair", "of adjacent matrices. In this paper, we address the more complex cases of", "biases, convolutions, max-pooling or skip-connections to be able to balance modern CNN architectures.However, BN has some limitations. In particular, BN only works well with sufficiently", "large batch sizes (Ioffe & Szegedy, 2015; Wu & He, 2018) . For sizes below 16 or 32, the batch statistics have", "a high variance and the test error increases significantly. This prevents the investigation of highercapacity models", "because large, memory-consuming batches are needed in order for BN to work in its optimal range. In many use cases, including video recognition (Carreira", "& Zisserman, 2017) and image segmentation (He et al., 2017) , the batch size restriction is even more challenging because the size of the models allows for only a few samples per batch. Another restriction of BN is that it is computationally", "intensive, typically consuming 20% to 30% of the training time. Variants such as Group Normalization (GN) (Wu & He, 2018", ") cover some of the failure modes of BN.In this paper, we introduce a novel algorithm to improve both the training speed and generalization accuracy of networks by using their over-parameterization to regularize them. In particular, we focus on neural networks that are positive-rescaling", "equivalent BID8 , i.e. whose weights are identical up to positive scalings and matching inverse scalings. The main principle of our method, referred to as Equi-normalization (ENorm", "), is illustrated in Figure 1 for the fullyconnected case. We scale two consecutive matrices with rescaling coefficients that minimize", "the joint p norm of those two matrices. This amounts to re-parameterizing the network under the constraint of implementing", "the same function. We conjecture that this particular choice of rescaling coefficients ensures a smooth", "propagation of the gradients during training.A limitation is that our current proposal, in its current form, can only handle learned skipconnections like those proposed in type-C ResNet. For this reason, we focus on architectures, in particular ResNet18, for which the learning", "converges with learned skip-connection, as opposed to architectures like ResNet-50 for which identity skip-connections are required for convergence.In summary,• We introduce an iterative, batch-independent algorithm that re-parametrizes the network within the space of rescaling equivalent networks, thus preserving the function implemented by the network; • We prove that the proposed Equi-normalization algorithm converges to a unique canonical parameterization of the network that minimizes the global p norm of the weights, or equivalently, when p = 2, the weight decay regularizer; • We extend ENorm to modern convolutional architectures, including the widely used ResNets, and show that the theoretical computational overhead is lower compared to BN (×50) and even compared to GN (×3); • We show that applying one ENorm step after each SGD step outperforms both BN and GN on the CIFAR-10 (fully connected) and ImageNet (ResNet-18) datasets.• Our code is available at https://github.com/facebookresearch/enorm. The paper is organized", "as follows. Section 2 reviews related work. Section 3 defines our Equinormalization", "algorithm for fully-connected networks", "and proves the convergence. Section", "4 shows how to adapt ENorm to convolutional neural networks (CNNs). Section 5 details how to employ ENorm", "for training neural networks and Section 6 presents our experimental results", "." ]

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[ "Fast iterative algorithm to balance the energy of a network while staying in the same functional equivalence class" ]

[ "Reinforcement learning agents are typically trained and evaluated according to their performance averaged over some distribution of environment settings.", "But does the distribution over environment settings contain important biases, and do these lead to agents that fail in certain cases despite high average-case performance?", "In this work, we consider worst-case analysis of agents over environment settings in order to detect whether there are directions in which agents may have failed to generalize.", "Specifically, we consider a 3D first-person task where agents must navigate procedurally generated mazes, and where reinforcement learning agents have recently achieved human-level average-case performance.", "By optimizing over the structure of mazes, we find that agents can suffer from catastrophic failures, failing to find the goal even on surprisingly simple mazes, despite their impressive average-case performance.", "Additionally, we find that these failures transfer between different agents and even significantly different architectures.", "We believe our findings highlight an important role for worst-case analysis in identifying whether there are directions in which agents have failed to generalize.", "Our hope is that the ability to automatically identify failures of generalization will facilitate development of more general and robust agents.", "To this end, we report initial results on enriching training with settings causing failure.", "Reinforcement Learning (RL) methods have achieved great success over the past few years, achieving human-level performance on a range of tasks such as Atari BID17 , Go BID20 , Labyrinth , and Capture the Flag BID13 .On", "these tasks, and more generally in reinforcement learning, agents are typically trained and evaluated using their average reward over environment settings as the measure of performance, i.e. E P (e) [R(π(θ) , e)] , where π(θ) denotes a policy with parameters θ, R denotes the total reward the policy receives over the course of an episode, and e denotes environment settings such as maze structure in a navigation task, appearance of objects in the environment, or even the physical rules governing environment dynamics. But", "what biases does the distribution P (e) contain, and what biases, or failures to generalize, do these induce in the strategies agents learn?To help", "uncover biases in the training distribution and in the strategies that agents learn, we propose evaluating the worst-case performance of agents over environment settings, i.e.min DISPLAYFORM0 where E is some set of possible environment settings.Worst-case analysis can provide an important tool for understanding robustness and generalization in RL agents. For example", ", it can help us with:• Understanding biases in training Catastrophic failures can help reveal situations that are rare enough during training that the agent does not learn a strategy that is general enough to cope with them. Frames from", "top left to bottom right correspond to agent observations as it takes the path from spawn to goal. Note that while", "the navigation task may look simple given a top down view, the agent only receives very partial information about the maze at every step, making navigation a difficult task.• Robustness For", "critical systems, one would want to eliminate, or at least greatly reduce, the probability of extreme failures.• Limiting exploitability", "If agents have learned strategies that fail to generalize to particular environment settings, then an adversary could try and exploit an agent by trying to engineer such environment settings leading to agent failure.In this work, we use worst-case analysis to investigate the performance of a state-of-the-art agent in solving a first-person 3D navigation task; a task on which agents have recently achieved average-case human-level performance BID23 . By optimizing mazes to minimize", "the performance of agents, we discover the existence of mazes where agents repeatedly fail to find the goal (which we refer to as a Catastrophic Failure).Our Contributions To summarize,", "the key contributions of this paper are as follows:1. We introduce an effective and intuitive", "approach for finding simple environment settings leading to failure (Section 2).2. We show that state-of-the-art agents carrying", "out navigation tasks suffer from drastic and often surprising failure cases (Sections 3.1 and 3.2).3. We demonstrate that mazes leading to failure", "transfer across agents with different hyperparameters and, notably, even different architectures (Section 3.3).4. We present an initial investigation into how", "the training distribution can be adapted by incorporating adversarial and out-of-distribution examples (Section 4).", "Our results suggest that if a richer training distribution is to yield more robust agents, we may need to use a very large set of environment settings leading to failure.", "This is similar to how adversarial training in supervised learning is performed where more adversarial examples are used than the original training examples.", "We describe below what we see as two significant challenges that need to be overcome before such an approach can be thoroughly evaluated in the RL setting.Expensive generation The cost of generating a single adversarial setting is on the order of 1000's episodes using the method in this work.", "This implies that generating a set of adversarial settings which is similar in size to the set trained on would require orders of magnitude more computational than training itself.", "This could be addressed with faster methods for generating adversarial settings.Expensive training Since agents receive very little reward in adversarial settings, the training signal is incredibly sparse.", "Therefore, it is possible that many more training iterations are necessary for agents to learn to perform well in each adversarial setting.", "A possible solution to this challenge is to design a curriculum over adversity, whereby easier variants of the adversarial settings are injected into the training distribution.", "For example, for the navigation tasks considered here, one could include training settings with challenging mazes where the goal is in any position on the shortest path between the starting location of the agent and the challenging goal.We hope that these challenges can be overcome so that, in the context of RL, the utility of adversarial retraining can be established -an approach which has proved useful in supervised learning tasks.", "However, since significant challenges remain, we suspect that much effort and many pieces of work will be required before a conclusive answer is achieved.", "In this work, we have shown that despite the strong average-case performance often reported of RL agents, worst-case analysis can uncover environment settings which agents have failed to generalize to.", "Notably, we have found that not only do catastrophic failures exist, but also that simple catastrophic failures exist which we would hope agents would have generalized to, and that failures also transfer between agents and architectures.As agents are trained to perform increasingly complicated tasks in more sophisticated environments, for example AirSim BID18 and CARLA BID5 , it is of interest to understand their worst-case performance and modes of generalization.", "Further, in real world applications such as self-driving cars, industrial control, and robotics, searching over environment settings to investigate and address such behaviours is likely to be critical on the path to robust and generalizable agents.To conclude, while this work has focused mostly on evaluation and understanding, it is only a first step towards the true goal of building more robust, general agents.", "Initial results we report indicate that enriching the training distribution with settings leading to failure may need to be done at a large scale if it is to work, which introduces significant challenges.", "While training robust agents is likely an endeavour requiring significant effort, we believe it is important if agents are to carry out critical tasks and on the path to finding more generally intelligent agents." ]

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[ "We find environment settings in which SOTA agents trained on navigation tasks display extreme failures suggesting failures in generalization." ]

[ "In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates.", "To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties.", "In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space.", "We show that this MMD-Bayes posterior is consistent and robust to model misspecification.", "As the posterior obtained in this way might be intractable, we also prove that reasonable variational approximations of this posterior enjoy the same properties.", "We provide details on a stochastic gradient algorithm to compute these variational approximations.", "Numerical simulations indeed suggest that our estimator is more robust to misspecification than the ones based on the likelihood.\n", "Bayesian methods are very popular in statistics and machine learning as they provide a natural way to model uncertainty.", "Some subjective prior distribution π is updated using the negative log-likelihood n via Bayes' rule to give the posterior π n (θ) ∝ π(θ) exp(− n (θ)).", "Nevertheless, the classical Bayesian methodology is not robust to model misspecification.", "There are many cases where the posterior is not consistent (Barron et al., 1999; Grünwald and Van Ommen, 2017) , and there is a need to develop methodologies yielding robust estimates.", "A way to fix this problem is to replace the log-likelihood n by a relevant risk measure.", "This idea is at the core of the PAC-Bayes theory (Catoni, 2007) and Gibbs posteriors (Syring and Martin, 2018) ; its connection with Bayesian principles are discussed in Bissiri et al. (2016) .", "Knoblauch et al (2019) builds a general representation of Bayesian inference in the spirit of Bissiri et al. (2016) and extends the representation to the approximate inference case.", "In particular, the use of a robust divergence has been shown to provide an estimator that is robust to misspecification (Knoblauch et al, 2019) .", "For instance, Hooker and Vidyashankar (2014) investigated the case of Hellinger-based divergences, Ghosal and Basu (2016) , Futami et al (2017), and Nakagawa et al. (2019) used robust β-and γ-divergences, while Catoni (2012) , Baraud and Birgé (2017) and Holland (2019) replaced the logarithm of the log-likelihood by wisely chosen bounded functions.", "Refer to Jewson et al (2018) for a complete survey on robust divergence-based Bayes inference.", "In this paper, we consider the Maximum Mean Discrepancy (MMD) as the alternative loss used in Bayes' formula, leading to a pseudo-posterior that we shall call MMD-Bayes in the following.", "MMD is built upon an embedding of distributions into a reproducing kernel Hilbert space (RKHS) that generalizes the original feature map to probability measures, and allows to apply tools from kernel methods in parametric estimation.", "Our MMD-Bayes posterior is related to the kernel-based posteriors in Fukumizu et al. (2013) , Park et al. (2016) and Ridgway (2017) , even though it is different.", "More recently, Briol et al. (2019) introduced a frequentist minimum distance estimator based on the MMD distance, that is shown to be consistent and robust to small deviations from the model.", "We show that our MMD-Bayes retains the same properties, i.e is consistent at the minimax optimal rate of convergence as the minimum MMD estimator, and is also robust to misspecification, including data contamination and outliers.", "Moreover, we show that these guarantees are still valid when considering a tractable approximation of the MMD-Bayes via variational inference, and we support our theoretical results with experiments showing that our approximation is robust to outliers for various estimation problems.", "All the proofs are deferred to the appendix.", "In this paper, we showed that the MMD-Bayes posterior concentrates at the minimax convergence rate and is robust to model misspecification.", "We also proved that reasonable variational approximations of this posterior retain the same properties, and we proposed a stochastic gradient algorithm to compute such approximations that we supported with numerical simulations.", "An interesting future line of research would be to investigate if the i.i.d assumption can be relaxed and if the MMD-based estimator is also robust to dependency in the data.", "Appendix A. Proof of Theorem 1.", "In order to prove Theorem 1, we first need two preliminary lemmas.", "The first one ensures the convergence of the empirical measureP n to the true distribution P 0 (in MMD distance D k ) at the minimax rate n −1/2 , and which is an expectation variant of Lemma 1 in Briol et al. (2019) that holds with high probability:", "The rate n −1/2 is known to be minimax in this case, see Theorem 1 in Tolstikhin et al. (2017) .", "The second lemma is a simple triangle-like inequality that will be widely used throughout the proofs of the paper:", "Lemma 6 We have for any distributions P , P and Q:", "Proof The chain of inequalities follow directly from the triangle inequality and inequality 2ab ≤ a 2 + b 2 .", "Let us come back to the proof of Theorem 1.", "An important point is that the MMDBayes can also be defined using an argmin over the set M 1 + (Θ) of all probability distributions absolutely continuous with respect to π and the Kullback-Leibler divergence KL(· ·):", "This is an immediate consequence of Donsker and Varadhan's variational inequality, see e.g Catoni (2007) .", "Using the triangle inequality, Lemma 5, Lemma 6 for different settings of P , P and Q, and Jensen's inequality:", "which gives, using Lemma 5 and the triangle inequality again:", "We remind that θ * = arg min θ∈Θ D k (P θ , P 0 ).", "This bound can be formulated in the following way when ρ is chosen to be equal to π restricted to B n :", "Finally, as soon as the prior mass condition C(π, β) is satisfied, we get:", "Appendix B. Proof of Theorem 2.", "In case of well-specification, Formula (3.1) simply becomes according to Jensen's inequality:", "Hence, it is sufficient to show that the inequality above implies the concentration of the MMD-Bayes to the true distribution.", "This is a simple consequence of Markov's inequality.", "Indeed, for any M n → +∞:", "which guarantees the convergence in mean of π β n D k (P θ , P 0 ) > M n · n −1/2 to 0, which leads to the convergence in probability of π β n D k (P θ , P 0 ) > M n ·n −1/2 to 0, i.e. the concentration of MMD-Bayes to P 0 at rate n −1/2 ." ]

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[ "Robust Bayesian Estimation via Maximum Mean Discrepancy" ]

[ "The standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest.", "We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series.", "If parameterized by an encoder-decoder architecture, the parameters of the encoder can be optimized to minimize its variance of this estimator.", "We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.", "This estimator also allows use of latent variable models for tasks where unbiased estimators, rather than marginal likelihood lower bounds, are preferred, such as minimizing reverse KL divergences and estimating score functions.", "Latent variable models are powerful tools for constructing highly expressive data distributions and for understanding how high-dimensional observations might possess a simpler representation.", "Latent variable models are often framed as probabilistic graphical models, allowing these relationships to be expressed in terms of conditional independence.", "Mixture models, probabilistic principal component analysis (Tipping & Bishop, 1999) , hidden Markov models, and latent Dirichlet allocation (Blei et al., 2003) are all examples of powerful latent variable models.", "More recently there has been a surge of interest in probabilistic latent variable models that incorporate flexible nonlinear likelihoods via deep neural networks (Kingma & Welling, 2014) .", "These models can blend the advantages of highly structured probabilistic priors with the empirical successes of deep learning (Johnson et al., 2016; Luo et al., 2018) .", "Moreover, these explicit latent variable models can often yield relatively interpretable representations, in which simple interpolation in the latent space can lead to semantically-meaningful changes in high-dimensional observations (e.g., Higgins et al. (2017) ).", "It can be challenging, however, to fit the parameters of a flexible latent variable model, since computing the marginal probability of the data requires integrating out the latent variables in order to maximize the likelihood with respect to the model parameters.", "Typical approaches to this problem include the celebrated expectation maximization algorithm (Dempster et al., 1977) , Markov chain Monte Carlo, and the Laplace approximation.", "Variational inference generalizes expectation maximization by forming a lower bound on the aforementioned (log) marginal likelihood, using a tractable approximation to the unmanageable posterior over latent variables.", "The maximization of this lower bound-rather than the true log marginal likelihood-is often relatively straightforward when using automatic differentiation and Monte Carlo sampling.", "However, a lower bound may be ill-suited for tasks such as posterior inference and other situations where there exists an entropy maximization objective; for example in entropy-regularized reinforcement learning (Williams & Peng, 1991; Mnih et al., 2016; Norouzi et al., 2016) which requires minimizing the log probability of the samples under the model.", "While there is a long history in Bayesian statistics of estimating the marginal likelihood (e.g., Newton & Raftery (1994) ; Neal (2001)), we often want high-quality estimates of the logarithm of the marginal likelihood, which is better behaved when the data is high dimensional; it is not as susceptible to underflow and it has gradients that are numerically sensible.", "However, the log transformation introduces some challenges: Monte Carlo estimation techniques such as importance sampling do not straightforwardly give unbiased estimates of this quantity.", "Nevertheless, there has been significant work to construct estimators of the log marginal likelihood in which it is possible to explicitly trade off between bias against computational cost (Burda et al., 2016; Bamler et al., 2017; Nowozin, 2018) .", "Unfortunately, while there are asymptotic regimes where the bias of these estimators approaches zero, it is always possible to optimize the parameters to increase this bias to infinity.", "In this work, we construct an unbiased estimator of the log marginal likelihood.", "Although there is no theoretical guarantee that this estimator has finite variance, we find that it can work well in practice.", "We show that this unbiased estimator can train latent variable models to achieve higher test log-likelihood than lower bound estimators at the same expected compute cost.", "More importantly, this unbiased estimator allows us to apply latent variable models in situations where these models were previously problematic to optimize with lower bound estimators.", "Such applications include latent variable modeling for posterior inference and for reinforcement learning in high-dimensional action spaces, where an ideal model is one that is highly expressive yet efficient to sample from.", "We introduced SUMO, a new unbiased estimator of the log probability for latent variable models, and demonstrated tasks for which this estimator performs better than standard lower bounds.", "Specifically, we investigated applications involving entropy maximization where a lower bound performs poorly, but our unbiased estimator can train properly with relatively smaller amount of compute.", "In the future, we plan to investigate new families of gradient-based optimizers which can handle heavy-tailed stochastic gradients.", "It may also be fruitful to investigate the use of convex combination of consistent estimators within the SUMO approach, as any convex combination is unbiased, or to apply variance reduction methods to increase stability of training with SUMO.", "Brian D Ziebart.", "Modeling purposeful adaptive behavior with the principle of maximum causal entropy.", "PhD thesis, figshare, 2010.", "A APPENDIX", "where z 1 , ..", ", z k are sampled independently from q(z; x). And we define the k-th term of the infinite", ". Using the properties of IWAE in equation 6, we have∆ k (x) ≥ 0, and", "which means the series converges absolutely.", "This is a sufficient condition for finite expectation of the Russian roulette estimator (Chen et al. (2019) ; Lemma 3).", "Applying equation 7 to the series:", "Let", ", Hence our estimator is constructed:", "And it can be easily seen from equation 22 and equation 23 that SUMO is an unbiased estimator of the log marginal likelihood:", "A.2", "CONVERGENCE OF ∆ k", "We follow the analysis of JVI (Nowozin, 2018) , which applied the delta method for moments to show the asymptotic results on the bias and variance of IWAE k both at a rate of O( and we define Y k := 1 k k i=1 w i as the sample mean and we have E[", "We note that we rely on ||Y k − µ|| < 1 for this power series to converge.", "This condition was implicitly assumed, but not explicitly noted, in (Nowozin, 2018) .", "This condition will hold for sufficiently large k so long as the moments of w i exist: one could bound the probability ||Y k −µ|| ≥ 1 by Chebyshev's inequality or by the Central Limit Theorem.", "We use the central moments", "Expanding Eq. 28 to order two gives", "Since we use cumulative sum to compute Y k and Y k+1 , we obtain", "We note that", "Without loss of generality, suppose j ≥ k + 1,", "For clarity, let C k = Y k − µ be the zero-mean random variable.", "Nowozin (2018) gives the relations", "Expanding both the sums inside the brackets to order two:", "We will proceed by bounding each of the terms (1), (2), (3), (4).", "First, we decompose C j .", "Let", "We know that B k,j is independent of C k and", "Now we show that (1) is zero:", "We now investigate (2):", "We now show that (3) is zero:", "Finally, we investigate (4):", "Using the relation in equation 36, we have" ]

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[ "We create an unbiased estimator for the log probability of latent variable models, extending such models to a larger scope of applications." ]

[ "This paper makes two contributions towards understanding how the hyperparameters of stochastic gradient descent affect the final training loss and test accuracy of neural networks.", "First, we argue that stochastic gradient descent exhibits two regimes with different behaviours; a noise dominated regime which typically arises for small or moderate batch sizes, and a curvature dominated regime which typically arises when the batch size is large.", "In the noise dominated regime, the optimal learning rate increases as the batch size rises, and the training loss and test accuracy are independent of batch size under a constant epoch budget.", "In the curvature dominated regime, the optimal learning rate is independent of batch size, and the training loss and test accuracy degrade as the batch size rises.", "We support these claims with experiments on a range of architectures including ResNets, LSTMs and autoencoders.", "We always perform a grid search over learning rates at all batch sizes.", "Second, we demonstrate that small or moderately large batch sizes continue to outperform very large batches on the test set, even when both models are trained for the same number of steps and reach similar training losses.", "Furthermore, when training Wide-ResNets on CIFAR-10 with a constant batch size of 64, the optimal learning rate to maximize the test accuracy only decays by a factor of 2 when the epoch budget is increased by a factor of 128, while the optimal learning rate to minimize the training loss decays by a factor of 16.", "These results confirm that the noise in stochastic gradients can introduce beneficial implicit regularization.", "Stochastic gradient descent (SGD) is the most popular optimization algorithm in deep learning, but it remains poorly understood.", "A number of papers propose simple scaling rules that predict how changing the learning rate and batch size will influence the final performance of popular network architectures (Hoffer et al., 2017; Goyal et al., 2017; Jastrzębski et al., 2017) .", "Some of these scaling rules are contradictory, and Shallue et al. (2018) argue that none of these simple prescriptions work reliably across multiple architectures.", "Some papers claim SGD with Momentum significantly outperforms SGD without Momentum (Sutskever et al., 2013) , but others observe little difference between both algorithms in practice (Kidambi et al., 2018; Zhang et al., 2019) .", "We hope to clarify this debate.", "We argue that minibatch stochastic gradient descent exhibits two regimes with different behaviours: a noise dominated regime and a curvature dominated regime (Ma et al., 2017b; McCandlish et al., 2018; Liu & Belkin, 2018) .", "The noise dominated regime typically arises for small or moderate batch sizes, while the curvature dominated regime typically arises when the batch size is large.", "The curvature dominated regime may also arise if the epoch budget is small or the loss is poorly conditioned (McCandlish et al., 2018) .", "Our extensive experiments demonstrate that, 1.", "In the noise dominated regime, the final training loss and test accuracy are independent of batch size under a constant epoch budget, and the optimal learning rate increases as the batch size rises.", "In the curvature dominated regime, the optimal learning rate is independent of batch size, and the training loss and test accuracy degrade with increasing batch size.", "The critical learning rate which separates the two regimes varies between architectures.", "2. If specific assumptions are satisfied, then the optimal learning rate is proportional to batch size in the noise dominated regime.", "These assumptions hold for most tasks.", "However we observe a square root scaling rule when performing language modelling with an LSTM.", "This is not surprising, since consecutive gradients in a language model are not independent.", "3. SGD with Momentum and learning rate warmup do not outperform vanilla SGD in the noise dominated regime, but they can outperform vanilla SGD in the curvature dominated regime.", "There is also an active debate regarding the role of stochastic gradients in promoting generalization.", "It has been suspected for a long time that stochastic gradients sometimes generalize better than full batch gradient descent (Heskes & Kappen, 1993; LeCun et al., 2012) .", "This topic was revived by Keskar et al. (2016) , who showed that the test accuracy often falls if one holds the learning rate constant and increases the batch size, even if one continues training until the training loss ceases to fall.", "Many authors have studied this effect (Jastrzębski et al., 2017; Chaudhari & Soatto, 2018) , but to our knowledge no paper has demonstrated a clear generalization gap between small and large batch training under a constant step budget on a challenging benchmark while simultaneously tuning the learning rate.", "This phenomenon has also been questioned by a number of authors.", "Shallue et al. (2018) argued that one can reduce the generalization gap between small and large batch sizes if one introduces additional regularization (we note that this is consistent with the claim that stochastic gradients can enhance generalization).", "Zhang et al. (2019) suggested that a noisy quadratic model is sufficient to describe the performance of neural networks on both the training set and the test set.", "In this work, we verify that small or moderately large batch sizes substantially outperform very large batches on the test set in some cases, even when compared under a constant step budget.", "However the batch size at which the test accuracy begins to degrade can be larger than previously thought.", "We find that the test accuracy of a 16-4 Wide-ResNet (Zagoruyko & Komodakis, 2016 ) trained on CIFAR-10 for 9725 updates falls from 94.7% at a batch size of 4096 to 92.8% at a batch size of 16384.", "When performing language modelling with an LSTM on the Penn TreeBank dataset for 16560 updates (Zaremba et al., 2014) , the test perplexity rises from 81.7 to 92.2 when the batch size rises from 64 to 256.", "We observe no degradation in the final training loss as the batch size rises in either model.", "These surprising results motivated us to study how the optimal learning rate depends on the epoch budget for a fixed batch size.", "As expected, the optimal test accuracy is maximized for a finite epoch budget, consistent with the well known phenomenon of early stopping (Prechelt, 1998) .", "Meanwhile the training loss falls monotonically as the epoch budget increases, consistent with classical optimization theory.", "More surprisingly, the learning rate that maximizes the final test accuracy decays very slowly as the epoch budget increases, while the learning rate that minimizes the training loss decays rapidly.", "1 These results provide further evidence that the noise in stochastic gradients can enhance generalization in some cases, and they suggest novel hyper-parameter tuning strategies that may reduce the cost of identifying the optimal learning rate and optimal epoch budget.", "We describe the noise dominated and curvature dominated regimes of SGD with and without Momentum in section 2.", "We focus on the analogy between SGD and stochastic differential equations (Gardiner et al., 1985; Welling & Teh, 2011; Mandt et al., 2017; Li et al., 2017) , but our primary contributions are empirical and many of our conclusions can be derived from different assumptions (Ma et al., 2017b; Zhang et al., 2019) .", "In section 3, we provide an empirical study of the relationship between the optimal learning rate and the batch size under a constant epoch budget, which verifies the existence of the two regimes in practice.", "In section 4, we study the relationship between the optimal learning rate and the batch size under a constant step budget, which confirms that stochastic gradients can introduce implicit regularization enhancing the test set accuracy.", "Finally in section 5, we fix the batch size and consider the relationship between the optimal learning rate and the epoch budget.", "The contributions of this work are twofold.", "First, we verified that SGD exhibits two regimes with different behaviours.", "In the noise dominated regime which arises when the batch size is small, the test accuracy is independent of batch size under a constant epoch budget, the optimal learning rate increases as the batch size rises, and acceleration techniques do not outperform vanilla SGD.", "Meanwhile in the curvature dominated regime which arises when the batch size is large, the optimal learning rate is independent of batch size, acceleration techniques outperform vanilla SGD, and the test accuracy degrades with batch size.", "If certain assumptions are satisfied, the optimal learning rate in the noise dominated regime is proportional to batch size.", "These assumptions hold for most tasks.", "Second, we confirm that a gap in test accuracy between small or moderately large batch sizes and very large batches persists even when one trains under a constant step budget.", "When training a 16-4 Wide-ResNet on CIFAR-10 for 9765 updates, the test accuracy drops from 94.7% at a batch size of 4096 to 92.5% at a batch size of 16384.", "We also find that the optimal learning rate which maximizes the test accuracy of Wide-ResNets depends very weakly on the epoch budget while the learning rate which minimizes the training loss falls rapidly as the epoch budget increases.", "These results confirm that stochastic gradients introduce implicit regularization which enhances generalization, and they provide novel insights which could be used to reduce the cost of identifying the optimal learning rate." ]

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[ "Smaller batch sizes can outperform very large batches on the test set under constant step budgets and with properly tuned learning rate schedules." ]

[ "Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games.", "However, CFR's reliance on full game-tree traversals limits its scalability and generality.", "Therefore, the game's state- and action-space is often abstracted (i.e. simplified) for CFR, and the resulting strategy is then mapped back to the full game.", "This requires extensive expert-knowledge, is not practical in many games outside of poker, and often converges to highly exploitable policies.", "A recently proposed method, Deep CFR, applies deep learning directly to CFR, allowing the agent to intrinsically abstract and generalize over the state-space from samples, without requiring expert knowledge.", "In this paper, we introduce Single Deep CFR (SD-CFR), a variant of Deep CFR that has a lower overall approximation error by avoiding the training of an average strategy network.", "We show that SD-CFR is more attractive from a theoretical perspective and empirically outperforms Deep CFR with respect to exploitability and one-on-one play in poker.", "In perfect information games, players usually seek to play an optimal deterministic strategy.", "In contrast, sound policy optimization algorithms for imperfect information games converge towards a Nash equilibrium, a distributional strategy characterized by minimizing the losses against a worst-case opponent.", "The most popular family of algorithms for finding such equilibria is Counterfactual Regret Minimization (CFR) (Zinkevich et al., 2008) .", "Conventional CFR methods iteratively traverse the game-tree to improve the strategy played in each state.", "For instance, CFR + (Tammelin, 2014), a fast variant of CFR, was used to solve two-player Limit Texas Hold'em Poker (Bowling et al., 2015; Tammelin et al., 2015) , a variant of poker frequently played by humans.", "However, the scalability of such tabular CFR methods is limited since they need to visit a given state to update the policy played in it.", "In games too large to fully traverse, practitioners hence often employ domain-specific abstraction schemes (Ganzfried & Sandholm, 2014; Brown et al., 2015) that can be mapped back to the full game after training has finished.", "Unfortunately, these techniques have been shown to lead to highly exploitable policies in the large benchmark game Heads-Up No-Limit Texas Hold'em Poker (HUNL) (Lisy & Bowling, 2016) and typically require extensive expert knowledge.", "To address these two problems, researchers started to augment CFR with neural network function approximation, first resulting in DeepStack (Moravčík et al., 2017) .", "Concurrently with Libratus , DeepStack was one of the first algorithms to defeat professional poker players in HUNL, a game consisting of 10 160 states and thus being far too large to fully traverse.", "While tabular CFR has to visit a state of the game to update its policy in it, a parameterized policy may be able to play an educated strategy in states it has never seen before.", "Purely parameterized (i.e. non-tabular) policies have led to great breakthroughs in AI for perfect information games (Mnih et al., 2015; Schulman et al., 2017; Silver et al., 2017) and were recently also applied to large imperfect information games by Deep CFR to mimic a variant of tabular CFR from samples.", "Deep CFR's strategy relies on a series of two independent neural approximations.", "In this paper, we introduce Single Deep CFR (SD-CFR), a simplified variant of Deep CFR that obtains its final strategy after just one neural approximation by using what Deep CFR calls value networks directly instead of training an additional network to approximate the weighted average strategy.", "This reduces the overall sampling-and approximation error and makes training more efficient.", "We show experimentally that SD-CFR improves upon the convergence of Deep CFR in poker games and outperforms Deep CFR in one-one-one matches.", "We introduced Single Deep CFR (SD-CFR), a new variant of CFR that uses function approximation and partial tree traversals to generalize over the game's state space.", "In contrast to previous work, SD-CFR extracts the average strategy directly from a buffer of value networks from past iterations.", "We show that SD-CFR is more attractive in theory and performs much better in practise than Deep CFR." ]

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[ "Better Deep Reinforcement Learning algorithm to approximate Counterfactual Regret Minimization" ]

[ "While generative models have shown great success in generating high-dimensional samples conditional on low-dimensional descriptors (learning e.g. stroke thickness in MNIST, hair color in CelebA, or speaker identity in Wavenet), their generation out-of-sample poses fundamental problems.", "The conditional variational autoencoder (CVAE) as a simple conditional generative model does not explicitly relate conditions during training and, hence, has no incentive of learning a compact joint distribution across conditions.", "We overcome this limitation by matching their distributions using maximum mean discrepancy (MMD) in the decoder layer that follows the bottleneck.", "This introduces a strong regularization both for reconstructing samples within the same condition and for transforming samples across conditions, resulting in much improved generalization.", "We refer to the architecture as transformer VAE (trVAE).", "Benchmarking trVAE on high-dimensional image and tabular data, we demonstrate higher robustness and higher accuracy than existing approaches.", "In particular, we show qualitatively improved predictions for cellular perturbation response to treatment and disease based on high-dimensional single-cell gene expression data, by tackling previously problematic minority classes and multiple conditions.", "For generic tasks, we improve Pearson correlations of high-dimensional estimated means and variances with their ground truths from 0.89 to 0.97 and 0.75 to 0.87, respectively.\n", "The task of generating high-dimensional samples x conditional on a latent random vector z and a categorical variable s has established solutions (Mirza & Osindero, 2014; Ren et al., 2016) .", "The situation becomes more complicated if the support of z is divided into different domains d with different semantic meanings: say d ∈ {men, women} and one is interested in out-of-sample generation of samples x in a domain and condition (d, s) that is not part of the training data.", "If one predicts how a given black-haired man would look with blonde hair, which we refer to as transforming x men, black-hair → x men, blonde-hair , this becomes an out-of-sample problem if the training data does not have instances of blonde-haired men, but merely of blonde-and black-haired woman and blacked haired men.", "In an application with higher relevance, there is strong interest in how untreated (s = 0) humans (d = 0) respond to drug treatment (s = 1) based on training data from in vitro (d = 1) and mice (d = 2) experiments.", "Hence, the target domain of interest (d = 0) does not offer training data for s = 1, but only for s = 0.", "In the present paper, we suggest to address the challenge of transforming out-of-sample by regularizing the joint distribution across the categorical variable s using maximum mean discrepancy (MMD) in the framework of a conditional variational autoencoder (CVAE) (Sohn et al., 2015) .", "This produces a more compact representation of a distribution that displays high variance in the vanilla CVAE, which incentivizes learning of features across s and results in more accurate out-of-sample prediction.", "MMD has proven successful in a variety of tasks.", "In particular, matching distributions with MMD in variational autoencoders (Kingma & Welling, 2013) has been put forward for unsupervised domain adaptation (Louizos et al., 2015) or for learning statistically independent latent dimensions (Lopez et al., 2018b) .", "In supervised domain adaptation approaches, MMD-based regularization has been shown to be a viable strategy of learning label-predictive features with domain-specific information removed (Long et al., 2015; Tzeng et al., 2014) .", "In further related work, the out-of-sample transformation problem was addressed via hard-coded latent space vector arithmetics (Lotfollahi et al., 2019) and histogram matching (Amodio et al., 2018) .", "The approach of the present paper, however, introduce a data-driven end-to-end approach, which does not involve hard-coded elements and generalizes to more than one condition.", "By arguing that the vanilla CVAE yields representations in the first layer following the bottleneck that vary strongly across categorical conditions, we introduced an MMD regularization that forces these representations to be similar across conditions.", "The resulting model (trVAE) outperforms existing modeling approaches on benchmark and real-world data sets.", "Within the bottleneck layer, CVAEs already display a well-controlled behavior, and regularization does not improve performance.", "Further regularization at later layers might be beneficial but is numerically costly and unstable as representations become high-dimensional.", "However, we have not yet systematically investigated this and leave it for future studies.", "Further future work will concern the application of trVAE on larger and more data, focusing on interaction effects among conditions.", "For this, an important application is the study of drug interaction effects, as previously noted by Amodio et al. (2018) .", "Future conceptual investigations concern establishing connections to causal-inference-inspired models such as CEVAE (Louizos et al., 2017) : faithful modeling of an interventional distribution might possibly be re-framed as successful perturbation effect prediction across domains.", "A HYPER-PARAMETERS" ]

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[ "Generates never seen data during training from a desired condition " ]

[ "We analyze speed of convergence to global optimum for gradient descent training a deep linear neural network by minimizing the L2 loss over whitened data. ", "Convergence at a linear rate is guaranteed when the following hold: (i) dimensions of hidden layers are at least the minimum of the input and output dimensions; (ii) weight matrices at initialization are approximately balanced; and (iii) the initial loss is smaller than the loss of any rank-deficient solution. ", "The assumptions on initialization (conditions (ii) and (iii)) are necessary, in the sense that violating any one of them may lead to convergence failure. ", "Moreover, in the important case of output dimension 1, i.e. scalar regression, they are met, and thus convergence to global optimum holds, with constant probability under a random initialization scheme. ", "Our results significantly extend previous analyses, e.g., of deep linear residual networks (Bartlett et al., 2018).", "Deep learning builds upon the mysterious ability of gradient-based optimization methods to solve related non-convex problems.", "Immense efforts are underway to mathematically analyze this phenomenon.", "The prominent landscape approach focuses on special properties of critical points (i.e. points where the gradient of the objective function vanishes) that will imply convergence to global optimum.", "Several papers (e.g. Ge et al. (2015) ; Lee et al. (2016) ) have shown that (given certain smoothness properties) it suffices for critical points to meet the following two conditions:", "(i) no poor local minima -every local minimum is close in its objective value to a global minimum; and", "(ii) strict saddle property -every critical point that is not a local minimum has at least one negative eigenvalue to its Hessian.", "While condition", "(i) does not always hold (cf.", "Safran and Shamir (2018) ), it has been established for various simple settings (e.g. Soudry and Carmon (2016) ; Kawaguchi (2016) ).", "Condition", "(ii) on the other hand seems less plausible, and is in fact provably false for models with three or more layers (cf. Kawaguchi FORMULA1 ), i.e. for deep networks.", "It has only been established for problems involving shallow (two layer) models, e.g. matrix factorization (Ge et al. (2016) ; BID12 ).", "The landscape approach as currently construed thus suffers from inherent limitations in proving convergence to global minimum for deep networks.A potential path to circumvent this obstacle lies in realizing that landscape properties matter only in the vicinity of trajectories that can be taken by the optimizer, which may be a negligible portion of the overall parameter space.", "Several papers (e.g. Saxe et al. (2014) ; BID1 ) have taken this trajectory-based approach, primarily in the context of linear neural networks -fully-connected neural networks with linear activation.", "Linear networks are trivial from a representational perspective, but not so in terms of optimization -they lead to non-convex training problems with multiple minima and saddle points.", "Through a mix of theory and experiments, BID1 argued that such non-convexities may in fact be beneficial for gradient descent, in the sense that sometimes, adding (redundant) linear layers to a classic linear prediction model can accelerate the optimization.", "This phenomenon challenges the holistic landscape view, by which convex problems are always preferable to non-convex ones.Even in the linear network setting, a rigorous proof of efficient convergence to global minimum has proved elusive.", "One recent progress is the analysis of BID3 for linear residual networks -a particular subclass of linear neural networks in which the input, output and all hidden dimensions are equal, and all layers are initialized to be the identity matrix (cf.", "Hardt and Ma (2016) ).", "Through a trajectory-based analysis of gradient descent minimizing 2 loss over a whitened dataset (see Section 2), BID3 show that convergence to global minimum at a linear rateloss is less than > 0 after O(log 1 ) iterations -takes place if one of the following holds:", "(i) the objective value at initialization is sufficiently close to a global minimum; or", "(ii) a global minimum is attained when the product of all layers is positive definite.The current paper carries out a trajectory-based analysis of gradient descent for general deep linear neural networks, covering the residual setting of BID3 , as well as many more settings that better match practical deep learning.", "Our analysis draws upon the trajectory characterization of BID1 for gradient flow (infinitesimally small learning rate), together with significant new ideas necessitated due to discrete updates.", "Ultimately, we show that when minimizing 2 loss of a deep linear network over a whitened dataset, gradient descent converges to the global minimum, at a linear rate, provided that the following conditions hold:", "(i) the dimensions of hidden layers are greater than or equal to the minimum between those of the input and output;", "(ii) layers are initialized to be approximately balanced (see Definition 1) -this is met under commonplace near-zero, as well as residual (identity) initializations; and", "(iii) the initial loss is smaller than any loss obtainable with rank deficiencies -this condition will hold with probability close to 0.5 if the output dimension is 1 (scalar regression) and standard (random) near-zero initialization is employed.", "Our result applies to networks with arbitrary depth and input/output dimensions, as well as any configuration of hidden layer widths that does not force rank deficiency (i.e. that meets condition", "(i)).", "The assumptions on initialization (conditions", "(ii) and", "(iii)) are necessary, in the sense that violating any one of them may lead to convergence failure.", "Moreover, in the case of scalar regression, they are met with constant probability under a random initialization scheme.", "We are not aware of any similarly general analysis for efficient convergence of gradient descent to global minimum in deep learning.The remainder of the paper is organized as follows.", "In Section 2 we present the problem of gradient descent training a deep linear neural network by minimizing the 2 loss over a whitened dataset.", "Section 3 formally states our assumptions, and presents our convergence analysis.", "Key ideas brought forth by our analysis are demonstrated empirically in Section 4.", "Section 5 gives a review of relevant literature, including a detailed comparison of our results against those of BID3 .", "Finally, Section 6 concludes.", "For deep linear neural networks, we have rigorously proven convergence of gradient descent to global minima, at a linear rate, provided that the initial weight matrices are approximately balanced and the initial end-to-end matrix has positive deficiency margin.", "The result applies to networks with arbitrary depth, and any configuration of input/output/hidden dimensions that supports full rank, i.e. in which no hidden layer has dimension smaller than both the input and output.Our assumptions on initialization -approximate balancedness and deficiency margin -are both necessary, in the sense that violating any one of them may lead to convergence failure, as we demonstrated explicitly.", "Moreover, for networks with output dimension 1 (scalar regression), we have shown that a balanced initialization, i.e. a random choice of the end-to-end matrix followed by a balanced partition across all layers, leads assumptions to be met, and thus convergence to take place, with constant probability.", "Rigorously proving efficient convergence with significant probability under customary layer-wise independent initialization remains an open problem.", "The recent work of Shamir (2018) suggests that this may not be possible, as at least in some settings, the number of iterations required for convergence is exponential in depth with overwhelming probability.", "This negative result, a theoretical manifestation of the \"vanishing gradient problem\", is circumvented by balanced initialization.", "Through simple experiments we have shown that the latter can lead to favorable convergence in deep learning practice, as it does in theory.", "Further investigation of balanced initialization, including development of variants for convolutional layers, is regarded as a promising direction for future research.The analysis in this paper uncovers special properties of the optimization landscape in the vicinity of gradient descent trajectories.", "We expect similar ideas to prove useful in further study of gradient descent on non-convex objectives, including training losses of deep non-linear neural networks.A 2 LOSS OVER WHITENED DATA Recall the 2 loss of a linear predictor W ∈ R dy×dx as defined in Section 2: DISPLAYFORM0 By definition, when data is whitened, Λ xx is equal to identity, yielding: For approximate balancedness we have the following claim, which shows that it becomes more and more likely the smaller the standard deviation of initialization is: DISPLAYFORM1 Claim 2.", "Assume all entries in the matrices W j ∈ R dj ×dj−1 , j = 1, . . . , N , are drawn independently at random from a Gaussian distribution with mean zero and standard deviation s > 0.", "Then, for any δ > 0, the probability of W 1 , . . . , W N being δ-balanced is at least max{0, 1 − 10δ DISPLAYFORM2 In terms of deficiency margin, the claim below treats the case of a single output model (scalar regression), and shows that if the standard deviation of initialization is sufficiently small, with probability close to 0.5, a deficiency margin will be met.", "However, for this deficiency margin to meet a chosen threshold c, the standard deviation need be sufficiently large.Claim 3.", "There is a constant C 1 > 0 such that the following holds.", "Consider the case where DISPLAYFORM3 13 and suppose all entries in the matrices W j ∈ R dj ×dj−1 , j = 1, . . . , N , are drawn independently at random from a Gaussian distribution with mean zero, whose standard deviation s > 0 is small with respect to the target, i.e. DISPLAYFORM4 , the probability of the end-to-end matrix W 1:N having deficiency margin c with respect to Φ is at least 0.49 if: DISPLAYFORM5 Proof.", "See Appendix D.5.", "13 The requirement d0 ≥ 20 is purely technical, designed to simplify expressions in the claim.", "14 The probability 0.49 can be increased to any p < 1/2 by increasing the constant 10 5 in the upper bounds for s and c.15", "It is not difficult to see that the latter threshold is never greater than the upper bound for s, thus sought-after standard deviations always exist." ]

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[ "We analyze gradient descent for deep linear neural networks, providing a guarantee of convergence to global optimum at a linear rate." ]

[ "One of the fundamental problems in supervised classification and in machine learning in general, is the modelling of non-parametric invariances that exist in data.", "Most prior art has focused on enforcing priors in the form of invariances to parametric nuisance transformations that are expected to be present in data.", "However, learning non-parametric invariances directly from data remains an important open problem.", "In this paper, we introduce a new architectural layer for convolutional networks which is capable of learning general invariances from data itself.", "This layer can learn invariance to non-parametric transformations and interestingly, motivates and incorporates permanent random connectomes there by being called Permanent Random Connectome Non-Parametric Transformation Networks (PRC-NPTN).", "PRC-NPTN networks are initialized with random connections (not just weights) which are a small subset of the connections in a fully connected convolution layer.", "Importantly, these connections in PRC-NPTNs once initialized remain permanent throughout training and testing. ", "Random connectomes makes these architectures loosely more biologically plausible than many other mainstream network architectures which require highly ordered structures.", "We motivate randomly initialized connections as a simple method to learn invariance from data itself while invoking invariance towards multiple nuisance transformations simultaneously.", "We find that these randomly initialized permanent connections have positive effects on generalization, outperform much larger ConvNet baselines and the recently proposed Non-Parametric Transformation Network (NPTN) on benchmarks that enforce learning invariances from the data itself.", "invariances directly from the data, with the only prior being the structure that allows them to do so.", "with an enhanced ability to learn non-parametric invariances through permanent random connectivity.", "we do not explore these biological connections in more detail, it is still an interesting observation." ]

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[ "A layer modelling local random connectomes in the cortex within deep networks capable of learning general non-parametric invariances from the data itself." ]

[ "We propose a fully-convolutional conditional generative model, the latent transformation neural network (LTNN), capable of view synthesis using a light-weight neural network suited for real-time applications.", "In contrast to existing conditional\n", "generative models which incorporate conditioning information via concatenation, we introduce a dedicated network component, the conditional transformation unit (CTU), designed to learn the latent space transformations corresponding to specified target views.", "In addition, a consistency loss term is defined to guide the network toward learning the desired latent space mappings, a task-divided decoder is constructed to refine the quality of generated views, and an adaptive discriminator is introduced to improve the adversarial training process.", "The generality of the proposed methodology is demonstrated on a collection of three diverse tasks: multi-view reconstruction on real hand depth images, view synthesis of real and synthetic faces, and the rotation of rigid objects.", "The proposed model is shown to exceed state-of-the-art results in each category while simultaneously achieving a reduction in the computational demand required for inference by 30% on average.", "Generative models have been shown to provide effective frameworks for representing complex, structured datasets and generating realistic samples from underlying data distributions BID8 .", "This concept has also been extended to form conditional models capable of sampling from conditional distributions in order to allow certain properties of the generated data to be controlled or selected BID20 .", "These generative models are designed to sample from broad classes of the data distribution, however, and are not suitable for inference tasks which require identity preservation of the input data.", "Models have also been proposed which incorporate encoding components to overcome this by learning to map input data to an associated latent space representation within a generative framework BID18 .", "The resulting inference models allow for the defining structure/features of inputs to be preserved while specified target properties are adjusted through conditioning BID34 .", "Conventional conditional models have largely relied on rather simple methods, such as concatenation, for implementing this conditioning process; however, BID21 have shown that utilizing the conditioning information in a less trivial, more methodical manner has the potential to significantly improve the performance of conditional generative models.", "In this work, we provide a general framework for effectively performing inference with conditional generative models by strategically controlling the interaction between conditioning information and latent representations within a generative inference model.In this framework, a conditional transformation unit (CTU), Φ, is introduced to provide a means for navigating the underlying manifold structure of the latent space.", "The CTU is realized in the form of a collection of convolutional layers which are designed to approximate the latent space operators defined by mapping encoded inputs to the encoded representations of specified targets (see FIG7 ).", "This is enforced by introducing a consistency loss term to guide the CTU mappings during training.", "In addition, a conditional discriminator unit (CDU), Ψ, also realized as a collection of convolutional layers, is included in the network's discriminator.", "This CDU is designed to improve the network's ability to identify and eliminate transformation specific artifacts in the network's predictions.The network has also been equipped with RGB balance parameters consisting of three values {θ R , θ G , θ B } designed to give the network the ability to quickly adjust the global color balance of FIG7 : The conditional transformation unit Φ constructs a collection of mappings {Φ k } in the latent space which produce high-level attribute changes to the decoded outputs.", "Conditioning information is used to select the appropriate convolutional weights ω k for the specified transformation; the encoding l x of the original input image x is transformed to l y k = Φ k (l x ) = conv(l x , ω k ) and provides an approximation to the encoding l y k of the attribute-modified target image y k .the", "images it produces to better align with that of the true data distribution. In", "this way, the network is easily able to remove unnatural hues and focus on estimating local pixel values by adjusting the three RGB parameters rather than correcting each pixel individually. In", "addition, we introduce a novel estimation strategy for efficiently learning shape and color properties simultaneously; a task-divided decoder is designed to produce a coarse pixel-value map along with a refinement map in order to split the network's overall task into distinct, dedicated network components.", "In this work, we have introduced an effective, general framework for incorporating conditioning information into inference-based generative models.", "We have proposed a modular approach to incorporating conditioning information using CTUs and a consistency loss term, defined an efficient task-divided decoder setup for deconstructing the data generation process into managable subtasks, and shown that a context-aware discriminator can be used to improve the performance of the adversarial training process.", "The performance of this framework has been assessed on a diverse range of tasks and shown to outperform state-of-the-art methods.", "At the bottle-neck between the encoder and decoder, a conditional transformation unit (CTU) is applied to map the 2×2 latent features directly to the transformed 2×2 latent features on the right.", "This CTU is implemented as a convolutional layer with filter weights selected based on the conditioning information provided to the network.", "The noise vector z ∈ R 4 from normal distribution N (0, 1) is concatenated to the transformed 2×2 features and passed to the decoder for the face attributes task only.", "The 32×32 features near the end of the decoder component are processed by two independent convolution transpose layers: one corresponding to the value estimation map and the other corresponding to the refinement map.", "The channels of the value estimation map are rescaled by the RGB balance parameters, and the Hadamard product is taken with the refinement map to produce the final network output.", "For the ALOI data experiment, we have followed the IterGAN Galama & Mensink (2018) encoder and decoder structure, and for the stereo face dataset BID5 experiment, we have added an additional Block v1 layer in the encoder and decoder to utilize the full 128×128×3 resolution images.The encoder incorporates two main block layers, as defined in Figure A. 2, which are designed to provide efficient feature extraction; these blocks follow a similar design to that proposed by , but include dense connections between blocks, as introduced by BID10 .", "We normalize the output of each network layer using the batch normalization method as described in BID12 .", "For the decoder, we have opted for a minimalist design, inspired by the work of BID24 .", "Standard convolutional layers with 3 × 3 filters and same padding are used through the penultimate decoding layer, and transpose convolutional layers with 5 × 5 filters and same padding are used to produce the value-estimation and refinement maps.", "All parameters have been initialized using the variance scaling initialization method described in BID9 .Our", "method has been implemented and developed using the TensorFlow framework. The", "models have been trained using stochastic gradient descent (SGD) and the ADAM optimizer BID15 with initial parameters: learning rate = 0.005, β 1 = 0.9, and β 2 = 0.999 (as defined in the TensorFlow API r1.6 documentation for tf.train.AdamOptimizer). , along", "with loss function hyperparameters: λ = 0.8, ρ = 0.2, γ = 0.0002, and κ = 0.00005 (as introduced in FORMULA8 ). The discriminator", "is updated once every two encoder/decoder updates, and one-sided label smoothing BID28 has been used to improve stability of the discriminator training procedure. All datasets have", "also been normalized to the interval [0, 1] for training. Once the total number", "of output channels, N out , is specified, the remaining N out − N in output channels are allocated to the non-identity filters (where N in denotes the number of input channels). For the Block v1 layer", "at the start of the proposed LTNN model, for example, the input is a single grayscale image with N in = 1 channel and the specified number of output channels is N out = 32. One of the 32 channels", "is accounted for by the identity component, and the remaining 31 channels are the three non-identity filters. When the remaining channel", "count is not divisible by 3 we allocate the remainder of the output channels to the single 3 × 3 convolutional layer. Swish activation functions", "are used for each filter, however the filters with multiple convolutional layers (i.e. the right two filters in the Block v1 diagram) do not use activation functions for the intermediate 3 × 3 convolutional layers (i.e. those after the 1 × 1 layers and before the final 3 × 3 layers)." ]

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[ "We introduce an effective, general framework for incorporating conditioning information into inference-based generative models." ]

[ "We describe three approaches to enabling an extremely computationally limited embedded scheduler to consider a small number of alternative activities based on resource availability.", "We consider the case where the scheduler is so computationally limited that it cannot backtrack search.", "The first two approaches precompile resource checks (called guards) that only enable selection of a preferred alternative activity if sufficient resources are estimated to be available to schedule the remaining activities.", "The final approach mimics backtracking by invoking the scheduler multiple times with the alternative activities.", "We present an evaluation of these techniques on mission scenarios (called sol types) from NASA's next planetary rover where these techniques are being evaluated for inclusion in an onboard scheduler.", "Embedded schedulers must often operate with very limited computational resources.", "Due to such limitations, it is not always feasible to develop a scheduler with a backtracking search algorithm.", "This makes it challenging to perform even simple schedule optimization when doing so may use resources needed for yet unscheduled activities.In this paper, we present three algorithms to enable such a scheduler to consider a very limited type of preferred activity while still scheduling all required (hereafter called mandatory) activities.", "Preferred activities are grouped into switch groups, sets of activities, where each activity in the set is called a switch case, and exactly one of the activities in the set must be scheduled.", "They differ only by how much time, energy, and data volume they consume and the goal is for the scheduler to schedule the most desirable activity (coincidentally the most resource consuming activity) without sacrificing any other mandatory activity.The target scheduler is a non-backtracking scheduler to be onboard the NASA Mars 2020 planetary rover BID9 that schedules in priority first order and never removes or moves an activity after it is placed during a single run of the scheduler.", "Because the scheduler does not backtrack, it is challenging to ensure that scheduling a consumptive switch case will not use too many resources Copyright c 2019, California Institute of Technology.", "Government Sponsorship Acknowledged.", "and therefore prevent a later (in terms of scheduling order, not necessarily time order) mandatory activity from being scheduled.The onboard scheduler is designed to make the rover more robust to run-time variations by rescheduling multiple times during execution BID4 .", "If an activity ends earlier or later than expected, then rescheduling will allow the scheduler to consider changes in resource consumption and reschedule accordingly.", "Our algorithms to schedule switch groups must also be robust to varying execution durations and rescheduling.We have developed several approaches to handle scheduling switch groups.", "The first two, called guards, involve reserving enough sensitive resources (time, energy, data volume) to ensure all later required activities can be scheduled.", "The third approach emulates backtracking under certain conditions by reinvoking the scheduler multiple times.", "These three techniques are currently being considered for implementation in the Mars 2020 onboard scheduler.", "There are many areas for future work.", "Currently the time guard heavily limits the placement of activities.", "As we saw, using preferred time to address this issue resulted in dropping mandatory activities.", "Ideally analysis of start time windows and dependencies could determine where an activity could be placed without blocking other mandatory activities.Additionally, in computing the guard for Minimum SOC using the Sol Wide Guard, instead of increasing the guard value by a predetermined fixed amount which could result in over-conservatism, binary search via Monte Carlo analysis could more precisely determine the guard amount.Currently we consider only a single switch group per plan, the Mars 2020 rover mission desires support for multiple switch groups in the input instead.", "Additional work is needed to extend to multiple switch groups.Further exploration of all of the MSI variants is needed.", "Study of starting MSI invocations if an activity ends early by at least some amount and the switch case is the next activity is planned.", "We would like to analyze the effects of evenly spacing the MSI invocations in order to avoid relying on throttling and we would like to try disabling rescheduling after MSI is complete until the switch case has been committed and understand if this results in major drawbacks.We have studied the effects of time and energy on switch cases, and we would like to extend these approaches and analysis to data volume.", "We have presented several algorithms to allow a very computationally limited, non-backtracking scheduler to consider a schedule containing required, or mandatory, activities and sets of activities called switch groups where each activity in such sets differs only by its resource consumption.", "These algorithms strive to schedule the most preferred, which happens to be the most consumptive, activity possible in the set without dropping any other mandatory activity.", "First, we discuss two guard methods which use different approaches to reserve enough resources to schedule remaining mandatory activities.", "We then discuss a third algorithm, MSI, which emulates backtracking by reinvoking the scheduler at most once per level of switch case.", "We present empirical analysis using input sets of activities derived from data on expected planetary rover operations to show the effects of using each of these methods.", "These implementations and empirical evaluation are currently being evaluated in the context of the Mars 2020 onboard scheduler." ]

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[ "This paper describes three techniques to allow a non-backtracking, computationally limited scheduler to consider a small number of alternative activities based on resource availability." ]

[ "Inspired by the modularity and the life-cycle of biological neurons,we introduce Continual Learning via Neural Pruning (CLNP), a new method aimed at lifelong learning in fixed capacity models based on the pruning of neurons of low activity.", "In this method, an L1 regulator is used to promote the presence of neurons of zero or low activity whose connections to previously active neurons is permanently severed at the end of training.", "Subsequent tasks are trained using these pruned neurons after reinitialization and cause zero deterioration to the performance of previous tasks.", "We show empirically that this biologically inspired method leads to state of the art results beating or matching current methods of higher computational complexity.", "Continual learning, the ability of models to learn to solve new tasks beyond what has previously been trained, has garnered much attention from the machine learning community in recent years.", "The main obstacle for effective continual learning is the problem of catastrophic forgetting: machines trained on new problems forget about the tasks that they were previously trained on.", "There are multiple approaches to this problem, from employing networks with many submodules [1, 8, 12 ] to methods which penalize changing the weights of the network that are deemed important for previous tasks [3, 5, 16] .", "These approaches either require specialized training schemes or still suffer catastrophic forgetting, albeit at a smaller rate.", "Furthermore, from a biological perspective, the current fixed capacity approaches generally require the computation of a posterior in weight space which is non-local and hence biologically implausible.", "Motivated by the life-cycle of biological neurons [6] , we introduce a simple continual learning algorithm for fixed capacity networks which can be trained using standard gradient descent methods and suffers zero deterioration on previously learned problems during the training of new tasks.", "In this method, the only modifications to standard machine learning algorithms are simple and biologically plausible: i.e. a sparsifying L 1 regulator and activation threshold based neural pruning.", "We demonstrate empirically that these modifications to standard practice lead to state of the art performance on standard catastrophic forgetting benchmarks.", "In this work we have introduced an intuitive lifelong learning method which leverages the over-parametrization of neural networks to train new tasks in the inactive neurons/filters of the network without suffering any catastrophic forgetting in the previously trained tasks.", "We implemented a controlled way of graceful forgetting by sacrificing some accuracy at the end of the training of each task in order to regain network capacity for training new tasks.", "We showed empirically that this method leads to results which exceed or match the current state-of-the-art while being less computationally intensive.", "Because of this, we can employ larger models than otherwise possible, given fixed computational resources.", "Our methodology comes with simple diagnostics based on the number of free neurons left for the training of new tasks.", "Model capacity usage graphs are informative regarding the transferability and sufficiency of the features of different layers.", "Using such graphs, we have verified the notion that the features learned in earlier layers are more transferable.", "We can leverage these diagnostic tools to pinpoint any layers that run out of capacity prematurely, and resolve these bottlenecks in the network by increasing the number of neurons in these layers when moving on to the next task.", "In this way, our method can expand to accommodate more tasks and compensate for sub-optimal network width choices." ]

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[ "We use simple and biologically motivated modifications of standard learning techniques to achieve state of the art performance on catastrophic forgetting benchmarks." ]

[ "There has been an increasing use of neural networks for music information retrieval tasks.", "In this paper, we empirically investigate different ways of improving the performance of convolutional neural networks (CNNs) on spectral audio features.", "More specifically, we explore three aspects of CNN design: depth of the network, the use of residual blocks along with the use of grouped convolution, and global aggregation over time.", "The application context is singer classification and singing performance embedding and we believe the conclusions extend to other types of music analysis using convolutional neural networks.", "The results show that global time aggregation helps to improve the performance of CNNs the most.", "Another contribution of this paper is the release of a singing recording dataset that can be used for training and evaluation.", "Deploying deep neural networks to solve music information retrieval problems has benefited from advancements in other areas such as computer vision and natural language processing.", "In this paper, experiments are designed to investigate whether a few of the recent signature advancements in the deep learning community can improve the learning capability of deep neural networks when applied on time-frequency representations.", "Because time-frequency representations are frequently treated as 2-D images similarly to image input for computer vision models, convolution layers are popular choices as the first processing layers for time-frequency representations in audio and music analysis applications.", "One of the recent convolutional layer variants is the residual neural network with a bottleneck design , ResNet.", "Another variant built upon ResNet is to use grouped convolution inside the bottleneck as a generalization of the Inception Net BID12 BID22 , ResNeXt.", "These two variants have enabled more deepening of the convolutional layers of deep neural networks.", "Most existing music information retrieval research using convolutional neural networks (CNNs), utilizes vanilla convolutional layers with no more than 5 layers.", "In this paper, the two convolution layer variants mentioned and a deeper architecture with more than 5 convolution layers is proposed and shown to be effective on audio time-frequency representations.Conceptually, convolution layers take care of learning local patterns (neighboring pixels in images or time frame/frequency bins in time-frequency representations) presented in the input matrices.", "After learning feature maps from the convolution layers, one of the reoccurring issues, when the input is a time-frequency representation, is how to model or capture temporal relations.", "Recurrent neural networks has been used to solve this problem BID6 BID1 BID3 BID4 .", "Recent developments from natural language processing in attention mechanisms BID0 BID3 BID15 provide a different approach to model temporal dependencies and relations.", "In this paper, the attention mechanism is viewed as a special case of a global aggregation operation along the timeaxis that has learnable parameters.", "Typical aggregation operations such as average or max have no learnable parameters.", "The effects of global aggregation along the time axis using either average, max or the attention mechanism is investigated experimentally.Two specific applications are investigated in this paper:", "1) singer classification of monophonic recordings, and", "2) singing performance embedding.", "The goal of singer classification is to predict the singer's identity given an audio recording as input.", "A finite set of possible singers is considered so this is a classification task.", "In singer performance embedding the goal is to create an embedding space in which singers with similar styles can be projected to be closer to each other compared to singers with different styles.", "Ideally, it should be possible to identify \"singing style\" or \"singing characteristics\" by examining (and listening to) the clusters formed from the projections of audio recordings onto the embedding space.", "Many tasks in music and audio analysis can be formulated in a similar way, in which similarity plays an essential role, therefore we believe that the conclusions of this paper generalize to other audio and music tasks.", "In this paper, empirical investigations into how recent developments in the deep learning community could help solving singer identification and embedding problems were conducted.", "From the experiment results, the obvious take away is that global aggregation over time improves performance by a considerable margin in general.", "The performances among the three aggregation strategies; max, average and feed-forward attention, are very close.", "The advantage of using feedforward attention from observing the experiment results is that it accelerates the learning process compared to other non-learnable global aggregations.", "One way to explain such observation is that the feed-forward attention layer learns a \"frequency template\" for each convolutional channel fed into it.", "These \"frequency templates\" are encoded in w and enable each convolutional channel fed into it to focus on different parts along the frequency axis (Since w ∈ R D with D = num of channels × num of frequency bins).", "In this paper we also have shown that training a deep neural networks having more than 15 convolutional layers on time-frequency input is definitely feasible with the help of global time aggregation.", "To the authors' knowledge, there is no previous music information retrieval research utilizing neural networks having more than 10 convolutional layers.", "A dataset consisting of over 20000 single singing voice recordings is also released and described in this paper.", "The released dataset, DAMP-balanced, could be partitioned in a way that for singer classification, the performed songs for each singer are the same.For future works, replacing max-pooling with striding in convolutional layers which recent works in CNN suggest will be experimented.", "To improve global-aggregation, taking temporal order into consideration during the global-aggregation operation as suggested in BID21 will also be experimented.", "Also the proposed neural network configurations will be experimented in other music information retrieval tasks such as music structure segmentation." ]

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[ "Using deep learning techniques on singing voice related tasks." ]

[ "The Softmax function is used in the final layer of nearly all existing sequence-to-sequence models for language generation.", "However, it is usually the slowest layer to compute which limits the vocabulary size to a subset of most frequent types; and it has a large memory footprint.", "We propose a general technique for replacing the softmax layer with a continuous embedding layer.", "Our primary innovations are a novel probabilistic loss, and a training and inference procedure in which we generate a probability distribution over pre-trained word embeddings, instead of a multinomial distribution over the vocabulary obtained via softmax.", "We evaluate this new class of sequence-to-sequence models with continuous outputs on the task of neural machine translation.", "We show that our models obtain upto 2.5x speed-up in training time while performing on par with the state-of-the-art models in terms of translation quality.", "These models are capable of handling very large vocabularies without compromising on translation quality.", "They also produce more meaningful errors than in the softmax-based models, as these errors typically lie in a subspace of the vector space of the reference translations.", "Due to the power law distribution of word frequencies, rare words are extremely common in any language BID45 ).", "Yet, the majority of language generation tasks-including machine translation BID39 BID1 BID24 , summarization BID36 BID37 BID30 , dialogue generation BID40 , question answering BID44 , speech recognition BID13 Xiong et al., 2017) , and others-generate words by sampling from a multinomial distribution over a closed output vocabulary.", "This is done by computing scores for each candidate word and normalizing them to probabilities using a softmax layer.Since softmax is computationally expensive, current systems limit their output vocabulary to a few tens of thousands of most frequent words, sacrificing linguistic diversity by replacing the long tail of rare words by the unknown word token, unk .", "Unsurprisingly, at test time this leads to an inferior performance when generating rare or out-of-vocabulary words.", "Despite the fixed output vocabulary, softmax is computationally the slowest layer.", "Moreover, its computation follows a large matrix multiplication to compute scores over the candidate words; this makes softmax expensive in terms of memory requirements and the number of parameters to learn BID26 BID27 BID8 .", "Several alternatives have been proposed for alleviating these problems, including sampling-based approximations of the softmax function BID2 BID26 , approaches proposing a hierarchical structure of the softmax layer BID27 BID7 , and changing the vocabulary to frequent subword units, thereby reducing the vocabulary size BID38 .We", "propose a novel technique to generate low-dimensional continuous word representations, or word embeddings BID25 BID31 BID4 instead of a probability distribution over the vocabulary at each output step. We", "train sequence-to-sequence models with continuous outputs by minimizing the distance between the output vector and the pretrained word embedding of the reference word. At", "test time, the model generates a vector and then searches for its nearest neighbor in the target embedding space to generate the corresponding word. This", "general architecture can in principle be used for any language generation (or any recurrent regression) task. In this", "work, we experiment with neural machine translation, implemented using recurrent sequence-to-sequence models BID39 with attention BID1 BID24 .To the best", "of our knowledge, this is the first work that uses word embeddings-rather than the softmax layer-as outputs in language generation tasks. While this", "idea is simple and intuitive, in practice, it does not yield competitive performance with standard regression losses like 2 . This is because", "2 loss implicitly assumes a Gaussian distribution of the output space which is likely false for embeddings. In order to correctly", "predict the outputs corresponding to new inputs, we must model the correct probability distribution of the target vector conditioned on the input BID3 . A major contribution", "of this work is a new loss function based on defining such a probability distribution over the word embedding space and minimizing its negative log likelihood ( §3).We evaluate our proposed", "model with the new loss function on the task of machine translation, including on datasets with huge vocabulary sizes, in two language pairs, and in two data domains ( §4). In §5 we show that our models", "can be trained up to 2.5x faster than softmax-based models while performing on par with state-of-the-art systems in terms of generation quality. Error analysis ( §6) reveals", "that the models with continuous outputs are better at correctly generating rare words and make errors that are close to the reference texts in the embedding space and are often semantically-related to the reference translation.", "This work makes several contributions.", "We introduce a novel framework of sequence to sequence learning for language generation using word embeddings as outputs.", "We propose new probabilistic loss functions based on vMF distribution for learning in this framework.", "We then show that the proposed model trained on the task of machine translation leads to reduction in trainable parameters, to faster convergence, and a dramatic speed-up, up to 2.5x in training time over standard benchmarks.", "TAB5 visualizes a comparison between different types of softmax approximations and our proposed method.State-of-the-art results in softmax-based models are highly optimized after a few years on research in neural machine translation.", "The results that we report are comparable or slightly lower than the strongest baselines, but these setups are only an initial investigation of translation with the continuous output layer.", "There are numerous possible directions to explore and improve the proposed setups.", "What are additional loss functions?", "How to setup beam search?", "Should we use scheduled sampling?", "What types of embeddings to use?", "How to translate with the embedding output into morphologically-rich languages?", "Can low-resource neural machine translation benefit from translation with continuous outputs if large monolingual corpora are available to pre-train strong target-side embeddings?", "We will explore these questions in future work.Furthermore, the proposed architecture and the probabilistic loss (NLLvMF) have the potential to benefit other applications which have sequences as outputs, e.g. speech recognition.", "NLLvMF could be used as an objective function for problems which currently use cosine or 2 distance, such as learning multilingual word embeddings.", "Since the outputs of our models are continuous (rather than class-based discrete symbols), these models can potentially simplify training of generative adversarial networks for language generation.", "DISPLAYFORM0 where C m (κ) is given as: DISPLAYFORM1 The normalization constant is not directly differentiable because Bessel function cannot be written in a closed form.", "The gradient of the first component (log (C m ê )) of the loss is given as DISPLAYFORM2 .", "In Table 9 : Translation quality experiments using beam search with BPE based baseline models with a beam size of 5With our proposed models, in principle, it is possible to generate candidates for beam search by using K-Nearest Neighbors.", "But how to rank the partially generated sequences is not trivial (one could use the loss values themselves to rank, but initial experiments with this setting did not result in significant gains).", "In this work, we focus on enabling training with continuous outputs efficiently and accurately giving us huge gains in training time.", "The question of decoding with beam search requires substantial investigation and we leave it for future work." ]

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[ "Language generation using seq2seq models which produce word embeddings instead of a softmax based distribution over the vocabulary at each step enabling much faster training while maintaining generation quality" ]

[ "We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory.", "Correlations between the weights within the same layer can be described by symmetries in that layer, and networks generalize better if such symmetries are broken to reduce the redundancies of the weights.", "Using a two parameter field theory, we find that the network can break such symmetries itself towards the end of training in a process commonly known in physics as spontaneous symmetry breaking.", "This corresponds to a network generalizing itself without any user input layers to break the symmetry, but by communication with adjacent layers.", "In the layer decoupling limit applicable to residual networks (He et al., 2015), we show that the remnant symmetries that survive the non-linear layers are spontaneously broken based on empirical results.", "The Lagrangian for the non-linear and weight layers together has striking similarities with the one in quantum field theory of a scalar.", "Using results from quantum field theory we show that our framework is able to explain many experimentally observed phenomena, such as training on random labels with zero error (Zhang et al., 2017), the information bottleneck and the phase transition out of it (Shwartz-Ziv & Tishby, 2017), shattered gradients (Balduzzi et al., 2017), and many more.", "Deep neural networks have been used in image recognition tasks with great success.", "The first of its kind, AlexNet BID8 , led to many other neural architectures have been proposed to achieve start-of-the-art results in image processing at the time.", "Some of the notable architectures include, VGG BID12 , Inception BID14 and Residual networks (ResNet) BID3 .Understanding", "the inner workings of deep neural networks remains a difficult task. It has been discovered", "that the training process ceases when it goes through an information bottleneck (ShwartzZiv & Tishby, 2017 ) until learning rate is decreased to a suitable amount then the network under goes a phase transition. Deep networks appear to", "be able to regularize themselves and able to train on randomly labeled data BID18 with zero training error. The gradients in deep neural", "networks behaves as white noise over the layers BID1 . And many other unexplained phenomena", ".A recent work BID0 showed that the ensemble behavior and binomial path lengths BID15 of ResNets can be explained by just a Taylor series expansion to first order in the decoupling limit. They found that the series approximation", "generates a symmetry breaking layer that reduces the redundancy of weights, leading to a better generalization. Because the ResNet does not contain such", "symmetry breaking layers in the architecture. They suggest that ResNets are able to break", "the symmetry by the communication between the layers. Another recent work also employed the Taylor", "expansion to investigate ResNets BID6 .In statistical terms, a quantum theory describes", "errors from the mean of random variables. We wish to study how error propagate through each", "layer in the network, layer by layer. In the limit of a continuous sample space, the quantum", "theory becomes a quantum field theory. The effects of sampling error and labelling error can", "then be investigated. It is well known in physics that a scalar field can drive", "a phase transition. Using a scalar field theory we show that a phase transition", "must exist towards the end of training based on empirical results. It is also responsible for the remarkable performance of deep", "networks compared to other classical models. In Appendix D, We explain that quantum field theory is likely", "one of the simplest model that can describe a deep network layer by layer in the decoupling limit.Much of the literature on neural network design focuses on different neural architecture that breaks symmetry explicitly, rather than spontaneously. For instance, non-linear layers explicitly breaks the symmetry", "of affine transformations. There is little discussion on spontaneous symmetry breaking. In", "neural networks, the Goldstone theorem in field theory states", "that for every continuous symmetry that is spontaneously broken, there exists a weight with zero Hessian eigenvalue at the loss minimum. No such weights would appear if the symmetries are explicitly broken", ". It turns out that many seemingly different experimental results can", "be explained by the presence of these zero eigenvalue weights. In this work, we exploit the layer decoupling limit applicable to ResNets", "to approximate the loss functions with a power series in symmetry invariant quantities and illustrate that spontaneous symmetry breaking of affine symmetries is the sufficient and necessary condition for a deep network to attain its unprecedented power.The organization of this paper is as follows. The background on deep neural networks and field theory is given in Section", "2. Section 3 shows that remnant symmetries can exist in a neural network and that", "the weights can be approximated by a scalar field. Experimental results that confirm our theory is given in Section 4. We summarize", "more evidence from other experiments in Appendix A. A review of field", "theory is given in Appendix B. An explicit example of spontaneous symmetry breaking is shown in Appendix C." ]

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[ "Closed form results for deep learning in the layer decoupling limit applicable to Residual Networks" ]

[ "During the last years, a remarkable breakthrough has been made in AI domain\n", "thanks to artificial deep neural networks that achieved a great success in many\n", "machine learning tasks in computer vision, natural language processing, speech\n", "recognition, malware detection and so on.", "However, they are highly vulnerable\n", "to easily crafted adversarial examples.", "Many investigations have pointed out this\n", "fact and different approaches have been proposed to generate attacks while adding\n", "a limited perturbation to the original data.", "The most robust known method so far\n", "is the so called C&W attack [1].", "Nonetheless, a countermeasure known as fea-\n", "ture squeezing coupled with ensemble defense showed that most of these attacks\n", "can be destroyed [6].", "In this paper, we present a new method we call Centered\n", "Initial Attack (CIA) whose advantage is twofold : first, it insures by construc-\n", "tion the maximum perturbation to be smaller than a threshold fixed beforehand,\n", "without the clipping process that degrades the quality of attacks.", "Second, it is\n", "robust against recently introduced defenses such as feature squeezing, JPEG en-\n", "coding and even against a voting ensemble of defenses.", "While its application is\n", "not limited to images, we illustrate this using five of the current best classifiers\n", "on ImageNet dataset among which two are adversarialy retrained on purpose to\n", "be robust against attacks.", "With a fixed maximum perturbation of only 1.5% on\n", "any pixel, around 80% of attacks (targeted) fool the voting ensemble defense and\n", "nearly 100% when the perturbation is only 6%.", "While this shows how it is difficult\n", "to defend against CIA attacks, the last section of the paper gives some guidelines\n", "to limit their impact.", "Since the skyrocketing of data volumes and parallel computation capacities with GPUs during the last years, deep neural networks (DNN) have become the most effective approaches in solving many machine learning problems in several domains like computer vision, speech recognition, games playing etc.", "They are even intended to be used in critical systems like autonomous vehicle BID17 , BID18 .", "However, DNN as they are currently built and trained using gradient based methods, are very vulnerable to attacks a.k.a. adversarial examples BID1 .", "These examples aim to fool a classifier to make it predict the class of an input as another one, different from the real class, after bringing only a very limited perturbation to this input.", "This can obviously be very dangerous when it comes to systems where human life is in stake like in self driven vehicles.", "Companies IT networks and plants are also vulnerable if DNN based intrusion detection systems were to be deployed BID20 .Many", "approaches have been proposed to craft adversarial examples since the publication by Szegedy et al. of the first paper pointing out DNN vulnerability issue BID4 . In their", "work, they generated adversarial examples using box-constrained L-BFGS. Later in", "BID1 , a fast gradient sign method (FGSM) that uses gradients of a loss function to determine in which direction the pixels intensity should be changed is presented. It is designed", "to be fast not optimize the loss function. Kurakin et al.", "introduced in BID13 a straightforward simple improvement of this method where instead of taking a single step of size in the direction of the gradient-sign, multiple smaller steps are taken, and the result is clipped in the end. Papernot et al.", "introduced in BID3 an attack, optimized under L0 distance, known as the Jacobian-based Saliency Map Attack (JSMA). Another simple", "attack known as Deepfool is provided in [34] . It is an untargeted", "attack technique optimized for the L2 distance metric. It is efficient and", "produces closer adversarial examples than the L-BFGS approach discussed earlier. Evolutionary algorithms", "are also used by authors in BID14 to find adversarial example while maintaining the attack close to the initial data. More recently, Carlini", "and Wagner introduced in BID0 the most robust attack known to date as pointed out in BID5 . They consider different", "optimization functions and several metrics for the maximum perturbation. Their L2-attack defeated", "the most powerful defense known as distillation BID7 . However, authors in BID6", "showed that feature squeezing managed to destroy most of the C&W attacks. Many other defenses have", "been published, like adversarial training BID3 , gradient masking BID9 , defenses based on uncertainty using dropout BID10 as done with Bayesian networks, based on statistics BID11 , BID12 , or principal components BID22 , BID23 . Later, while we were carrying", "out our investigation, paper BID16 showed that not less than ten defense approaches, among which are the previously enumerated defenses, can be defeated by C&W attacks. It also pointed out that feature", "squeezing also can be defeated but no thorough investigation actually was presented. Another possible defense but not", "investigated is based on JPEG encoding when dealing with images. It has never been explicitly attacked", "even after it is shown in BID13 that most attacks are countered by this defense. Also, to our knowledge, no investigation", "has been conducted when dealing with ensemble defenses. Actually, attacks transferability between", "models that is well investigated and demonstrated in BID19 in the presence of an oracle (requesting defense to get labels to train a substitute model) is not guaranteed at all when it is absent. Finally, when the maximum perturbation added", "to the original data is strictly limited, clipping is needed at the end of training (adversarial crafting) even if C&W attacks are used. The quality of crafted attacks is therefore", "degraded as the brought perturbation during the training is brutally clipped. We tackle all these points in our work while", "introducing a new attack we call Centered Initial Attack (CIA). This approach considers the perturbation limits", "by construction and consequently no alteration is done on the CIA resulting examples.To make it clearer for the reader, an example is given below to illustrate the clipping issue. FIG0 shows a comparison between CIA and C&W L2", "attack before and after clipping on an example, a guitar targeted as a potpie with max perturbation equal to 4.0 (around 1.5%). The same number of iterations FORMULA4 is considered", "for both methods. As can be seen on FIG0 , CIA generates the best attack", "with 96% confidence. C&W is almost as good with a score of 95% but it is degraded", "to 88% after applying the clipping to respect the imposed max perturbation. Avoiding this degradation due to clipping is the core motivation", "of our investigation.The remaining of this paper is organized as follows. Section I presents some mathematical formulations and the principle", "of CIA strategy. Then Section II investigates the application of CIA against ensemble", "defense, feature squeezing and JPEG encoding defenses. Then Section III provides some guidelines to limit the impact of CIA", "attacks. Finally, we give some possible future investigations in the conclusion", ".", "In this paper we presented a new strategy called CIA for crafting adversarial examples while insuring the maximum perturbation added to the original data to be smaller than a fixed threshold.", "We demonstrated also its robustness against some defenses, feature squeezing, ensemble defenses and even JPEG encoding.", "For future work, it would be interesting to investigate the transferability of CIA attacks to the physical world as it is shown in BID13 that only a very limited amount of FGDM attacks, around 20%, survive this transfer.", "Another interesting perspective is to consider partial crafting attacks while selecting regions taking into account the content of the data.", "With regard to images for instance, this would be interesting to hide attacks with big but imperceptible perturbations." ]

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[ " In this paper, a new method we call Centered Initial Attack (CIA) is provided. It insures by construction the maximum perturbation to be smaller than a threshold fixed beforehand, without the clipping process." ]

[ "Answering complex logical queries on large-scale incomplete knowledge graphs (KGs) is a fundamental yet challenging task.", "Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space such that entities that answer the query are embedded close to the query.", "However, prior work models queries as single points in the vector space, which is problematic because a complex query represents a potentially large set of its answer entities, but it is unclear how such a set can be represented as a single point.", "Furthermore, prior work can only handle queries that use conjunctions ($\\wedge$) and existential quantifiers ($\\exists$).", "Handling queries with logical disjunctions ($\\vee$) remains an open problem.", "Here we propose query2box, an embedding-based framework for reasoning over arbitrary queries with $\\wedge$, $\\vee$, and $\\exists$ operators in massive and incomplete KGs.", "Our main insight is that queries can be embedded as boxes (i.e., hyper-rectangles), where a set of points inside the box corresponds to a set of answer entities of the query.", "We show that conjunctions can be naturally represented as intersections of boxes and also prove a negative result that handling disjunctions would require embedding with dimension proportional to the number of KG entities.", "However, we show that by transforming queries into a Disjunctive Normal Form, query2box is capable of handling arbitrary logical queries with $\\wedge$, $\\vee$, $\\exists$ in a scalable manner.", "We demonstrate the effectiveness of query2box on two large KGs and show that query2box achieves up to 25% relative improvement over the state of the art.\n", "Knowledge graphs (KGs) capture different types of relationships between entities, e.g., Canada citizen −−−−→ Hinton.", "Answering arbitrary logical queries, such as \"where did Canadian citizens with Turing Award graduate?\", over such KGs is a fundamental task in question answering, knowledge base reasoning, as well as AI more broadly.", "First-order logical queries can be represented as Directed Acyclic Graphs (DAGs) ( Fig. 1(A) ) and be reasoned according to the DAGs to obtain a set of answers ( Fig. 1(C) ).", "While simple and intuitive, such approach has many drawbacks: (1) Computational complexity of subgraph matching is exponential in the query size, and thus cannot scale to modern KGs; (2) Subgraph matching is very sensitive as it cannot correctly answer queries with missing relations.", "To remedy (2) one could impute missing relations (Koller et al., 2007; Džeroski, 2009; De Raedt, 2008; Nickel et al., 2016) but that would only make the KG denser, which would further exacerbate issue (1) (Dalvi & Suciu, 2007; Krompaß et al., 2014) .", "Recently, a promising alternative approach has emerged, where logical queries as well as KG entities are embedded into a low-dimensional vector space such that entities that answer the query are embedded close to the query (Guu et al., 2015; Hamilton et al., 2018; Das et al., 2017) .", "Such approach robustly handles missing relations (Hamilton et al., 2018) and is also orders of magnitude faster, as answering an arbitrary logical query is reduced to simply identifying entities nearest to the embedding of the query in the vector space.", "However, prior work embeds a query into a single point in the vector space.", "This is problematic because answering a logical query requires modeling a set of active entities while traversing the KG ( Fig. 1(C) ), and how to effectively model a set with a single point is unclear.", "Furthermore, it We then obtain query embedding according to the computation graph (B) as a sequence of box operations: start with two nodes TuringAward and Canada and apply Win and Citizen projection operators, followed by an intersection operator (denoted as a shaded intersection of yellow and orange boxes) and another projection operator.", "The final embedding of the query is a green box and query's answers are the entities inside the box.", "is also unnatural to define logical operators (e.g., set intersection) of two points in the vector space.", "Another fundamental limitation of prior work is that it can only handle conjunctive queries, a subset of first-order logic that only involves conjunction (∧) and existential quantifier (∃), but not disjunction (∨).", "It remains an open question how to handle disjunction effectively in the vector space.", "Here we present QUERY2BOX, an embedding-based framework for reasoning over KGs that is capable of handling arbitrary Existential Positive First-order (EPFO) logical queries (i.e., queries that include any set of ∧, ∨, and ∃) in a scalable manner.", "First, to accurately model a set of entities, our key idea is to use a closed region rather than a single point in the vector space.", "Specifically, we use a box (axis-aligned hyper-rectangle) to represent a query ( Fig. 1(D) ).", "This provides three important benefits: (1) Boxes naturally model sets of entities they enclose; (2) Logical operators (e.g., set intersection) can naturally be defined over boxes similarly as in Venn diagrams (Venn, 1880); (3) Executing logical operators over boxes results in new boxes, which means that the operations are closed; thus, logical reasoning can be efficiently performed in QUERY2BOX by iteratively updating boxes according to the query computation graph ( Fig. 1(B)(D) ).", "We show that QUERY2BOX can naturally handle conjunctive queries.", "We first prove a negative result that embedding EPFO queries to only single points or boxes is intractable as it would require embedding dimension proportional to the number of KG entities.", "However, we provide an elegant solution, where we transform a given EPFO logical query into a Disjunctive Normal Form (DNF) (Davey & Priestley, 2002) , i.e., disjunction of conjunctive queries.", "Given any EPFO query, QUERY2BOX represents it as a set of individual boxes, where each box is obtained for each conjunctive query in the DNF.", "We then return nearest neighbor entities to any of the boxes as the answers to the query.", "This means that to answer any EPFO query we first answer individual conjunctive queries and then take the union of the answer entities.", "We evaluate QUERY2BOX on standard KG benchmarks and show: (1) QUERY2BOX provides strong generalization as it can answer complex queries that it has never seen during training; (2) QUERY2BOX is robust as it can answer any EPFO query with high accuracy even when relations involving answering the query are missing in the KG; (3) QUERY2BOX provides up to 25% relative improvement in accuracy of answering EPFO queries over state-of-the-art baselines.", "In this paper we proposed a reasoning framework called QUERY2BOX that can effectively model and reason over sets of entities as well as handle EPFO queries in a vector space.", "Given a logical query, we first transform it into DNF, embed each conjunctive query into a box, and output entities closest to their nearest boxes.", "Our approach is capable of handling all types of EPFO queries scalably and accurately.", "Experimental results on standard KGs demonstrate that QUERY2BOX significantly outperforms the existing work in answering diverse logical queries." ]

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[ "Answering a wide class of logical queries over knowledge graphs with box embeddings in vector space" ]

[ "Driven by the need for parallelizable hyperparameter optimization methods, this paper studies open loop search methods: sequences that are predetermined and can be generated before a single configuration is evaluated.", "Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions.\n", "In particular, we propose the use of k-determinantal point processes in hyperparameter optimization via random search.", "Compared to conventional uniform random search where hyperparameter settings are sampled independently, a k-DPP promotes diversity. ", "We describe an approach that transforms hyperparameter search spaces for efficient use with a k-DPP.", "In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from k-DPPs defined over any space from which uniform samples can be drawn, including spaces with a mixture of discrete and continuous dimensions or tree structure.", "Our experiments show significant benefits in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel.", "Hyperparameter values-regularization strength, model family choices like depth of a neural network or which nonlinear functions to use, procedural elements like dropout rates, stochastic gradient descent step sizes, and data preprocessing choices-can make the difference between a successful application of machine learning and a wasted effort.", "To search among many hyperparameter values requires repeated execution of often-expensive learning algorithms, creating a major obstacle for practitioners and researchers alike.In general, on iteration (evaluation) k, a hyperparameter searcher suggests a d-dimensional hyperparameter configuration x k ∈ X (e.g., X = R d but could also include discrete dimensions), a worker trains a model using x k , and returns a validation loss of y k ∈ R computed on a hold out set.", "In this work we say a hyperparameter searcher is open loop if x k depends only on {x i } k−1 i=1 ; examples include choosing x k uniformly at random BID3 , or x k coming from a low-discrepancy sequence (c.f., BID13 ).", "We say a searcher is closed loop if x k depends on both the past configurations and validation losses {(x i , y i )} k−1 i=1 ; examples include Bayesian optimization BID23 and reinforcement learning methods BID30 .", "Note that open loop methods can draw an infinite sequence of configurations before training a single model, whereas closed loop methods rely on validation loss feedback in order to make suggestions.While sophisticated closed loop selection methods have been shown to empirically identify good hyperparameter configurations faster (i.e., with fewer iterations) than open loop methods like random search, two trends have rekindled interest in embarrassingly parallel open loop methods:", "1) modern deep learning model are taking longer to train, sometimes up to days or weeks, and", "2) the rise of cloud resources available to anyone that charge not by the number of machines, but by the number of CPU-hours used so that 10 machines for 100 hours costs the same as 1000 machines for 1 hour.", "This paper explores the landscape of open loop methods, identifying tradeoffs that are rarely considered, if at all acknowledged.", "While random search is arguably the most popular open loop method and chooses each x k independently of {x i } k−1 i=1 , it is by no means the only choice.", "In many ways uniform random search is the least interesting of the methods we will discuss because we will advocate for methods where x k depends on {x i } k−1 i=1 to promote diversity.", "In particular, we will focus on k i=1 from a k-determinantal point process (DPP) BID18 .", "We introduce a sampling algorithm which allows DPPs to support real, integer, and categorical dimensions, any of which may have a tree structure, and we describe connections between DPPs and Gaussian processes (GPs).In", "synthetic experiments, we find our diversity-promoting open-loop method outperforms other open loop methods. In", "practical hyperparameter optimization experiments, we find that it significantly outperforms other approaches in cases where the hyperparameter values have a large effect on performance. Finally", ", we compare against a closed loop Bayesian optimization method, and find that sequential Bayesian optimization takes, on average, more than ten times as long to find a good result, for a gain of only 0.15 percent accuracy on a particular hyperparameter optimization task.Open source implementations of both our hyperparameter optimization algorithm (as an extension to the hyperopt package BID4 ) and the MCMC algorithm introduced in Algorithm 2 are available. 1 2 RELATED", "WORK While this work focuses on open loop methods, the vast majority of recent work on hyperparameter tuning has been on closed loop methods, which we briefly review.", "We have explored open loop hyperparameter optimization built on sampling from a k-DPP.", "We described how to define a k-DPP over hyperparameter search spaces, and showed that k-DPPs retain the attractive parallelization capabilities of random search.", "In synthetic experiments, we showed k-DPP samples perform well on a number of important metrics, even for large values of k.", "In hyperprameter optimization experiments, we see k-DPP-RBF outperform other open loop methods.", "Additionally, we see that sequential methods, even when using more than ten times as much wall clock time, gain less than 0.16 percent accuracy on a particular hyperparameter optimization problem.", "An open-source implementation of our method is available.", "A STAR DISCREPANCY DISPLAYFORM0 It is well-known that a sequence chosen uniformly at random from [0, 1] d has an expected star discrepancy of at least 1 k (and is no greater than DISPLAYFORM1 ) BID22 whereas sequences are known to exist with star discrepancy less than BID24 , where both bounds depend on absolute constants.", "DISPLAYFORM2 Comparing the star discrepancy of sampling uniformly and Sobol, the bounds suggest that as d grows large relative to k, Sobol starts to suffer.", "Indeed, BID2 notes that the Sobol rate is not even valid until k = Ω(2 d ) which motivates them to study a formulation of a DPP that has a star discrepancy between Sobol and random and holds for all k, small and large.", "They primarily approached this problem from a theoretical perspective, and didn't include experimental results.", "Their work, in part, motivates us to look at DPPs as a solution for hyperparameter optimization.B KOKSMA-HLAWKA INEQUALITY Let B be the d-dimensional unit cube, and let f have bounded Hardy and Krause variation V ar HK (f ) on B. Let x = (x 1 , x 2 , . . . , x k ) be a set of points in B at which the function f will be evaluated to approximate an integral.", "The Koksma-Hlawka inequality bounds the numerical integration error by the product of the star discrepancy and the variation: DISPLAYFORM3 We can see that for a given f , finding x with low star discrepancy can improve numerical integration approximations." ]

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[ "We address fully parallel hyperparameter optimization with Determinantal Point Processes. " ]

[ "Graph embedding techniques have been increasingly deployed in a multitude of different applications that involve learning on non-Euclidean data.", "However, existing graph embedding models either fail to incorporate node attribute information during training or suffer from node attribute noise, which compromises the accuracy.", "Moreover, very few of them scale to large graphs due to their high computational complexity and memory usage.", "In this paper we propose GraphZoom, a multi-level framework for improving both accuracy and scalability of unsupervised graph embedding algorithms.", "GraphZoom first performs graph fusion to generate a new graph that effectively encodes the topology of the original graph and the node attribute information.", "This fused graph is then repeatedly coarsened into a much smaller graph by merging nodes with high spectral similarities.", "GraphZoom allows any existing embedding methods to be applied to the coarsened graph, before it progressively refine the embeddings obtained at the coarsest level to increasingly finer graphs.", "We have evaluated our approach on a number of popular graph datasets for both transductive and inductive tasks.", "Our experiments show that GraphZoom increases the classification accuracy and significantly reduces the run time compared to state-of-the-art unsupervised embedding methods.", "Recent years have seen a surge of interest in graph embedding, which aims to encode nodes, edges, or (sub)graphs into low dimensional vectors that maximally preserve graph structural information.", "Graph embedding techniques have shown promising results for various applications such as vertex classification, link prediction, and community detection (Zhou et al., 2018) ; (Cai et al., 2018) ; (Goyal & Ferrara, 2018 ).", "However, current graph embedding methods have several drawbacks.", "On the one hand, random-walk based embedding algorithms, such as DeepWalk (Perozzi et al., 2014) and node2vec (Grover & Leskovec, 2016) , attempt to embed a graph based on its topology without incorporating node attribute information, which limits their embedding power.", "Later, graph convolutional networks (GCN) are developed with the basic notion that node embeddings should be smooth over the graph (Kipf & Welling, 2016) .", "While GCN leverages both topology and node attribute information for simplified graph convolution in each layer, it may suffer from high frequency noise in the initial node features, which compromises the embedding quality (Maehara, 2019) .", "On the other hand, few embedding algorithms can scale well to large graphs with millions of nodes due to their high computation and storage cost (Zhang et al., 2018a) .", "For example, graph neural networks (GNNs) such as GraphSAGE (Hamilton et al., 2017) collectively aggregate feature information from the neighborhood.", "When stacking multiple GNN layers, the final embedding vector of a node involves the computation of a large number of intermediate embeddings from its neighbors.", "This will not only drastically increase the number of computations among nodes but also lead to high memory usage for storing the intermediate results.", "In literature, increasing the accuracy and improving the scalability of graph embedding methods are largely viewed as two orthogonal problems.", "Hence most research efforts are devoted to addressing only one of the problems.", "For instance, and Fu et al. (2019) proposed multi-level methods to obtain high-quality embeddings by training unsupervised models at every level; but their techniques do not improve scalability due to the additional training overhead.", "Liang et al. (2018) developed a heuristic algorithm to coarsen the graph by merging nodes with similar local structures.", "They use GCN to refine the embedding results on the coarsened graphs, which not only is timeconsuming to train but may also degrade accuracy when multiple GCN layers are stacked together.", "More recently, Akbas & Aktas (2019) proposed a similar strategy to coarsen the graph, where certain properties of the graph structure are preserved.", "However, this work lacks proper refinement methods to improve the embedding quality.", "In this paper we propose GraphZoom, a multi-level spectral approach to enhancing the quality and scalability of unsupervised graph embedding methods.", "Specifically, GraphZoom consists of four kernels: (1) graph fusion, (2) spectral graph coarsening, (3) graph embedding, and (4) embedding refinement.", "More concretely, graph fusion first converts the node feature matrix into a feature graph and then fuses it with the original topology graph.", "The fused graph provides richer information to the ensuing graph embedding step to achieve a higher accuracy.", "Spectral graph coarsening produces a series of successively coarsened graphs by merging nodes based on their spectral similarities.", "We show that our coarsening algorithm can efficiently and effectively retain the first few eigenvectors of the graph Laplacian matrix, which is critical for preserving the key graph structures.", "During the graph embedding step, any of the existing unsupervised graph embedding techniques can be applied to obtain node embeddings for the graph at the coarsest level.", "1 Embedding refinement is then employed to refine the embeddings back to the original graph by applying a proper graph filter to ensure embeddings are smoothed over the graph.", "We validate the proposed GraphZoom framework on three transductive benchmarks: Cora, Citeseer and Pubmed citation networks as well as two inductive dataset: PPI and Reddit for vertex classification task.", "We further test on friendster dataset which contains 8 million nodes and 400 million edges to show the scalability of GraphZoom.", "Our experiments show that GraphZoom can improve the classification accuracy over all baseline embedding methods for both transductive and inductive tasks.", "Our main technical contributions are summarized as follows:", "• GraphZoom generates high-quality embeddings.", "We propose novel algorithms to encode graph structures and node attribute information in a fused graph and exploit graph filtering during refinement to remove high frequency noise.", "This results in an increase of the embedding accuracy over the prior arts by up to 19.4%.", "• GraphZoom improves scalability.", "Our approach can significantly reduce the embedding run time by effectively coarsening the graph without losing the key spectral properties.", "Experiments show that GraphZoom can accelerate the entire embedding process by up to 40.8x while producing a similar or better accuracy than state-of-the-art techniques.", "• GraphZoom is highly composable.", "Our framework is agnostic to underlying graph embedding techniques.", "Any of the existing unsupervised embedding methods, either transductive or inductive, can be incorporated by GraphZoom in a plug-and-play manner.", "In this work we propose GraphZoom, a multi-level framework to improve embedding quality and scalability of underlying unsupervised graph embedding techniques.", "GraphZoom encodes graph structure and node attribute in a single graph and exploiting spectral coarsening and refinement methods to remove high frequency noise from the graph.", "Experiments show that GraphZoom improves both classification accuracy and embedding speed on a number of popular datasets.", "An interesting direction for future work is to derive a proper way to propagate node labels to the coarsest graph, which would allow GraphZoom to support supervised graph embedding models." ]

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[ "A multi-level spectral approach to improving the quality and scalability of unsupervised graph embedding." ]

[ "Deep generative models have been enjoying success in modeling continuous data.", "However it remains challenging to capture the representations for discrete structures with formal grammars and semantics, e.g., computer programs and molecular structures.", "How to generate both syntactically and semantically correct data still remains largely an open problem.", "Inspired by the theory of compiler where syntax and semantics check is done via syntax-directed translation (SDT), we propose a novel syntax-directed variational autoencoder (SD-VAE) by introducing stochastic lazy attributes.", "This approach converts the offline SDT check into on-the-fly generated guidance for constraining the decoder.", "Comparing to the state-of-the-art methods, our approach enforces constraints on the output space so that the output will be not only syntactically valid, but also semantically reasonable.", "We evaluate the proposed model with applications in programming language and molecules, including reconstruction and program/molecule optimization.", "The results demonstrate the effectiveness in incorporating syntactic and semantic constraints in discrete generative models, which is significantly better than current state-of-the-art approaches.", "Recent advances in deep representation learning have resulted in powerful probabilistic generative models which have demonstrated their ability on modeling continuous data, e.g., time series signals BID20 BID6 and images BID22 BID15 .", "Despite the success in these domains, it is still challenging to correctly generate discrete structured data, such as graphs, molecules and computer programs.", "Since many of the structures have syntax and semantic formalisms, the generative models without explicit constraints often produces invalid ones.Conceptually an approach in generative model for structured data can be divided in two parts, one being the formalization of the structure generation and the other one being a (usually deep) generative model producing parameters for stochastic process in that formalization.", "Often the hope is that with the help of training samples and capacity of deep models, the loss function will prefer the valid patterns and encourage the mass of the distribution of the generative model towards the desired region automatically.Arguably the simplest structured data are sequences, whose generation with deep model has been well studied under the seq2seq BID25 framework that models the generation of sequence as a series of token choices parameterized by recurrent neural networks (RNNs).", "Its widespread success has encourage several pioneer works that consider the conversion of more complex structure data into sequences and apply sequence models to the represented sequences.", "BID11 (CVAE) is a representative work of such paradigm for the chemical molecule generation, using the SMILES line notation BID26 for representing molecules.", "Figure 1: Illustration on left shows the hierarchy of the structured data decoding space w.r.t different works and theoretical classification of corresponding strings from formal language theory.", "SD-VAE, our proposed model with attribute grammar reshapes the output space tighter to the meaningful target space than existing works.", "On the right we show a case where CFG is unable to capture the semantic constraints, since it successfully parses an invalid program.However, because of the lack of formalization of syntax and semantics serving as the restriction of the particular structured data, underfitted general-purpose string generative models will often lead to invalid outputs.", "Therefore, to obtain a reasonable model via such training procedure, we need to prepare large amount of valid combinations of the structures, which is time consuming or even not practical in domains like drug discovery.To tackle such a challenge, one approach is to incorporate the structure restrictions explicitly into the generative model.", "For the considerations of computational cost and model generality, contextfree grammars (CFG) have been taken into account in the decoder parametrization.", "For instance, in molecule generation tasks, BID18 proposes a grammar variational autoencoder (GVAE) in which the CFG of SMILES notation is incorporated into the decoder.", "The model generates the parse trees directly in a top-down direction, by repeatedly expanding any nonterminal with its production rules.", "Although the CFG provides a mechanism for generating syntactic valid objects, it is still incapable to regularize the model for generating semantic valid objects BID18 .", "For example, in molecule generation, the semantic of the SMILES languages requires that the rings generated must be closed; in program generation, the referenced variable should be defined in advance and each variable can only be defined exactly once in each local context (illustrated in Fig 1b) .All", "the examples require cross-serial like dependencies which are not enforceable by CFG, implying that more constraints beyond CFG are needed to achieve semantic valid production in VAE.In the theory of compiler, attribute grammars, or syntax-directed definition has been proposed for attaching semantics to a parse tree generated by context-free grammar. Thus", "one straightforward but not practical application of attribute grammars is, after generating a syntactic valid molecule candidate, to conduct offline semantic checking. This", "process needs to be repeated until a semantically valid one is discovered, which is at best computationally inefficient and at worst infeasible, due to extremely low rate of passing checking. As a", "remedy, we propose the syntax-direct variational autoencoder (SD-VAE), in which a semantic restriction component is advanced to the stage of syntax tree generator. This", "allows the generator with both syntactic and semantic validation. The", "proposed syntax-direct generative mechanism in the decoder further constraints the output space to ensure the semantic correctness in the tree generation process. The", "relationships between our proposed model and previous models can be characterized in Figure 1a .Our", "method brings theory of formal language into stochastic generative model. The", "contribution of our paper can be summarized as follows:• Syntax and semantics enforcement: We propose a new formalization of semantics that systematically converts the offline semantic check into online guidance for stochastic generation using the proposed stochastic lazy attribute. This", "allows us effectively address both syntax and semantic constraints.• Efficient", "learning and inference: Our approach has computational cost O(n) where n is the length of structured data. This is the", "same as existing methods like CVAE and GVAE which do not enforce semantics in generation. During inference", ", the SD-VAE runs with semantic guiding onthe-fly, while the existing alternatives generate many candidates for semantic checking.• Strong empirical", "performance: We demonstrate the effectiveness of the SD-VAE through applications in two domains, namely (1) the subset of Python programs and (2) molecules. Our approach consistently", "and significantly improves the results in evaluations including generation, reconstruction and optimization.", "In this paper we propose a new method to tackle the challenge of addressing both syntax and semantic constraints in generative model for structured data.", "The newly proposed stochastic lazy attribute presents a the systematical conversion from offline syntax and semantic check to online guidance for stochastic generation, and empirically shows consistent and significant improvement over previous models, while requiring similar computational cost as previous model.", "In the future work, we would like to explore the refinement of formalization on a more theoretical ground, and investigate the application of such formalization on a more diverse set of data modality." ]

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[ "A new generative model for discrete structured data. The proposed stochastic lazy attribute converts the offline semantic check into online guidance for stochastic decoding, which effectively addresses the constraints in syntax and semantics, and also achieves superior performance" ]

[ "Modeling informal inference in natural language is very challenging.", "With the recent availability of large annotated data, it has become feasible to train complex models such as neural networks to perform natural language inference (NLI), which have achieved state-of-the-art performance.", "Although there exist relatively large annotated data, can machines learn all knowledge needed to perform NLI from the data?", "If not, how can NLI models benefit from external knowledge and how to build NLI models to leverage it?", "In this paper, we aim to answer these questions by enriching the state-of-the-art neural natural language inference models with external knowledge.", "We demonstrate that the proposed models with external knowledge further improve the state of the art on the Stanford Natural Language Inference (SNLI) dataset.", "Reasoning and inference are central to both human and artificial intelligence.", "Natural language inference (NLI) is concerned with determining whether a natural-language hypothesis h can be inferred from a natural-language premise p.", "Modeling inference in human language is very challenging but is a basic problem towards true natural language understanding -NLI is regarded as a necessary (if not sufficient) condition for true natural language understanding BID20 .The", "most recent years have seen advances in modeling natural language inference. An", "important contribution is the creation of much larger annotated datasets such as SNLI BID5 and MultiNLI BID37 . This", "makes it feasible to train more complex inference models. Neural", "network models, which often need relatively large amounts of annotated data to estimate their parameters, have shown to achieve the state of the art on SNLI and MultiNLI BID5 BID25 BID27 BID30 BID26 BID8 BID1 . While", "these neural networks have shown to be very effective in estimating the underlying inference functions by leveraging large training data to achieve the best results, they have focused on end-toend training, where all inference knowledge is assumed to be learnable from the provided training data. In this", "paper, we relax this assumption, by exploring whether external knowledge can further help the best reported models, for which we propose models to leverage external knowledge in major components of NLI. Consider", "an example from the SNLI dataset:• p: An African person standing in a wheat field.• h: A person", "standing in a corn field.If the machine cannot learn useful or plenty information to distinguish the relationship between wheat and corn from the large annotated data, it is difficult for a model to predict that the premise contradicts the hypothesis.In this paper, we propose neural network-based NLI models that can benefit from external knowledge. Although in many", "tasks learning tabula rasa achieved state-of-the-art performance, we believe complicated NLP problems such as NLI would benefit from leveraging knowledge accumulated by humans, at least in a foreseeable future when machines are unable to learn that with limited data.A typical neural-network-based NLI model consists of roughly four components -encoding the input sentences, performing co-attention across premise and hypothesis, collecting and computing local inference, and performing sentence-level inference judgment by aggregating or composing local information information. In this paper, we", "propose models that are capable of leveraging external knowledge in co-attention, local inference collection, and inference composition components. We demonstrate that", "utilizing external knowledge in neural network models outperforms the previously reported best models. The advantage of using", "external knowledge is more significant when the size of training data is restricted, suggesting that if more knowledge can be obtained, it may yielding more benefit. Specifically, this study", "shows that external semantic knowledge helps mostly in attaining more accurate local inference information, but also benefits co-attention and aggregation of local inference.", "Our enriched neural network-based model for natural language inference with external knowledge, namely KIM, achieves a new state-of-the-art accuracy on the SNLI dataset.", "The model is equipped with external knowledge in the major informal inference components, specifically, in calculating co-attention, collecting local inference, and composing inference.", "The proposed models of infusing neural networks with external knowledge may also help shed some light on tasks other than NLI, such as question answering and machine translation." ]

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[ "the proposed models with external knowledge further improve the state of the art on the SNLI dataset." ]

[ "High intra-class diversity and inter-class similarity is a characteristic of remote sensing scene image data sets currently posing significant difficulty for deep learning algorithms on classification tasks.", "To improve accuracy, post-classification\n", "methods have been proposed for smoothing results of model predictions.", "However, those approaches require an additional neural network to perform the smoothing operation, which adds overhead to the task.", "We propose an approach that involves learning deep features directly over neighboring scene images without requiring use of a cleanup model.", "Our approach utilizes a siamese network to improve the discriminative power of convolutional neural networks on a pair\n", "of neighboring scene images.", "It then exploits semantic coherence between this pair to enrich the feature vector of the image for which we want to predict a label.\n", "Empirical results show that this approach provides a viable alternative to existing methods.", "For example, our model improved prediction accuracy by 1 percentage point and dropped the mean squared error value by 0.02 over the baseline, on a disease density estimation task.", "These performance gains are comparable with results from existing post-classification methods, moreover without implementation overheads.", "Remote sensing scene image analysis is emerging as an important area of research for application of deep learning algorithms.", "Application areas include land-use land-cover analysis, urban planning, and natural disaster detection.", "A deep learning task for labeling a scene image is typically formulated as conditional probability of the form in Eq. 1 Liu et al. (2019) , Albert et al. (2017) , Nogueira et al. (2016) , Castelluccio et al. (2015) , Mnih (2013) , Mnih & Hinton (2010) ,", "where l i is label for image patch s i .", "This formulation is sufficient for problems where spatial situatedness of a scene, which embodies knowledge of semantic likeness between neighborhoods in the geophysical world, is not important.", "However, for problems which require knowledge of neighborhood the formulation in Eq. 1 becomes inadequate.", "An example of such a problem would be estimating disease density for a small geographical region of interest, in which case the probability of label l is likely to depend on the labels for neighboring regions due to semantic coherence among them.", "The problem of how to improve model prediction by leveraging semantic coherence among neighboring scene images has previously been considered in the literature.", "Previous studies consider the problem as a post-classification task.", "For example, Bischof et al. (1992) used a second classifier to do pixel smoothing to refine predictions made by another classifier.", "Based on a 5x5 window, a filter assigns pixels to the majority class if it had been assigned a different class.", "In Mnih (2013) , a post-processing architecture is suggested for incorporating structure into image patch prediction.", "It involves stacking neural networks (NN) such that the output from a previous one becomes input for the next.", "Idea is for each network to clean up predictions of previous one in order to progressively improve overall accuracy.", "While improved model performance was achieved by these methods, they have overhead of performing same classification task in at least two stages.", "In other words, you need a minimum of two NN to perform the same classification task.", "Unlike post-classification methods, this work considers the problem of improving model accuracy on scene images by exploiting knowledge of neighboring scenes as part of the model training process.", "We make the assumption that l is conditionally co-dependent on information embedded in scene image i and in other similar, neighboring image j such that the problem is formulated as probability of the form in Eq. 2,", "where s j is image for a neighboring tile that is most similar to index tile i and P (l i |S i , S j ) is observed probability distribution.", "We used Convolutional Neural Networks (CNN) for modeling the observed probability distribution in Eq. 2.", "A network architecture is proposed for training our model consisting of four components: a siamese sub-network, a similarity metric learning component, a convolutional network, and a decision layer.", "The siamese sub-network takes two neighboring scene images as input and extracts features from each.", "The similarity learning component evaluates how similar the input images are, using the extracted features.", "If the two input images are found to be similar the convolutional network learns additional features based on the merged feature vector, otherwise those from the index tile are used alone.", "We implemented the decision layer to perform classification or regression.", "A baseline model was implemented that takes a single image, the index tile i, as input.", "Empirical results show the proposed model consistently outperforms the baseline.", "In addition to improving predictive performance with a relatively small training set, our model is fast to train since it uses a pre-trained model for the siamese sub-network.", "Furthermore, it does not require another NN to smooth out its predictions as is the case with post-classification approaches, while achieving comparable performance gain.", "In summary,our contributions include the following.", "1. We propose an approach for training a probabilistic deep learning model to improve prediction accuracy by exploiting semantic coherence between neighboring tiles in aerial scene images.", "A CNN architecture is suggested for this purpose.", "2. We provide empirical evidence that demonstrates the viability of this approach on a disease density estimation task.", "3. Lastly, we discovered an important limitation of the synthetic minority over-sampling technique (SMOTE).", "This method fails when used for oversampling an under-represented class whereby knowledge of spatial proximity between scene image data points must be preserved, an important requirement under the framework of learning deep features over neighboring scene images introduced in this work.", "Our model performed better than the baseline in both the classification and regression tasks for disease density estimation.", "For example, our model achieved 1 percentage point gain in accuracy over the baseline model.", "While a gain as result of deploying a siamese network to boost discriminative power of CNN for aerial scene image classification is consistent with findings in previous studies overall results from our model are poor.", "For instance, our model was only able to attain a maximum overall accuracy of 34 percent on the classification task.", "We would like to pin these poor results to a combination of three factors.", "First, the small data set used to train our model (12,070 images) could have impacted accuracy negatively, despite the use of regularization methods.It is therefore, possible that our model suffered the problem of overfitting.", "Secondly, our data set was unbalanced.", "It is likely that the extra parameter we introduced in the loss function to weight classes by giving higher importance to under-represented classes did not work as expected.", "The result could have been that our model did not learn all the necessary features required to make a prediction but rather could have resorted to guessing the output and hence, failing to generalize well over the test set.", "Class imbalance in our data set could also have negatively affected feature correlation which in turn could have reduced model performance.", "Besides, well-known methods for mitigating sample size bias in imbalanced data sets, for example by over-sampling under-represented classes Chawla et al. (2002) could not be applied directly to our data set without modifying the algorithm.", "That is because it was not immediately clear how to preserve spatial proximity between neighboring tiles, an idea that is central to learning deep features over neighboring scene images.However, despite the low overall performance by our model we have been able to demonstrate that it is possible to improve model accuracy by learning deep features over neighboring scene images in a disease density estimation task.", "Figure 2: Finding a neighboring image j that is semantically most similar to image i." ]

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[ "Approach for improving prediction accuracy by learning deep features over neighboring scene images in satellite scene image analysis." ]

[ "Sparsely available data points cause a numerical error on finite differences which hinder to modeling the dynamics of physical systems.", "The discretization error becomes even larger when the sparse data are irregularly distributed so that the data defined on an unstructured grid, making it hard to build deep learning models to handle physics-governing observations on the unstructured grid.", "In this paper, we propose a novel architecture named Physics-aware Difference Graph Networks (PA-DGN) that exploits neighboring information to learn finite differences inspired by physics equations.", "PA-DGN further leverages data-driven end-to-end learning to discover underlying dynamical relations between the spatial and temporal differences in given observations.", "We demonstrate the superiority of PA-DGN in the approximation of directional derivatives and the prediction of graph signals on the synthetic data and the real-world climate observations from weather stations.", "Modeling real world phenomena, such as climate observations, traffic flow, physics and chemistry simulation (Li et al., 2018; Geng et al., 2019; Long et al., 2018; de Bezenac et al., 2018; SanchezGonzalez et al., 2018; Gilmer et al., 2017) , is important but extremely challenging.", "While deep learning has achieved remarkable successes in prediction tasks by learning latent representations from data-rich applications such as image recognition (Krizhevsky et al., 2012 ), text understanding (Wu et al., 2016) , and speech recognition , we are confronted with many challenging scenarios in modeling natural phenomena by deep neural networks when a limited number of observations are only available.", "Particularly, the sparsely available data points cause substantial numerical error and the limitation requires a more principled way to redesign deep learning models.", "Although many works have been proposed to model physics-simulated observations using deep learning, many of them are designed under the assumption that input is on a continuous domain.", "For example, Raissi et al. (2017a; proposed Physics-informed neural networks (PINNs) to learn nonlinear relations between input (spatial-and temporal-coordinates (x, t)) and output simulated by a given PDE.", "Since Raissi et al. (2017a; use the coordinates as input and compute derivatives based on the coordinates to represent a given PDE, the setting is only valid when the data are continuously observed over spatial and temporal space.", "Under the similar direction of PINNs, Chen et al. (2015) proposed a method to leverage the nonlinear diffusion process for image restoration.", "de Bezenac et al. (2018) incorporated the transport physics (advection-diffusion equation) with deep neural networks for forecasting sea surface temperature by extracting the motion field.", "Lutter et al. (2019) introduced Deep Lagrangian Networks specialized to learn Lagrangian mechanics with learnable parameters.", "Seo & Liu (2019) proposed a physicsinformed regularizer to impose data-specific physics equations.", "In common, the methods in Chen et al. (2015) ; de Bezenac et al. (2018) ; Lutter et al. (2019) are not efficiently applicable to sparsely discretized input as only a small number of data points are available and continuous properties on given space are not easily recovered.", "It is inappropriate to directly use continuous differential operators to provide local behaviors because it is hard to approximate the continuous derivatives precisely with the sparse points (Amenta & Kil, 2004; Luo et al., 2009; Shewchuk, 2002) .", "Furthermore, they are only applicable when the specific physics equations are explicitly given and still hard to be generalized to incorporate other types of equations.", "As another direction to modeling physics-simulated data, Long et al. (2018) proposed PDE-Net which uncovers the underlying hidden PDEs and predicts the dynamics of complex systems.", "Ruthotto & Haber (2018) derived new CNNs: parabolic and hyperbolic CNNs based on ResNet (He et al., 2016) architecture motivated by PDE theory.", "While Long et al. (2018) ; Ruthotto & Haber (2018) are flexible to uncover hidden physics from the constrained kernels, it is still restrictive to a regular grid where the proposed constraints on the learnable filters are easily defined.", "Reasoning physical dynamics of discrete objects has been actively studied Battaglia et al., 2016; Chang et al., 2016) as the appearance of graph-based neural networks (Kipf & Welling, 2017; Santoro et al., 2017; Gilmer et al., 2017) .", "Although these models can handle sparsely located data points without explicitly given physics equations, they are purely data-driven so that the physics-inspired inductive bias, exploiting finite differences, is not considered at all.", "In contrast, our method consists of physics-aware modules allowing efficiently leveraging the inductive bias to learn spatiotemporal data from the physics system.", "In this paper, we propose Physics-aware Difference Graph Networks (PA-DGN) whose architecture is motivated to leverage differences of sparsely available data from the physical systems.", "The differences are particularly important since most of the physics-related dynamic equations (e.g., Navier-Stokes equations) handle differences of physical quantities in spatial and temporal space instead of using the quantities directly.", "Inspired by the property, we first propose Spatial Difference Layer (SDL) to efficiently learn the local representations by aggregating neighboring information in the sparse data points.", "The layer is based on Graph Networks (GN) as it easily leverages structural features to learn the localized representations and the parameters for computing the localized features are shared.", "Then, the layer is connected with Recurrent Graph Networks (RGN) to be combined with temporal difference which is another core component of physics-related dynamic equations.", "PA-DGN is applicable to various tasks and we provide two representative tasks; the approximation of directional derivatives and the prediction of graph signals.", "In this paper, we introduce a novel architecture (PA-DGN) that approximates spatial derivatives to use them to represent PDEs which have a prominent role for physics-aware modeling.", "PA-DGN effectively learns the modulated derivatives for predictions and the derivatives can be used to discover hidden physics describing interactions between temporal and spatial derivatives." ]

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[ "We propose physics-aware difference graph networks designed to effectively learn spatial differences to modeling sparsely-observed dynamics." ]

[ "Solving long-horizon sequential decision making tasks in environments with sparse rewards is a longstanding problem in reinforcement learning (RL) research.", "Hierarchical Reinforcement Learning (HRL) has held the promise to enhance the capabilities of RL agents via operation on different levels of temporal abstraction.", "Despite the success of recent works in dealing with inherent nonstationarity and sample complexity, it remains difficult to generalize to unseen environments and to transfer different layers of the policy to other agents.", "In this paper, we propose a novel HRL architecture, Hierarchical Decompositional Reinforcement Learning (HiDe), which allows decomposition of the hierarchical layers into independent subtasks, yet allows for joint training of all layers in end-to-end manner.", "The main insight is to combine a control policy on a lower level with an image-based planning policy on a higher level.", "We evaluate our method on various complex continuous control tasks for navigation, demonstrating that generalization across environments and transfer of higher level policies can be achieved.", "See videos https://sites.google.com/view/hide-rl", "Reinforcement learning (RL) has been succesfully applied to sequential-decision making tasks, such as learning how to play video games in Atari (Mnih et al., 2013) , mastering the game of Go or continuous control in robotics (Lillicrap et al., 2015; Levine et al., 2015; .", "However, despite the success of RL agents in learning control policies for myopic tasks, such as reaching a nearby target, they lack the ability to effectively reason over extended horizons.", "In this paper, we consider continuous control tasks that require planning over long horizons in navigation environments with sparse rewards.", "The task becomes particularly challenging with sparse and delayed rewards since an agent needs to infer which actions caused the reward in a domain where most samples give no signal at all.", "Common techniques to mitigate the issue of sparse rewards include learning from demonstrations (Schaal, 1999; Peng et al., 2018) or using enhanced exploration strategies (Bellemare et al., 2016; Pathak et al., 2017; Andrychowicz et al., 2017) .", "Hierarchical Reinforcement Learning (HRL) has been proposed in part to solve such tasks.", "Typically, a sequential decision making task is split into several simpler subtasks of different temporal and functional abstraction levels (Sutton et al., 1999; Andre & Russell, 2002) .", "Although the hierarchies would ideally be learned in parallel, most methods resort to curriculum learning (Frans et al., 2017; Florensa et al., 2017; Bacon et al., 2016; Vezhnevets et al., 2017) .", "Recent goal-conditioned hierarchical architectures have successfully trained policies jointly via off-policy learning (Levy et al., 2019; Nachum et al., 2018; .", "However, these methods often do not generalize to unseen environments as we show in Section 5.1.", "We argue that this is due to a lack of true separation of planning and low-level control across the hierarchy.", "In this paper, we consider two main problems, namely functional decomposition of HRL architectures in navigation-based domains and generalization of RL agents to unseen environments (figure 1).", "To address these issues, we propose a novel multi-level HRL architecture that enables both functional decomposition and temporal abstraction.", "We introduce a 3-level hierarchy that decouples the major roles in a complex navigation task, namely planning and low-level control.", "The benefit of a modular design is twofold.", "First, layers have access to only task-relevant information for a predefined task, which significantly improves the generalization ability of the overall policy.", "Hence, this enables policies learned on a single task to solve randomly configured environments.", "Second, Figure 1 : Navigation environments.", "The red sphere indicates the goal an agent needs to reach, with the starting point at the opposite end of the maze.", "The agent is trained on environment", "a).", "To test generalization, we use the environments with", "b) reversed starting and goal positions,", "c) mirrored maze with reversed starting and goal positions and", "d) randomly generated mazes.", "the planning and control layers are modular and thus allow for composition of cross-agent architectures.", "We empirically show that the planning layer of the hierarchy can be transferred successfully to new agents.", "During training we provide global environment information only to the planning layer, whereas the full internal state of the agent is only accessible by the control layer.", "The actions of the top and middle layers are in the form of displacement in space.", "Similarly, the goals of the middle and lowest layers are relative to the current position.", "This prevents the policies from overfitting to the global position in an environment and hence encourages generalization to new environments.", "In our framework (see figure 2), the planner (i.e., the highest level policy π 2 ) learns to find a trajectory leading the agent to the goal.", "Specifically, we learn a value map of the environment by means of a value propagation network (Nardelli et al., 2019) .", "To prevent the policy from issuing too ambitious subgoals, an attention network estimates the range of the lower level policy π 0 (i.e., the agent).", "This attention mask also ensures that the planning considers the agent performance.", "The action of π 2 is the position which maximizes the masked value map, which serves as goal input to the policy π 1 .", "The middle layer implements an interface between the upper planner and lower control layer, which refines the coarser subgoals into shorter and reachable targets for the agent.", "The middle layer is crucial in functionally decoupling the abstract task of planning (π 2 ) from agent specific continuous control.", "The lowest layer learns a control policy π 0 to steer the agent to intermediate goals.", "While the policies are functionally decoupled, they are trained together and must learn to cooperate.", "In this work, we focus on solving long-horizon tasks with sparse rewards in complex continuous navigation domains.", "We first show in a maze environment that generalization causes challenges for state-of-the-art approaches.", "We then demonstrate that training with the same environment configuration (i.e., fixed start and goal positions) can generalize to randomly configured environments.", "Lastly, we show the benefits of functional decomposition via transfer of individual layers between different agents.", "In particular, we train our method with a simple 2DoF ball agent in a maze environment to learn the planning layer which is later used to steer a more complex agent.", "The results indicate that the proposed decomposition of policy layers is effective and can generalize to unseen environments.", "In summary our main contributions include:", "• A novel multi-layer HRL architecture that allows functional decomposition and temporal abstraction for navigation tasks.", "• This architecture enables generalization beyond training conditions and environments.", "• Functional decomposition that allows transfer of individual layers across different agents.", "In this paper, we introduce a novel HRL architecture that can solve complex navigation tasks in 3D-based maze environments.", "The architecture consists of a planning layer which learns an explicit value map and is connected with a subgoal refinement layer and a low-level control layer.", "The framework can be trained end-to-end.", "While training with a fixed starting and goal position, our method is able to generalize to previously unseen settings and environments.", "Furthermore, we demonstrate that transfer of planners between different agents can be achieved, enabling us to transfer a planner trained with a simplistic agent such as a ball to a more complex agent such as an ant or humanoid.", "In future work, we want to consider integration of a more general planner that is not restricted to navigation-based environments." ]

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[ "Learning Functionally Decomposed Hierarchies for Continuous Navigation Tasks" ]

[ "Sound correspondence patterns play a crucial role for linguistic reconstruction.", "Linguists\n", "use them to prove language relationship, to reconstruct proto-forms, and for classical\n", "phylogenetic reconstruction based on shared innovations.Cognate words which fail to\n", "conform with expected patterns can further point to various kinds of exceptions in sound\n", "change, such as analogy or assimilation of frequent words.", "Here we present an automatic\n", "method for the inference of sound correspondence patterns across multiple languages based\n", "on a network approach.", "The core idea is to represent all columns in aligned cognate sets as\n", "nodes in a network with edges representing the degree of compatibility between the nodes.\n", "The task of inferring all compatible correspondence sets can then be handled as the well-known minimum clique cover problem in graph theory, which essentially seeks to split the graph into the smallest number of cliques in which each node is represented by exactly one clique.", "The resulting partitions represent all correspondence patterns which can be\n", "inferred for a given dataset.", "By excluding those patterns which occur in only a few cognate\n", "sets, the core of regularly recurring sound correspondences can be inferred.", "Based on this\n", "idea, the paper presents a method for automatic correspondence pattern recognition, which\n", "is implemented as part of a Python library which supplements the paper.", "To illustrate the\n", "usefulness of the method, various tests are presented, and concrete examples of the output\n", "of the method are provided.", "In addition to the source code, the study is supplemented by\n", "a short interactive tutorial that illustrates how to use the new method and how to inspect\n", "its results.", "One of the fundamental insights of early historical linguistic research was that -as a result of systemic changes in the sound system of languages -genetically related languages exhibit structural similarities in those parts of their lexicon which were commonly inherited from their ancestral languages.", "These similarities surface in form of correspondence relations between sounds from different languages in cognate words.", "English th [θ] , for example, is usually reflected as d in German, as we can see from cognate pairs like English thou vs. German du, or English thorn and German Dorn.", "English t, on the other hand, is usually reflected as z [ts] in German, as we can see from pairs like English toe vs. German Zeh, or English tooth vs. German Zahn.", "The identification of these regular sound correspondences plays a crucial role in historical language comparison, serving not only as the basis for the proof of genetic relationship BID11 BID6 or the reconstruction of protoforms BID20 , 72-85, Anttila 1972 , but (indirectly) also for classical subgrouping based on shared innovations (which would not be possible without identified correspondence patterns).Given", "the increasing application of automatic methods in historical linguistics after the \"quantitative turn\" (Geisler and List 2013, 111) in the beginning of this millennium, scholars have repeatedly attempted to either directly infer regular sound correspondences across genetically related languages BID30 BID29 BID5 BID26 or integrated the inference into workflows for automatic cognate detection BID17 BID33 BID34 BID40 . What", "is interesting in this context, however, is that almost all approaches dealing with regular sound correspondences, be it early formal -but classically grounded -accounts BID16 BID20 or computer-based methods BID29 BID28 BID34 only consider sound correspondences between pairs of languages.A rare exception can be found in the work of Anttila (1972, 229-263) , who presents the search for regular sound correspondences across multiple languages as the basic technique underlying the comparative method for historical language comparison. Anttila", "'s description starts from a set of cognate word forms (or morphemes) across the languages under investigation. These", "words are then arranged in such a way that corresponding sounds in all words are placed into the same column of a matrix. The extraction", "of regularly recurring sound correspondences in the languages under investigation is then based on the identification of similar patterns recurring across different columns within the cognate sets. The procedure", "is illustrated in Figure 1 , where four cognate sets in Sanskrit, Ancient Greek, Latin, and Gothic are shown, two taken from Anttila (1972, 246) and two added by me.Two points are remarkable about Anttila's approach. First, it builds", "heavily on the phonetic alignment of sound sequences, a concept that was only recently adapted in linguistics (Covington 1996; BID27 BID34 , building heavily on approaches in bioinformatics and computer science BID55 BID45 , although it was implicitly always an integral part of the methodology of historical language comparison (compare Fox 1995, 67f, Dixon and BID9 . Second, it reflects", "a concrete technique by which regular sound correspondences for multiple languages can be detected and employed as a starting point for linguistic reconstruction. If we look at the framed", "columns in the four examples in Figure 1 , which are further labeled alphabetically, for example, we can easily see that the patterns A, E, and F are remarkably similar, with the missing reflexes in Gothic in the patterns E and F as the only difference. The same holds, however,", "for columns C, E, and F. Since A and C differ regarding the reflex sound of Gothic (u vs. au), they cannot be assigned to the same correspondence set at this stage, and if we want to solve the problem of finding the regular sound correspondences for the words in the figure, we need to make a decision which columns in the alignments we assign to the same correspondence sets, thereby 'imputing' missing sounds where we miss a reflex. Assuming that the \"regular", "\" pattern in our case is reflected by the group of A, E, and F, we can make predictions about the sounds missing in Gothic in E and F, concluding that, if ever we find the missing reflex in so far unrecognised sources of Gothic in the future, we would expect a -u-in the words for 'daughter-in-law' and 'red'.We can easily see how patterns", "of sound correspondences across multiple languages can serve as the basis for linguistic reconstruction. Strictly speaking, if two alignment", "columns are identical (ignoring missing data to some extent), they need to reflect the same proto-sound. But even if they are not identical,", "they could be assigned to the same proto-sound, provided that one can show that the differences are conditioned by phonetic context. This is the case for Gothic au [o]", "in pattern C, which has been shown to go back to u when preceding h (Meier-Brügger 2002, 210f) . As a result, scholars usually reconstruct", "Proto-Indo-European *u for A, C, E, and F.", "In this study I have presented a new method for the inference of sound correspondence patterns in multi-lingual wordlists.", "Thanks to its integration with the LingPy software package, the methods can be applied both in the form of fully automated workflows where both cognate sets, alignments, and correspondence patterns are computed, or in computer-assisted workflows where linguists manually annotate parts of the data at any step in the workflow.", "Having shown that the inference of correspondence patterns can be seen as the crucial step underlying the reconstruction of proto-forms, the method presented here provides a basis for many additional approaches in the fields of computational historical linguistics and computer-assisted language comparison.", "Among these are", "(a) automatic approaches for linguistic reconstruction,", "(b) alignment-based approaches to phylogenetic reconstruction,", "(c) the detection of borrowings and erroneous cognates, and", "(d) the prediction of missing reflexes in the data.", "The approach is not perfect in its current form, and many kinds of improvements are possible.", "Given its novelty, however, I consider it important to share the approach its current form, hoping that it may inspire colleagues in the field to expand and develop it further." ]

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[ "The paper describes a new algorithm by which sound correspondence patterns for multiple languages can be inferred." ]

[ "We describe Kernel RNN Learning (KeRNL), a reduced-rank, temporal eligibility trace-based approximation to backpropagation through time (BPTT) for training recurrent neural networks (RNNs) that gives competitive performance to BPTT on long time-dependence tasks.", "The approximation replaces a rank-4 gradient learning tensor, which describes how past hidden unit activations affect the current state, by a simple reduced-rank product of a sensitivity weight and a temporal eligibility trace.", "In this structured approximation motivated by node perturbation, the sensitivity weights and eligibility kernel time scales are themselves learned by applying perturbations.", "The rule represents another step toward biologically plausible or neurally inspired ML, with lower complexity in terms of relaxed architectural requirements (no symmetric return weights), a smaller memory demand (no unfolding and storage of states over time), and a shorter feedback time.", "Animals and humans excel at learning tasks that involve long-term temporal dependencies.", "A key challenge of learning such tasks is the problem of spatiotemporal credit assignment: the learner must find which of many past neural states is causally connected to the currently observed error, then allocate credit across neurons in the brain.", "When the time-dependencies between network states and errors are long, learning becomes difficult.In machine learning, the current standard for training recurrent architectures is Backpropagation Through Time (BPTT, Rumelhart et al. (1985) , BID18 ).", "BPTT assigns temporal credit or blame by unfolding a recurrent neural network in time up to a horizon length T , processing the input in a forward pass, and then backpropagating the error back in time in a backward pass (see FIG0 ).From", "a biological perspective, BPTT -like backpropagation in feedforward neural networks -is implausible for many reasons. For", "each weight update, BPTT requires using the transpose of the recurrent weights to transmit errors backwards in time and assign credit for how past activity affected present performance. Running", "the network with transposed weights requires that the network either has two-way synapses, or uses a symmetric copy of the feedforward weights to backpropagate error. In either", "case, the network must alternatingly gate its dynamical process to run forward or backward, and switch from nonlinear to linear dynamics, depending on whether activity or errors are being sent through the network.From both biological and engineering perspectives, there is a heavy memory demand: the complete network states, going T timesteps back in time, must be stored. The time-complexity", "of computation of the gradient in BPTT scales like T , making each iteration slow when training tasks with long time scale dependencies. Although T should match", "the length of the task or the maximum temporal lag between network states and errors for unbiased gradient learning, in practice T is often truncated to mitigate these computational costs, introducing a bias.The present work is another step in the direction of providing heuristics and relaxed approximations to backpropagation-based gradient learning for recurrent networks. KeRNL confronts the problems", "of efficiency and biological plausibility. It replaces the lengthy, linearized", "backward-flowing backpropagation phase with a product of a forward-flowing temporal eligibility trace and a spatial sensitivity weight. Instead of storing all details of past", "states in memory, synapses integrate their past activity during the forward pass (see FIG0 ). The network does not have to recompute", "the entire gradient at each update, as the time-scales of the eligibility trace and the sensitivity weight are learned over time." ]

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[ "A biologically plausible learning rule for training recurrent neural networks" ]

[ "We present Deep Graph Infomax (DGI), a general approach for learning node representations within graph-structured data in an unsupervised manner.", "DGI relies on maximizing mutual information between patch representations and corresponding high-level summaries of graphs---both derived using established graph convolutional network architectures.", "The learnt patch representations summarize subgraphs centered around nodes of interest, and can thus be reused for downstream node-wise learning tasks.", "In contrast to most prior approaches to unsupervised learning with GCNs, DGI does not rely on random walk objectives, and is readily applicable to both transductive and inductive learning setups.", "We demonstrate competitive performance on a variety of node classification benchmarks, which at times even exceeds the performance of supervised learning.", "We have presented Deep Graph Infomax (DGI), a new approach for learning unsupervised representations on graph-structured data.", "By leveraging local mutual information maximization across the graph's patch representations, obtained by powerful graph convolutional architectures, we are able to obtain node embeddings that are mindful of the global structural properties of the graph.", "This enables competitive performance across a variety of both transductive and inductive classification tasks, at times even outperforming relevant supervised architectures." ]

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[ "A new method for unsupervised representation learning on graphs, relying on maximizing mutual information between local and global representations in a graph. State-of-the-art results, competitive with supervised learning." ]

[ "In many environments only a tiny subset of all states yield high reward. ", "In these cases, few of the interactions with the environment provide a relevant learning signal.", "Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. \n", "To this end, we advocate for the use of a \\textit{backtracking model} that predicts the preceding states that terminate at a given high-reward state. ", "We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and samples which (state, action)-tuples may have led to that high value state.", "These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy.", "We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards.", "Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks. ", "Training control algorithms efficiently from interactions with the environment is a central issue in reinforcement learning (RL).", "Model-free RL methods, combined with deep neural networks, have achieved impressive results across a wide range of domains BID18 BID39 .", "However, existing model-free solutions lack sample efficiency, meaning that they require extensive interaction with the environment to achieve these levels of performance.Model-based methods in RL can mitigate this issue.", "These approaches learn an unsupervised model of the underlying dynamics of the environment, which does not necessarily require rewards, as the model observes and predicts state-to-state transitions.", "With a well-trained model, the algorithm can then simulate the environment and look ahead to future events to establish better value estimates, without requiring expensive interactions with the environment.", "Model-based methods can thus be more sample efficient than their model-free counterparts, but often do not achieve the same asymptotic performance BID6 BID28 .In", "this work, we propose a method that takes advantage of unsupervised observations of state-to-state transitions for increasing the sample efficiency of current model-free RL algorithms, as measured by the number of interactions with the environment required to learn a successful policy. Our", "idea stems from a simple observation: given a world model, finding a path between a starting state and a goal state can be done either forward from the start or backward from the goal. Here", ", we explore an idea for leveraging the latter approach and combining it with model-free algorithms. This", "idea is particularly useful when rewards are sparse. High-value", "states are rare and trajectories leading to them are particularly useful for a learner.The availability of an exact backward dynamics model of the environment is a strong and often unrealistic requirement for most domains. Therefore,", "we propose learning a backward dynamics model, which we refer to as a backtracking model, from the experiences performed by the agent. This backtracking", "model p(s t , a t |s t+1 ), is trained to predict, given a state s t+1 , which state s t the agent visited before s t+1 and what action a t ∼ π was performed in s t to reach s t+1 . Specifically, this", "is a model which, starting from a future high-value state, can be used to recall traces that have ended at this high value state, that is sequences of (state, action)-tuples. This allows the agent", "to simulate and be exposed to alternative possible paths to reach a high value state. A final state may be", "a previously experienced high-value state or a goal state may be explicitly given, or even produced by the agent using a generative model of high-value states BID19 . Our hypothesis is that", "using a backtracking model in this way should benefit learning, especially in the context of weak or sparse rewards. Indeed, in environments", "or tasks where the agent receives rewards infrequently, it must leverage this information effectively and efficiently. Exploration methods have", "been employed successfully BID2 BID19 BID32 to increase the frequency at which novel states are discovered. Our proposal can be viewed", "as a special kind of simulated exploration proceeding backward from presumed high-value states, in order to discover trajectories that may lead to high rewards. A backtracking model aims", "to augment the experience of the trajectory τ leading to a high-value state by generating other possible tracesτ that could have also caused it. To summarize: the main contribution", "of this paper is an RL method based on the use of a backtracking model, which can easily be integrated with existing on-and off-policy techniques for reducing sample complexity. Empirically, we show with experiments", "on eight RL environments that the proposed approach is more sample efficient.", "We advocate for the use of a backtracking model for improving sample efficiency and exploration in RL.", "The method can easily be combined with popular RL algorithms like TRPO and soft actorcritic.", "Our results indicate that the recall traces generated by such models are able to accelerate learning on a variety of tasks.", "We also show that the method can be combined with automatic goal generation.", "The Appendix provides more analysis on the sensitivity of our method to various factors and ablations.", "We show that a random model is outperformed by a trained backtracking model, confirming its usefulness and present plots showing the effect of varying the length of recall traces.For future work, while we observed empirically that the method has practical value and could relate its workings from a variational perspective, but more could be done to improve our theoretical understanding of its convergence behavior and what kind of assumptions need to hold about the environment.", "It would also be interesting to investigate how the backtracking model can be combined with forward models from a more conventional model-based system.", "Return argmax(V (s)) ∀s ∈ B 7: end if" ]

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[ "A backward model of previous (state, action) given the next state, i.e. P(s_t, a_t | s_{t+1}), can be used to simulate additional trajectories terminating at states of interest! Improves RL learning efficiency." ]

[ "Prepositions are among the most frequent words.", "Good prepositional representation is of great syntactic and semantic interest in computational linguistics.", "Existing methods on preposition representation either treat prepositions as content words (e.g., word2vec and GloVe) or depend heavily on external linguistic resources including syntactic parsing, training task and dataset-specific representations.", "In this paper we use word-triple counts (one of the words is a preposition) to capture the preposition's interaction with its head and children.", "Prepositional embeddings are derived via tensor decompositions on a large unlabeled corpus. ", "We reveal a new geometry involving Hadamard products and empirically demonstrate its utility in paraphrasing of phrasal verbs.", "Furthermore, our prepositional embeddings are used as simple features to two challenging downstream tasks: preposition selection and prepositional attachment disambiguation.", "We achieve comparable to or better results than state of the art on multiple standardized datasets. ", "Prepositions are a linguistically closed class comprising some of the most frequent words; they play an important role in the English language since they encode rich syntactic and semantic information.", "Many preposition-related tasks still remain unsolved in computational linguistics because of their polysemous nature and flexible usage patterns.", "An accurate understanding and representation of prepositions' linguistic role is key to several important NLP tasks such as grammatical error correction and prepositional phrase attachment.", "A first-order approach is to represent prepositions as real-valued vectors via word embeddings such as word2vec BID21 and GloVe BID25 .Word", "embeddings have brought a renaissance in NLP research; they have been very successful in capturing word similarities as well as analogies (both syntactic and semantic) and are now mainstream in nearly all downstream NLP tasks (such as question-answering). Despite", "this success, no specific properties of word embeddings of prepositions have been highlighted in the literature. Indeed,", "many of the common prepositions have very similar vector representations as shown in TAB0 for preposition vectors trained using word2vec and GloVe.While this suggests that using available representations for prepositions diminishes the distinguishing feature between prepositions, one could hypothesize that this is primarily because standard word embedding algorithms treat prepositions no different from other content words such as verbs and nouns, i.e., embeddings are created based on co-occurrences with other words. However", ", prepositions are very frequent and co-occur with nearly all words, which means that their co-occurrence ought to be treated differently. Modern", "descriptive linguistic theory proposes to understand a preposition via its interactions with both the head (attachment) and child (complement) BID12 ; BID8 . This theory", "naturally suggests that one should count co-occurrences of a given preposition with pairs of neighboring words. One way of", "achieving this would be by considering a tensor of triples (word 1 , word 2 , preposition), where we do not restrict word 1 and word 2 to be head-and child-words; instead we model a preposition's interaction with all pairs of neighboring words via a slice of a tensor X -the slice is populated by word co-occurrences restricted to a context window of the specific preposition. Thus, the", "tensor dimension is V × V × K where V is the vocabulary and K is the number of prepositions; since K ≈ 50, we note that V K.Using such a representation, we find that the resulting tensor is low rank and extract embeddings for both preposition and non-preposition words using a combination of standard ideas from word representations (such as weighted spectral decomposition as in GloVe BID25 ) and tensor decompositions (alternating least squares (ALS) methods BID29 ). The preposition", "embeddings are discriminative, see preposition similarity of the tensor embedding in TAB0 . We demonstrate", "that the resulting representation for prepositions captures the core linguistic property of prepositions. We do this using", "both intrinsic evaluations and downstream tasks, where we provide new state-of-the-art results on well-known NLP tasks involving prepositions.Intrinsic evaluations: We show that the Hadamard product of the embeddings of a verb and a preposition closely approximates the representation of this phrasal verb's paraphrase. Example: v made", "v from ≈ v produced where represents the Hadamard product (i.e., pointwise multiplication) of two vectors; this approximation does not hold for the standard word embeddings of prepositions (word2vec or GloVe). We provide a mathematical", "interpretation for this new geometry as well as empirically demonstrate the generalization on a new data set of compositional phrasal verbs.Extrinsic evaluations: Our preposition embeddings are used as features for a simple classifier in two well-known challenging downstream NLP classification tasks. In both tasks, we perform", "comparable to or strictly better than the state-of-the-art on multiple standardized datasets.Preposition selection: The choice of prepositions significantly influences (and is governed by) the semantics of the context they occur in. Furthermore, the prepositional", "choice is usually very subtle (and consequently is one of the most frequent error types made by second language English speakers BID19 ). This task tests the choice of", "a preposition in a large set of contexts (7, 000 instances of both CoNLL-2013 and SE datasets BID26 ). Our approach achieves 6% and", "2% absolute improvement over the previous state-of-the-art on the respective datasets.Prepositional attachment disambiguation: Prepositional phrase attachment is a common cause of structural ambiguity in natural language. In the sentence \"Pierre Vinken", "joined the board as a voting member\", the prepositional phrase \"as a voting member\" can attach to either \"joined\" (the VP) or \"the board\" (the NP); in this case the VP attachment is correct. Despite extensive study over decades", "of research, prepositional attachment continues to be a major source of syntactic parsing errors BID4 ; Kummerfeld et al. (2012); BID7 . We use our prepositional representations", "as simple features to a standard classifier on this task. Our approach tested on a widely studied", "standard dataset BID2 achieves 89% accuracy, essentially the same performance as state-of-the-art (90% accuracy). It is noteworthy that while the stateof-the-art", "results are obtained with significant linguistic resources, including syntactic parsers and WordNet, our approach does not rely on these resources to achieve a comparable performance.We emphasize two aspects of our contributions:(1) It is folklore within the NLP community that representations via pairwise word counts capture much of the benefits of the unlabeled sentence-data; example: BID29 reports that their word representations via word-triple counts are better than others, but still significantly worse than regular word2vec representations. One of our main observations is that considering", "word-triple counts makes most (linguistic) sense when one of the words is a preposition. Furthermore, the sparsity of the corresponding tensor", "is no worse than the sparsity of the regular word co-occurrence matrix (since prepositions are so frequent and co-occur with essentially every word). Taken together, these two points strongly suggest the", "benefits of tensor representations in the context of prepositions.(2) The word and preposition representations via tensor", "decomposition are simple features leading to a standard classifier. In particular, we do not use syntactic parsing (which many", "prior methods have relied on) or handcrafted features BID26 or train task-specific representations on the annotated training dataset BID2 . The simplicity combined with our strong empirical results", "(new state-of-the-art results on long standing datasets) lends credence to the strength of the prepositional representations found via tensor decompositions.", "Co-occurrence counts of word pairs in sentences and the resulting word vector representations (embeddings) have revolutionalized NLP research.", "A natural generalization is to consider co-occurrence counts of word triples, resulting in a third order tensor.", "Partly due to the size of the tensor (a vocabulary of 1M, leads to a tensor with 10 18 entries!) and partly due to the extreme dynamic range of entries (including sparsity), word vector representations via tensor decompositions have largely been inferior to their lower order cousins (i.e., regular word embeddings).In", "this work, we trek this well-trodden terrain but restricting word triples to the scenario when one of the words is a preposition. This", "is linguistically justified, since prepositions are understood to model interactions between pairs of words. Numerically", ", this is also very well justified since the sparsity and dynamic range of the resulting tensor is no worse than the original matrix of pairwise co-occurrence counts; this is because prepositions are very frequent and co-occur with essentially every word in the vocabulary.Our intrinsic evaluations and new state of the art results in downstream evaluations lend strong credence to the tensor-based approach to prepositional representation. We expect", "our vector representations of prepositions to be widely used in more complicated downstream NLP tasks where prepositional role is crucial, including \"text to programs\" BID10 ." ]

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[ "This work is about tensor-based method for preposition representation training." ]

[ "A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. ", "Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. ", "Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation.", "In this paper, we use Hutchinson’s trace estimator to give a scalable unbiased estimate of the log-density. ", "The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures.", "We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling.", "We have presented FFJORD, a reversible generative model for high-dimensional data which can compute exact log-likelihoods and can be sampled from efficiently.", "Our model uses continuoustime dynamics to produce a generative model which is parameterized by an unrestricted neural network.", "All required quantities for training and sampling can be computed using automatic differentiation, Hutchinson's trace estimator, and black-box ODE solvers.", "Our model stands in contrast to other methods with similar properties which rely on restricted, hand-engineered neural network architectures.", "We demonstrated that this additional flexibility allows our approach to achieve on-par or improved performance on density estimation and variational inference.We believe there is much room for further work exploring and improving this method.", "FFJORD is empirically slower to evaluate than other reversible models like Real NVP or Glow, so we are interested specifically in ways to reduce the number of function evaluations used by the ODE-solver without hurting predictive performance.", "Advancements like these will be crucial in scaling this method to even higher-dimensional datasets." ]

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[ "We use continuous time dynamics to define a generative model with exact likelihoods and efficient sampling that is parameterized by unrestricted neural networks." ]

[ "We propose a non-adversarial feature matching-based approach to train generative models.", "Our approach, Generative Feature Matching Networks (GFMN), leverages pretrained neural networks such as autoencoders and ConvNet classifiers to perform feature extraction.", "We perform an extensive number of experiments with different challenging datasets, including ImageNet.", "Our experimental results demonstrate that, due to the expressiveness of the features from pretrained ImageNet classifiers, even by just matching first order statistics, our approach can achieve state-of-the-art results for challenging benchmarks such as CIFAR10 and STL10.", "One of the key research focus in unsupervised learning is the training of generative methods that can model the observed data distribution.", "Good progress has been made in recent years with the advent of new approaches such as generative adversarial networks (GANs) BID10 and variational autoencoders (VAE) BID19 which use deep neural networks as building blocks.", "Both methods have advantages and disadvantages, and a significant number of recent works focus on addressing their issues BID20 BID5 .", "While the main disadvantage of VAEs is the generation of blurred images, the main issue with GANs is the training instability due to the adversarial learning.Feature matching has been explored to improve the stability of GANs BID41 .", "The key idea in feature matching GANs (FM-GANs) is to use the discriminator network as a feature extractor, and guide the generator to generate data that matches the feature statistics of the real data.", "Concretely, the objective function of the generator in FM-GAN consists in minimizing the mean squared error of the average features of a minibatch of generated data and a minibatch of real data.", "The features are extracted from one single layer of the discriminator.", "FM-GAN is somewhat similar to methods that use maximum mean discrepancy (MMD) BID11 BID12 .", "However, while in FM-GAN the objective is to match the mean of the extracted features, in MMD-based generative models BID9 , one normally aims to match all the moments of the two distributions using a Gaussian kernel.", "Although MMD-based generative models have strong theoretical guarantees, these models normally perform much worse than GANs on challenging benchmarks BID23 .In", "this work, we focus on answering the following research question: can we train effective generative models by performing feature matching on features extracted from a pretrained neural networks? In", "other words, we would like to know if adversarial training of the feature extractor together with the generator is a requirement for training effective generators. Towards", "answering this question, we propose Generative Feature Matching Networks (GFMN), a new feature matching-based approach to train generative models that uses features from pretrained neural networks, breaking away from the problematic min/max game completely. Some interesting", "properties of the proposed method include: (1) the loss function is directly correlated to the generated image quality; (2) mode collapsing is not an issue; (3) the same pretrained feature extractor can be used across different datasets; and (4) both supervised (classifiers) and unsupervised (autoencoder) models can be used as feature extractors.We perform an extensive number of experiments with different challenging datasets, including ILSVRC2012 (henceforth Imagenet) BID37 . We demonstrate that", ", due to the expressiveness of the features from pretrained Imagenet classifiers, even by just matching first order statistics, our approach can achieve state-of-the-art results for challenging benchmarks such as CIFAR10 and STL10. Moreover, we show", "that the same feature extractor is effective across different datasets. The main contributions", "of this work can be summarized as follows: (1) We propose a new effective feature matching-based approach to train generative models that does not use adversarial learning, have stable training and achieves state-of-the-art results; (2) We propose an ADAM-based moving average method that allows effective training with small minibatches; (3) Our extensive quantitative and qualitative experimental results demonstrate that pretrained autoencoders and deep convolutional net (DCNN) classifiers can be effectively used as feature extractors for the purpose of learning generative models.", "This work is driven towards answering the question of whether one can train effective generative models by performing feature matching on features extracted from pretrained neural networks.", "The goal is to avoid adversarial training, breaking away from the problematic min/max game completely.", "According to our experimental results, the answer to our research question is yes.", "We achieve successful non-adversarial training of generative feature matching networks by introducing different key ingredients: (1) a more robust way to compute the moving average of the mean features by using ADAM optimizer, which allows us to use small minibatches; (2) the use of features from all layers of pretrained neural networks; (3) the use of features from multiple neural networks at the same time (VGG19 + Resnet18); and (4) the initialization of the generator network.Our quantitative results in Tab.", "3 show that GFMN achieves better or similar results compared to the state-of-the-art Spectral GAN (SN-GAN) BID30 for both CIFAR10 and STL10.", "This is an impressive result for a non-adversarial feature matching-based approach that uses pretrained cross-domain feature extractors and has stable training.", "When compared to other MMD approaches BID23 3.47±.03", "GMMN+AE BID23 3.94±.04", "VAE BID27 (Berthelot et al., 2017) 5.62 MMD GAN BID23 6.17±.07", "MMD dist GAN BID2 6.39±.04 40.2 / -WGAN BID30 6.41±.11 42.6 / -7.57±.10 64.2 MMDrq GAN BID2 6.51±.03 39.9 / -WGAN-GP BID30 6.68±.06 40.2 / -8.42±.13 55.1 / -McGAN 6.97±.10", "SN-GANs BID30 7.58±.12 25.5 / -8.79±.14 43.2 / -MoLM-1024 BID36 7.55±.08 25.0 / 20.3 MoLM-1536 BID36 7.90±.10 23.3 / 18.9 BID9 BID23 BID2 BID36 , GFMN presents important distinctions (some of them already listed in Sec. 3) which make it an attractive alternative.", "Compared to GMMN and GMMN+AE , we can see in TAB2 that GFMN achieves far better results.", "In Appendix A.10, we also show a qualitative comparison between GFMN and GMMN results.", "The main reason why GFMN results are significantly better than GMMN is because GFMN uses a strong, robust kernel function (a pretrained DCNN), which, together with our AMA trick, allows the training with small minibatches.", "On the other hand, the Gaussian kernel used in GMMN requires a very large minibatch size in order to work well, which is impractical due to memory limitations and computational cost.", "Compared to recent adversarial MMD methods (MMD GAN) BID23 BID2 ) GFMN also presents significantly better results while avoiding the problematic min/max game.", "GFMN achieves similar results to the Method of Learned Moments (MoLM) BID36 , while using a much smaller number of features to perform matching.", "The best performing model from BID36 , MoLM-1536, uses around 42 million moments to train the CIFAR10 generator, while our best GFMN model uses around 850 thousand moments/features only, almost 50x less.", "In other words, MoLM-1536 can be used in large-scale environments only, while GFMN can be used in single GPU environments.One may argue that the best results from GFMN are obtained with feature extractors that were trained in a supervised manner (classifiers).", "However, there are two important points to note: (1) we use a cross domain feature extractor and do not use labels from the target datasets (CIFAR10, STL10, MNIST, CelebA); (2) since the accuracy of the classifier does not seem to be the most important factor for generating good features (VGG19 classifier produces better features although it is less accurate than Resnet18, see Appendix A.3); we are confident that GFMN will also achieve state-of-the-art results when trained with features from classifiers trained using unsupervised methods such as the one recently proposed by BID4 .", "In this work, we introduced GFMN, an effective non-adversarial approach to train generative models.", "GFMNs are demonstrated to achieve state-of-the-art results while avoiding the challenge of defining and training an adversarial discriminator.", "Our feature extractors can be easily obtained and provide for a robust and stable training of our generators.", "Some interesting open questions include: what type of feature extractors other than classifiers and auto-encoders are good for GFMN?", "What architecture designs are better suited for the purpose of feature extraction in GFMN?A", "APPENDIX" ]

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[ "A new non-adversarial feature matching-based approach to train generative models that achieves state-of-the-art results." ]

[ "We propose a novel architecture for k-shot classification on the Omniglot dataset.", "Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks.", "Prototypical networks learn a map between images and embedding vectors, and use their clustering for classification.", "In our model, a part of the encoder output is interpreted as a confidence region estimate about the embedding point, and expressed as a Gaussian covariance matrix.", "Our network then constructs a direction and class dependent distance metric on the embedding space, using uncertainties of individual data points as weights.", "We show that Gaussian prototypical networks are a preferred architecture over vanilla prototypical networks with an equivalent number of parameters.", "We report results consistent with state-of-the-art performance in 1-shot and 5-shot classification both in 5-way and 20-way regime on the Omniglot dataset.", "We explore artificially down-sampling a fraction of images in the training set, which improves our performance.", "Our experiments therefore lead us to hypothesize that Gaussian prototypical networks might perform better in less homogeneous, noisier datasets, which are commonplace in real world applications.", "In this paper we proposed Gaussian prototypical networks for few-shot classification -an improved architecture based on prototypical networks BID16 .", "We tested our models on the Omniglot dataset, and explored different approaches to generating a covariance matrix estimate together with an embedding vector.", "We showed that Gaussian prototypical networks outperform vanilla prototypical networks with a comparable number of parameters, and therefore that our architecture choice is beneficial.", "We found that estimating a single real number on top of an embedding vector works better than estimating a diagonal, or a full covariance matrix.", "We suspect that lower quality, less homogeneous datasets might prefer a more complex covariance matrix estimate.Contrary to BID16 , we found that the best results are obtained by training in the 1-shot regime.", "Our results are consistent with state-of-the-art in 1-shot and 5-shot classification both in Figure 5 : Predicted covariances for the original test set and a partially down-sampled version of it.", "The Gaussian network learned to down-weight damaged examples by predicting a higher s, as apparent from the heavier tail of the yellow distribution.", "The distributions are aligned together, as only the difference between the leading edge and a value influence classification.5-way and 20-way regime on the Omniglot dataset.", "Especially for 5-way classification, our results are very close to perfect performance.We got better accuracies (in particular for (k > 1)-shot classification) by artificially down-sampling fractions of our training dataset, encouraging the network to fully utilize covariance estimates.", "We hypothesize that the ability to learn the embedding as well as its uncertainty would be even more beneficial for poorer-quality, heterogeneous datasets, which are commonplace in real world applications.", "There, down-weighting some data points might be crucial for faithful classification.", "This is supported by our experiments with down-sampling Omniglot." ]

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[ "A novel architecture for few-shot classification capable of dealing with uncertainty." ]

[ "We show that the output of a (residual) CNN with an appropriate prior over the weights and biases is a GP in the limit of infinitely many convolutional filters, extending similar results for dense networks.", "For a CNN, the equivalent kernel can be computed exactly and, unlike \"deep kernels\", has very few parameters: only the hyperparameters of the original CNN.", "Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass through the original CNN with only one filter per layer.", "The kernel equivalent to a 32-layer ResNet obtains 0.84% classification error on MNIST, a new record for GP with a comparable number of parameters.", "Convolutional Neural Networks (CNNs) have powerful pattern-recognition capabilities that have recently given dramatic improvements in important tasks such as image classification BID13 .", "However, as CNNs are increasingly being applied in real-world, safety-critical domains, their vulnerability to adversarial examples BID27 BID15 , and their poor uncertainty estimates are becoming increasingly problematic.", "Bayesian inference is a theoretically principled and demonstrably successful BID26 BID7 framework for learning in the face of uncertainty, which may also help to address the problems of adversarial examples BID9 .", "Unfortunately, Bayesian inference in CNNs is extremely difficult due to the very large number of parameters, requiring highly approximate factorised variational approximations BID1 BID8 , or requiring the storage BID16 ) of large numbers of posterior samples (Welling & Teh, 2011; BID19 .Other", "methods such as those based on Gaussian Processes (GPs) are more amenable to Bayesian inference, allowing us to compute the posterior uncertainty exactly BID24 . This", "raises the question of whether it might be possible to combine the pattern-recognition capabilities of CNNs with exact probabilistic computations in GPs. Two", "such approaches exist in the literature. First", ", deep convolutional kernels (Wilson et al., 2016 ) parameterise a GP kernel using the weights and biases of a CNN, which is used to embed the input images into some latent space before computing their similarity. The", "CNN parameters of the resulting kernel then have to be optimised by gradient descent. However", ", the large number of kernel parameters in the CNN reintroduces the risk of overconfidence and overfitting. To avoid", "this risk, we need to infer a posterior over the CNN kernel parameters, which is as difficult as directly inferring a posterior over the parameters of the original CNN. Second,", "it is possible to define a convolutional GP BID22 or a Furthermore, we show that two properties of the GP kernel induced by a CNN allow it to be computed very efficiently. First,", "in previous work it was necessary to compute the covariance matrix for the output of a single convolutional filter applied at all possible locations within a single image BID22 , which was prohibitively computationally expensive. In contrast", ", under our prior, the downstream weights are independent with zero-mean, which decorrelates the contribution from each location, and implies that it is necessary only to track the patch variances, and not their covariances. Second, while", "it is still necessary to compute the variance of the output of a convolutional filter applied at all locations within the image, the specific structure of the kernel induced by the CNN means that the variance at every location can be computed simultaneously and efficiently as a convolution.Finally, we empirically demonstrate the performance increase coming from adding translationinvariant structure to the GP prior. Without computing", "any gradients, and without augmenting the training set (e.g. using translations), we obtain 0.84% error rate on the MNIST classification benchmark, setting a new record for nonparametric GP-based methods.", "Borovykh (2018) also suggests that a CNN exhibits GP behaviour.", "However, they take the infinite limit with respect to the filter size, not the number of filters.", "Thus, their infinite network is inapplicable to real data which is always of finite dimension.Finally, there is a series of papers analysing the mean-field behaviour of deep NNs and CNNs which aims to find good random initializations, i.e. those that do not exhibit vanishing or exploding gradients or activations BID25 Yang & Schoenholz, 2017) .", "Apart from their very different focus, the key difference to our work is that they compute the variance for a single training-example, whereas to obtain the GPs kernel, we additionally need to compute the output covariances for different training/test examples (Xiao et al., 2018) .", "We have shown that deep Bayesian CNNs with infinitely many filters are equivalent to a GP with a recursive kernel.", "We also derived the kernel for the GP equivalent to a CNN, and showed that, in handwritten digit classification, it outperforms all previous GP approaches that do not incorporate a parametric NN into the kernel.", "Given that most state-of-the-art neural networks incorporate structure (convolutional or otherwise) into their architecture, the equivalence between CNNs and GPs is potentially of considerable practical relevance.", "In particular, we hope to apply GP CNNs in domains as widespread as adversarial examples, lifelong learning and k-shot learning, and we hope to improve them by developing efficient multi-layered inducing point approximation schemes." ]

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[ "We show that CNNs and ResNets with appropriate priors on the parameters are Gaussian processes in the limit of infinitely many convolutional filters." ]

[ "We present an end-to-end design methodology for efficient deep learning deployment.", "Unlike previous methods that separately optimize the neural network architecture, pruning policy, and quantization policy, we jointly optimize them in an end-to-end manner.", "To deal with the larger design space it brings, we train a quantization-aware accuracy predictor that fed to the evolutionary search to select the best fit.", "We first generate a large dataset of <NN architecture, ImageNet accuracy> pairs without training each architecture, but by sampling a unified supernet.", "Then we use these data to train an accuracy predictor without quantization, further using predictor-transfer technique to get the quantization-aware predictor, which reduces the amount of post-quantization fine-tuning time.", "Extensive experiments on ImageNet show the benefits of the end-to-end methodology: it maintains the same accuracy (75.1%) as ResNet34 float model while saving 2.2× BitOps comparing with the 8-bit model; we obtain the same level accuracy as MobileNetV2+HAQ while achieving 2×/1.3× latency/energy saving; the end-to-end optimization outperforms separate optimizations using ProxylessNAS+AMC+HAQ by 2.3% accuracy while reducing orders of magnitude GPU hours and CO2 emission.\n", "Deep learning has prevailed in many real-world applications like autonomous driving, robotics, and mobile VR/AR, while efficiency is the key to bridge research and deployment.", "Given a constrained resource budget on the target hardware (e.g., latency, model size, and energy consumption), it requires an elaborated design of network architecture to achieve the optimal performance within the constraint.", "Traditionally, the deployment of efficient deep learning can be split into model architecture design and model compression (pruning and quantization).", "Some existing works (Han et al., 2016b; have shown that such a sequential pipeline can significantly reduce the cost of existing models.", "Nevertheless, careful hyper-parameter tuning is required to obtain optimal performance (He et al., 2018) .", "The number of hyper-parameters grows exponentially when we consider the three stages in the pipeline together, which will soon exceed acceptable human labor bandwidth.", "To tackle the problem, recent works have applied AutoML techniques to automate the process.", "Researchers proposed Neural Architecture Search (NAS) (Zoph & Le, 2017; Real et al., 2018; Liu et al., 2018a; b; Zhong et al., 2018; Elsken et al., 2018; Cai et al., 2018a; b; Luo et al., 2018; Kamath et al., 2018) to automate the model design, outperforming the human-designed models by a large margin.", "Based on a similar technique, researchers adopt reinforcement learning to compress the model by automated pruning (He et al., 2018) and automated quantization .", "However, optimizing these three factors in separate stages will lead to sub-optimal results: e.g., the best network architecture for the full-precision model is not necessarily the optimal one after pruning and quantization.", "Besides, this three-step strategy also requires considerable search time and energy consumption (Strubell et al., 2019) .", "Therefore, we need a joint, end-to-end solution to optimize the deep learning model for a certain hardware platform.", "However, directly extending existing AutoML techniques to our end-to-end model optimization setting can be problematic.", "Firstly, the joint search space is cubic compared to stage-wise search, making the search difficult.", "Introducing pruning and quantization into the pipeline will also greatly increase the total search time, as both of them require time-consuming post-processing (e.g., finetuning) to get accuracy approximation Yang et al., 2018) .", "Moreover, the search space of each step in pipeline is hard to be attested to be disentangle, and each step has its own optimization objective (eg. acc, latency, energy), so that the final policy of the pipeline always turns out to be sub-optimal.", "To this end, we proposed EMS, an end-to-end design method to solve this problem.", "Our approach is derived from one-shot NAS (Guo et al., 2019; Brock et al., 2018; Pham et al., 2018; Bender et al., 2018; Liu et al., 2019a; Yu & Huang, 2019) .", "We reorganize the traditional pipeline of \"model design→pruning→quantization\" into \"architecture search + mixed-precision search\".", "The former consists of both coarse-grained architecture search (topology, operator choice, etc.) and fine-grained channel search (replacing the traditional channel pruning (He et al., 2017) ).", "The latter aims to find the optimal mixed-precision quantization policy trading off between accuracy and resource consumption.", "We work on both aspects to address the search efficiency.", "For architecture search, we proposed to train a highly flexible super network that supports not only the operator change but also fine-grained channel change, so that we can perform joint search over architecture and channel number.", "For the mixed-precision search, since quantized accuracy evaluation requires time-consuming fine-tuning, we instead use a predictor to predict the accuracy after quantization.", "Nevertheless, collecting data pairs for predictor training could be expensive (also requires fine-tuning).", "We proposed PredictorTransfer Technique to dramatically improve the sample efficiency.", "Our quantization-aware accuracy predictor is transferred from full-precision accuracy predictor, which is firstly trained on cheap data points collected using our flexible super network (evaluation only, no training required).", "Once the predictor P (arch, prune, quantization) is trained, we can perform search at ultra fast speed just using the predictor.", "With the above design, we are able to efficiently perform joint search over model architecture, channel number, and mixed-precision quantization.", "The predictor can also be used for new hardware and deployment scenarios, without training the whole system again.", "Extensive experiment shows the superiority of our method: while maintaining the same level of accuracy (75.1%) with ResNet34 float model, we achieve 2.2× reduction in BitOps compared to the 8-bit version; we obtain the same level accuracy as MobileNetV2+HAQ, and achieve 2×/1.3× latency/energy saving; our models outperform separate optimizations using ProxylessNAS+AMC+HAQ by 2.3% accuracy under same latency constraints, while reducing orders of magnitude GPU hours and CO 2 emission.", "The contributions of this paper are:", "• We devise an end-to-end methodology EMS to jointly perform NAS-pruning-quantization, thus unifying the conventionally separated stages into an integrated solution.", "• We propose a predictor-transfer method to tackle the high cost of the quantization-aware accuracy predictor's dataset collection NN architecture, quantization policy, accuracy .", "• Such end-to-end method can efficiently search efficient models.", "With the supernet and the quantization-aware accuracy predictor, it only takes minutes to search a compact model for a new platform, enabling automatic model adjustment in diverse deployment scenarios.", "We propose EMS, an end-to-end design method for architecting mixed-precision model.", "Unlike former works that decouple into separated stages, we directly search for the optimal mixed-precision architecture without multi-stage optimization.", "We use predictor-base method that can have no extra evaluation for target dataset, which greatly saves GPU hours for searching under an upcoming scenario, thus reducing marginally CO 2 emission and cloud compute cost.", "To tackle the problem for high expense of data collection, we propose predictor-transfer technique to make up for the limitation of data.", "Comparisons with state-of-the-art models show the necessity of joint optimization and prosperity of our end-to-end design method." ]

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[ "We present an end-to-end design methodology for efficient deep learning deployment. " ]

[ "Distributed optimization is vital in solving large-scale machine learning problems.", "A widely-shared feature of distributed optimization techniques is the requirement that all nodes complete their assigned tasks in each computational epoch before the system can proceed to the next epoch.", "In such settings, slow nodes, called stragglers, can greatly slow progress.", "To mitigate the impact of stragglers, we propose an online distributed optimization method called Anytime Minibatch.", "In this approach, all nodes are given a fixed time to compute the gradients of as many data samples as possible.", "The result is a variable per-node minibatch size.", "Workers then get a fixed communication time to average their minibatch gradients via several rounds of consensus, which are then used to update primal variables via dual averaging.", "Anytime Minibatch prevents stragglers from holding up the system without wasting the work that stragglers can complete.", "We present a convergence analysis and analyze the wall time performance.", "Our numerical results show that our approach is up to 1.5 times faster in Amazon EC2 and it is up to five times faster when there is greater variability in compute node performance.", "The advent of massive data sets has resulted in demand for solutions to optimization problems that are too large for a single processor to solve in a reasonable time.", "This has led to a renaissance in the study of parallel and distributed computing paradigms.", "Numerous recent advances in this field can be categorized into two approaches; synchronous Dekel et al. (2012) ; Duchi et al. (2012) ; Tsianos & Rabbat (2016) ; Zinkevich et al. (2010) and asynchronous Recht et al. (2011); Liu et al. (2015) .", "This paper focuses on the synchronous approach.", "One can characterize synchronization methods in terms of the topology of the computing system, either master-worker or fully distributed.", "In a master-worker topology, workers update their estimates of the optimization variables locally, followed by a fusion step at the master yielding a synchronized estimate.", "In a fully distributed setting, nodes are sparsely connected and there is no obvious master node.", "Nodes synchronize their estimates via local communications.", "In both topologies, synchronization is a key step.Maintaining synchronization in practical computing systems can, however, introduce significant delay.", "One cause is slow processing nodes, known as stragglers Dean et al. (2012) ; Yu et al. (2017) ; Tandon et al. (2017) ; Lee et al. (2018) ; Pan et al. (2017) ; S. Dutta & Nagpurkar (2018) .", "A classical requirement in parallel computing is that all nodes process an equal amount of data per computational epoch prior to the initiation of the synchronization mechanism.", "In networks in which the processing speed and computational load of nodes vary greatly between nodes and over time, the straggling nodes will determine the processing time, often at a great expense to overall system efficiency.", "Such straggler nodes are a significant issue in cloud-based computing systems.", "Thus, an important challenge is the design of parallel optimization techniques that are robust to stragglers.To meet this challenge, we propose an approach that we term Anytime MiniBatch (AMB).", "We consider a fully distributed topologyand consider the problem of stochastic convex optimization via dual averaging Nesterov (2009); Xiao (2010) .", "Rather than fixing the minibatch size, we fix the computation time (T ) in each epoch, forcing each node to \"turn in\" its work after the specified fixed time has expired.", "This prevents a single straggler (or stragglers) from holding up the entire network, while allowing nodes to benefit from the partial work carried out by the slower nodes.", "On the other hand, fixing the computation time means that each node process a different amount of data in each epoch.", "Our method adapts to this variability.", "After computation, all workers get fixed communication time (T c ) to share their gradient information via averaging consensus on their dual variables, accounting for the variable number of data samples processed at each node.", "Thus, the epoch time of AMB is fixed to T + T c in the presence of stragglers and network delays.We analyze the convergence of AMB, showing that the online regret achieves O( √m ) performance, which is optimal for gradient based algorithms for arbitrary convex loss Dekel et al. (2012) .", "In here, m is the expected sum number of samples processed across all nodes.", "We further show an upper bound that, in terms of the expected wall time needed to attain a specified regret, AMB is O( √ n − 1) faster than methods that use a fixed minibatch size under the assumption that the computation time follows an arbitrary distribution where n is the number of nodes.", "We provide numerical simulations using Amazon Elastic Compute Cloud (EC2) and show that AMB offers significant acceleration over the fixed minibatch approach.", "We proposed a distributed optimization method called Anytime MiniBatch.", "A key property of our scheme is that we fix the computation time of each distributed node instead of minibatch size.", "Therefore, the finishing time of all nodes are deterministic and does not depend on the slowest processing node.", "We proved the convergence rate of our scheme in terms of the expected regret bound.", "We performed numerical experiments using Amazon EC2 and showed our scheme offers significant improvements over fixed minibatch schemes.", "A AMB ALGORITHM", "In this section, we present additional details regarding the numerical results of Section 6 of the main paper as well as some new results.", "In Appendix I.1, we detail the network used in Section 6 and, for a point of comparison, implement the same computations in a master-worker network topology.", "In Appendix I.2, we model the compute times of the nodes as shifted exponential random variables and, under this model, present results contrasting AMB and FMB performance for the linear regression problem.", "In Appendix I.3 we present an experimental methodology for simulating a wide variety of straggler distributions in EC2.", "By running background jobs on some of the EC2 nodes we slow the foreground job of interest, thereby simulating a heavily-loaded straggler node.", "Finally, in Appendix I.4, we present another experiment in which we also induce stragglers by forcing the nodes to make random pauses between two consecutive gradient calculations.", "We present numerical results for both settings as well, demonstrating the even greater advantage of AMB versus FMB when compared to the results presented in Section 6." ]

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[ "Accelerate distributed optimization by exploiting stragglers." ]

[ "Many machine learning image classifiers are vulnerable to adversarial attacks, inputs with perturbations designed to intentionally trigger misclassification.", "Current adversarial methods directly alter pixel colors and evaluate against pixel norm-balls: pixel perturbations smaller than a specified magnitude, according to a measurement norm.", "This evaluation, however, has limited practical utility since perturbations in the pixel space do not correspond to underlying real-world phenomena of image formation that lead to them and has no security motivation attached.", "Pixels in natural images are measurements of light that has interacted with the geometry of a physical scene.", "As such, we propose a novel evaluation measure, parametric norm-balls, by directly perturbing physical parameters that underly image formation.", "One enabling contribution we present is a physically-based differentiable renderer that allows us to propagate pixel gradients to the parametric space of lighting and geometry.", "Our approach enables physically-based adversarial attacks, and our differentiable renderer leverages models from the interactive rendering literature to balance the performance and accuracy trade-offs necessary for a memory-efficient and scalable adversarial data augmentation workflow.", "Research in adversarial examples continues to contribute to the development of robust (semi-)supervised learning (Miyato et al., 2018) , data augmentation BID14 Sun et al., 2018) , and machine learning understanding BID24 .", "One important caveat of the approach pursued by much of the literature in adversarial machine learning, as discussed recently (Goodfellow, original image parametric (lighting) texture color [Athalye 17] multi-step pixel [Moosavi Dezfooli 16] parametric (geometry) one-step pixel [Goodfellow 14] Figure 1: Traditional pixel-based adversarial attacks yield unrealistic images under a larger perturbation (L ∞ -norm ≈ 0.82), however our parametric lighting and geometry perturbations output more realistic images under the same norm (more results in Appendix A)." ]

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[ "Enabled by a novel differentiable renderer, we propose a new metric that has real-world implications for evaluating adversarial machine learning algorithms, resolving the lack of realism of the existing metric based on pixel norms." ]

[ "Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences.", "In spite of their relevance, the computational properties of these alternatives have not yet been fully explored.", "We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016).", "We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data.", "In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete.", "Our study also reveals some minimal sets of elements needed to obtain these completeness results.", "There is an increasing interest in designing neural network architectures capable of learning algorithms from examples BID6 BID7 BID10 BID11 BID13 BID4 .", "A key requirement for any such an architecture is thus to have the capacity of implementing arbitrary algorithms, that is, to be Turing complete.", "Turing completeness often follows for these networks as they can be seen as a control unit with access to an unbounded memory; as such, they are capable of simulating any Turing machine.On the other hand, the work by Siegelmann & Sontag (1995) has established a different way of looking at the Turing completeness of neural networks.", "In particular, their work establishes that recurrent neural networks (RNNs) are Turing complete even if only a bounded number of resources (i.e., neurons and weights) is allowed.", "This is based on two conditions: (1) the ability of RNNs to compute internal dense representations of the data, and (2) the mechanisms they use for accessing such representations.", "Hence, the view proposed by Siegelmann & Sontag shows that it is possible to release the full computational power of RNNs without arbitrarily increasing its model complexity.Most of the early neural architectures proposed for learning algorithms correspond to extensions of RNNs -e.g., Neural Turing Machines BID6 ) -, and hence they are Turing complete in the sense of Siegelmann & Sontag.", "However, a recent trend has shown the benefits of designing networks that manipulate sequences but do not directly apply a recurrence to sequentially process their input symbols.", "Architectures based on attention or convolutions are two prominent examples of this approach.", "In this work we look at the problem of Turing completenessà la Siegelmann & Sontag for two of the most paradigmatic models exemplifying these features: the Transformer (Vaswani et al., 2017) and the Neural GPU BID11 .The", "main contribution of our paper is to show that the Transformer and the Neural GPU are Turing complete based on their capacity to compute and access internal dense representations of the data. In", "particular, neither the Transformer nor the Neural GPU requires access to an external additional memory to become Turing complete. Thus", "the completeness holds for bounded architectures (bounded number of neurons and parameters). To prove", "this we assume that internal activations are represented as rational numbers with arbitrary precision. For the", "case of the Transformer we provide a direct simulation of a Turing machine, while for the case of the Neural GPU our result follows by simulating standard sequence-to-sequence RNNs. Our study", "also reveals some minimal sets of elements needed to obtain these completeness results. The computational", "power of Transformers and of Neural GPUs has been compared in the current literature BID4 , but both are only informally used. Our paper provides", "a formal way of approaching this comparison.For the sake of space, we only include sketch of some proofs in the body of the paper. The details for every", "proof can be found in the appendix.Background work The study of the computational power of neural networks can be traced back to BID14 which established an analogy between neurons with hard-threshold activations and first order logic sentences, and BID12 that draw a connection between neural networks and finite automata. As mentioned earlier,", "the first work showing the Turing completeness of finite neural networks with linear connections was carried out by BID18 1995) . Since being Turing complete", "does not ensure the ability to actually learn algorithms in practice, there has been an increasing interest in enhancing RNNs with mechanisms for supporting this task. One strategy has been the addition", "of inductive biases in the form of external memory, being the Neural Turing Machine (NTM) BID6 ) a paradigmatic example. To ensure that NTMs are differentiable", ", their memory is accessed via a soft attention mechanism . Other examples of architectures that", "extend RNNs with memory are the Stack-RNN BID10 , and the (De)Queue-RNNs BID7 . By Siegelmann & Sontag's results, all", "these architectures are Turing complete.The Transformer architecture (Vaswani et al., 2017) is almost exclusively based on the attention mechanism, and it has achieved state of the art results on many language-processing tasks. While not initially designed to learn", "general algorithms, BID4 have advocated the need for enriching its architecture with several new features as a way to learn general procedures in practice. This enrichment is motivated by the empirical", "observation that the original Transformer architecture struggles to generalize to input of lengths not seen during training. We, in contrast, show that the original Transformer", "architecture is Turing complete, based on different considerations. These results do not contradict each other, but show", "the differences that may arise between theory and practice. For instance, BID4 assume fixed precision, while we", "allow arbitrary internal precision during computation. We think that both approaches can be complementary", "as our theoretical results can shed light on what are the intricacies of the original architecture, which aspects of it are candidates for change or improvement, and which others are strictly needed. For instance, our proof uses hard attention while", "the Transformer is often trained with soft attention (Vaswani et al., 2017) . See Section 3.3 for a discussion on these differences", ".The Neural GPU is an architecture that mixes convolutions and gated recurrences over tridimensional tensors. It has been shown that NeuralGPUs are powerful enough", "to learn decimal multiplication from examples BID5 , being the first neural architecture capable of solving this problem end-to-end. The similarity of Neural GPUs and cellular automata has", "been used as an argument to state the Turing completeness of the architecture BID11 BID16 . Cellular automata are Turing complete (Smith III, 1971;", "BID15 and their completeness is established assuming an unbounded number of cells. In the Neural GPU architecture, in contrast, the number", "of cells that can be used during a computation is proportional to the size of the input sequence BID11 . One can cope with the need for more cells by padding the", "Neural GPU input with additional (dummy) symbols, as much as needed for a particular computation. Nevertheless, this is only a partial solution, as for a", "Turing-complete model of computation, one cannot decide a priori how much memory is needed to solve a particular problem. Our results in this paper are somehow orthogonal to the", "previous argument; we show that one can leverage the dense representations of the Neural GPU cells to obtain Turing completeness without requiring to add cells beyond the ones used to store the input." ]

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[ "We show that the Transformer architecture and the Neural GPU are Turing complete." ]

[ "It is usually hard for a learning system to predict correctly on the rare events, and there is no exception for segmentation algorithms.", "Therefore, we hope to build an alarm system to set off alarms when the segmentation result is possibly unsatisfactory.", "One plausible solution is to project the segmentation results into a low dimensional feature space, and then learn classifiers/regressors in the feature space to predict the qualities of segmentation results.", "In this paper, we form the feature space using shape feature which is a strong prior information shared among different data, so it is capable to predict the qualities of segmentation results given different segmentation algorithms on different datasets.", "The shape feature of a segmentation result is captured using the value of loss function when the segmentation result is tested using a Variational Auto-Encoder(VAE).", "The VAE is trained using only the ground truth masks, therefore the bad segmentation results with bad shapes become the rare events for VAE and will result in large loss value.", "By utilizing this fact, the VAE is able to detect all kinds of shapes that are out of the distribution of normal shapes in ground truth (GT).", "Finally, we learn the representation in the one-dimensional feature space to predict the qualities of segmentation results.", "We evaluate our alarm system on several recent segmentation algorithms for the medical segmentation task.", "The segmentation algorithms perform differently on different datasets, but our system consistently provides reliable prediction on the qualities of segmentation results.\n", "A segmentation algorithm usually fails on the rare events, and it is hard to fully avoid such issue.", "The rare events may occur due to the limited number of training data.", "To handle it, the most intuitive way is to increase the number of training data.", "However, the labelled data is usually hard to collect, e.g., to fully annotate a 3D medical CT scan requires professional radiology knowledge and several hours of work.", "In addition, the human labelling is unable to cover all possible cases.", "Previously, various methods have been proposed to make better use of training data, like sampling strategies paying more attention to the rare events BID17 .", "But still it may fail on the rare events which never occur in the training data.", "Another direction is to increase the robustness of the segmentation algorithm to the rare events.", "BID6 proposed the Bayesian neural network which can model the uncertainty as an additional loss to make the algorithm more robust to noisy data.", "These kinds of methods make the algorithm insensitive to certain types of perturbations, but the algorithms may still fail on other perturbations.Since it is hard to completely prevent the segmentation algorithm from failure, we consider to detect the failure instead: build up an alarm system cooperating with the segmentation algorithm, which will set off alarms when the system finds that the segmentation result is not good enough.", "This task is also called as quality assessment.", "Several works have been proposed in this field.", "BID5 applied Bayesian neural network to capture the uncertainty of the segmentation result and set off alarm based on that uncertainty.", "However, this system also suffers from rare events since the segmentation algorithms often make mistakes confidently on some rare events (Xie et al., 2017) .", "BID8 provided an effective way by projecting the segmentation results into a feature space and learn from this low dimension space.", "They manually design several heuristic features, e.g., size, intensity, and assume such features would indicate the quality of the segmentation results.", "After projecting the segmentation results into the feature space, they learned a classifier to CT image GT Recon-Prediction Recon-GT Prediction Entropy Alea-Uncertainty Epis-Uncertainty Figure 1 : The visualize on an NIH CT dataset for pancreas segmentation.", "The figures ReconPrediction and Recon-GT are reconstruction results from prediction and GT by VAE network respectively.", "The Dice score between the GT and prediction is 47.06 while the Dice score between the prediction and Recon-Prediction is 47.25.", "In our method, we use the later Dice score to predict the former real Dice score which is usually unknown at inference phase in real applications.", "This case shows how these two Dice scores are related to each other.", "On the other hand, for uncertainty based methods, different kinds of uncertainty distribute mainly on the boundary of predicted mask, which makes it a vague information when detecting the failure cases.predict its quality.", "Since the feature space is of relative low dimension now, it is able to distinguish good segmentation results from bad ones directly.", "In a reasonable feature space, when the segmentation algorithm fails, the failure output will be far from the ground truth.", "So the main problems is what these good features are and how to capture them.", "Many features that BID8 selected are actually less related with the quality of segmentation results, e.g., size.In our system, we choose a more representative feature, i.e., the shape feature.", "The shape feature is important because the segmenting objects (foreground in the volumetric mask) often have stable shapes among different cases, especially in 3D.", "So the shape feature is supposed to provide a strong prior information for judging the quality of a segmentation result, i.e., bad segmentation results tend to have bad shapes and vice versa.", "Furthermore, to model the prior from the segmentation mask space is much easier than in the image space and the shape prior can be shared among different datasets while the features like image intensity are affected by many factors.", "That means the shape feature can deal with not only rare events but also different data distributions in the image space, which shows great generalization power and potential in transfer learning.", "We propose to use the Variational Auto-Encoder(VAE) BID7 to capture the shape feature.", "The VAE is trained on the ground truth masks, and afterwards we define the value of the loss function as the shape feature of a segmentation result when it is tested with VAE network.", "Intuitively speaking, after the VAE is trained, the bad segmentation results with bad shapes are just rare events to VAE because it is trained using only the ground truth masks, which are under the distribution of normal shapes.", "Thus they will have larger loss value.", "In this sense we are utilizing the fact that the learning algorithms will perform badly on the rare events.", "Formally speaking, the loss function, known as the variational lower bound, is optimized to approximate the function log P (Y ) during the training process.", "So after the training, the value of the loss function given a segmentation resultŶ is close to log P (Ŷ ), thus being a good definition for the shape feature.In this paper, we proposed a VAE-based alarm system for segmentation algorithms.", "The qualities of the segmentation results can be well predicted using our system.", "To validate the effectiveness of our alarm system, we test it on multiple segmentation algorithms.", "These segmentation algorithms are trained on one dataset and tested on several other datasets to simulate when the rare events occur.", "The performance for the segmentation algorithms on the other datasets (rather than the training dataset) drops quickly but our system can still predict the qualities accurately.", "We compare our system with other alarm systems on the above tasks and our system outperforms them by a large margin, which shows the importance of shape feature in alarm system and the great power of VAE in capturing the shape feature.2", "RELATED WORK BID6 employed Bayesian neural network (BNN) to model the aleatoric and epistemic uncertainty.", "Afterwards, BID9 applied the BNN to calculate the aleatoric and epistemic uncertainty on medical segmentation tasks.", "BID5 utilized the BNN and model another kind of uncertainty based on the entropy of segmentation results.", "They calculated a doubt score by summing over weighted pixel-vise uncertainty.", "However we can see from Figure 1 that when the segmentation algorithm fails to provide correct prediction, the uncertainty still distributes mainly on the boundary of the wrong segmentation result, which means the algorithm is strongly confident on where it makes mistakes.Other method like Valindria et al. FORMULA0 used registration based method for quality assessment.", "It is a reliable method because it takes the prior of image by setting up a reference dataset.", "The problem of this method is inefficient testing.", "Every single case needs to do registration with all reference data to determine the quality but registration on 3D image is usually slow.", "Also the registration based method can hardly be transferred between datasets or modalities.", "Chabrier et al. FORMULA1 and BID3 use unsupervised method to estimate the segmentation quality using geometrical and other features.", "However the application in medical settings is not clear.", "Also BID14 tried a simple method using image-segmentation pair to directly regress the quality.Kohlberger et al. FORMULA0 introduced a feature space of shape and appearance to characterize a segmentation.", "The shape features in their system contain volume size, surface area, which are not necessarily related with the quality of the segmentation results.", "In our work we choose to learn a statistical prior of the segmentation mask and then determine the quality by how well a mask fits the prior.", "This is related with Out-of-Distribution (OOD) detection.", "Previous works in this field BID4 ) BID10 ) made use of the softmax output in the last layer of a classifier to calculate the out-of-distribution level.", "In our case, however, for a segmentation method, we can only get a voxel-wise out-of-distribution level using these methods.", "How to calculate the out-of-distribution level for the whole mask becomes another problem.", "In addition, the segmentation algorithm can usually predict most of background voxels correctly with a high confidence, making the out-of-distribution level on those voxels less representative.Auto-Encoder(AE), as a way of learning representation of data automatically, has been widely used in many areas such as anomaly detection BID21 , dimension reduction, etc.", "Variational autoencoder(VAE) BID7 , compared with AE, can better learn the representation for the latent space.", "We employ VAE to learn the shape representation from the volumetric mask.", "Unlike method of BID18 which needs to pre-train with RBM, VAE can be trained following an end-to-end fashion.", "BID13 learned the shape representation from point cloud form, while we choose the volumetric form as a more natural way to corporate with segmentation task.", "utilizes AE to evaluate difference between prediction and ground truth but not in an unsupervised way.", "We split NIH data into four folds and three of them are used for training segmentation algorithms and our pipeline; the remaining one, together with all training data from MSD and MLC forms the validation data to evaluate our evaluation method.", "First we learn the parameter of VAE using the training label of NIH dataset.", "Then we choose BNN as the preparation algorithm.", "The training strategy in section 3.3 is applied on it to learn the parameters of regression.", "For all the baseline methods, we employ the same training strategy of jackknifing as in our method and choose the BNN as preparation algorithm for fair comparison.", "Finally we predict the quality of predictive mask on the validation data for all the segmentation algorithms.", "Note that all segmentation algorithms are trained only on the NIH training set.", "Table 1 reports the results of using three baseline models and our method to evaluate the BNN model tested on three datasets.", "In general, our method achieves the lowest error and variance on all datasets.", "In our experiment, the BNN achieves 82.15, 57.10 and 66.36 average Dice score tested on NIH, MSD and MLC datasets respectively.", "The segmentation algorithm trained on NIH will fail on some cases of other datasets and that is why we need the alarm system.", "The spearman coefficient for direct regression method on NIH dataset is close to 0 because the testing results on NIH are all of high quality and the regression result is not sensitive to slight variation in quality.", "Uncertainty based methods can better predict the quality but as shown in Figure 1 , the uncertainty mainly distributes on the boundary of predictive mask but not on the missing parts or false positive parts.", "When the BNN is tested on the other two datasets, our method remains stable in predicting the quality.", "Table 2 shows the quality assessment results for 4 different segmentation algorithms.", "For each segmentation algorithm, When evaluating the segmentation results from DeepLab algorithm tested on MLC dataset, the accuracy is lower but the correlation between the predictive quality and real quality is high.", "In the paper we present a VAE based alarm system for segmentation algorithms which predicts the qualities of the segmentation results without using ground truth.", "We claim that the shape feature is useful in predicting the qualities of the segmentation results.", "To capture the shape feature, we train a VAE using only ground truth masks.", "We utilize the fact that rare events will achieve larger value for loss function, and successfully detect the out-of-distribution shape according to the value for loss function in the testing time.", "In the second step we collect the segmentation results of the segmentation algorithm on the training data and extract the shape feature of them to learn the parameters of regression.", "By applying jackknifing training on the segmentation algorithm, we will get segmentation results of different qualities on the training data, therefore obtain more accurate regression parameters.The reliable quality assessment results prove both that the shape feature capturing from VAE is meaningful and that the shape feature is useful for quality assessment in the segmentation task.", "Furthermore, our proposed method outperforms the uncertainty based methods and direct regression method, and possesses better transferability to other datasets and other segmentation algorithms." ]

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[ "We use VAE to capture the shape feature for automatic segmentation evaluation" ]

[ "The linear transformations in converged deep networks show fast eigenvalue decay.", "The distribution of eigenvalues looks like a Heavy-tail distribution, where the vast majority of eigenvalues is small, but not actually zero, and only a few spikes of large eigenvalues exist.\n", "We use a stochastic approximator to generate histograms of eigenvalues.", "This allows us to investigate layers with hundreds of thousands of dimensions.", "We show how the distributions change over the course of image net training, converging to a similar heavy-tail spectrum across all intermediate layers.", "Understanding the structure in the linear transformations might be an important aspect of understanding generalization in deep networks.", "To this end we have presented a stochastic approach that allows us to estimate the eigenvalue spectrum of these transformations.", "We show how the spectrum evolves during imagenet training using convolutional networks, more specifically squeeze_net networks.In the future we want to apply similar approaches to estimating the covariance structure of the intermediate feature representations and investigate the relations between covariance matrices and parameter matrices.", "Since the estimator we use is differentiable BID5 BID0 , it may be interesting to investigate its usefulness for regularization." ]

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[ "We investigate the eigenvalues of the linear layers in deep networks and show that the distributions develop heavy-tail behavior during training." ]

[ "Capturing long-range feature relations has been a central issue on convolutional neural networks(CNNs).", "To tackle this, attempts to integrate end-to-end trainable attention module on CNNs are widespread.", "Main goal of these works is to adjust feature maps considering spatial-channel correlation inside a convolution layer.", "In this paper, we focus on modeling relationships among layers and propose a novel structure, 'Recurrent Layer Attention network,' which stores the hierarchy of features into recurrent neural networks(RNNs) that concurrently propagating with CNN and adaptively scales feature volumes of all layers.", "We further introduce several structural derivatives for demonstrating the compatibility on recent attention modules and the expandability of proposed network.", "For semantic understanding on learned features, we also visualize intermediate layers and plot the curve of layer scaling coefficients(i.e., layer attention).", "Recurrent Layer Attention network achieves significant performance enhancement requiring a slight increase on parameters in an image classification task with CIFAR and ImageNet-1K 2012 dataset and an object detection task with Microsoft COCO 2014 dataset.", "Concatenating all features in the order of layers in convolutional neural network (CNN) provides new interpretation, features form a sequence, consisting of features with small receptive fields to large receptive fields.", "Interestingly, recurrent neural network (RNN) is one of the representatives for modeling the sequential information.", "(Sutskever et al., 2014; Hochreiter & Schmidhuber, 1997) .", "On the other hands, Recent attempts to utilize attention mechanism for empowering CNN a better representational power are prevalent (Hu et al., 2018b; Wang et al., 2017) .", "Motivated by intrinsic characteristics of CNN and RNN, and recent attention works on computer vision, we present the Recurrent Layer Attention Network (RLA network), which is differentiable and light-weight while improving the representational power of CNN by a slightly different way from other attention works in computer vision.", "The main goal of our work is applying global weights balance among layers by inheriting the feature hierarchy from previous CNN layers.", "We accomplish the goal by two main structural designs: employing our inter-layer attention mechanism to make the network re-adjust features, and utilizing RNN to memorize the feature hierarchy with concurrently propagating parallel with CNN.", "We hypothesize that RLA network gains additional class discriminability through inheriting the informative feature hierarchy, such as repetitive appearances of important features or relevant features with different receptive fields.", "For example, our network raises the activation of neurons that is responsible to the whole body of zebra, using a history of features of relatively smaller receptive field.", "We demonstrate our hypothesis through the Grad-CAM visualization of intermediate features and corresponding layer attention value (i.e., the importance of layer.)", "We evaluate RLA network on image classification and object detection tasks using benchmark datasets: CIFAR, ImageNet-1K, and Microsoft COCO.", "On both tasks, RLA network gets comparable results with the state-of-the-arts, Squeeze-and-Excitation network (Hu et al., 2018b) , and superior results than original ResNet architecture.", "Moreover, we suggest the compatibility of the RLA network by introducing the expansion of RLA network combining our inter-layer attention mechanism toward recent attention works (Hu et al., 2018b) on ablation study.", "Incorporating RLA network to recent attention works (Call these networks as intra-layer attention networks), further variations of RLA network can be recognized as the generalized attention network considering correlations among both inside and outside a layer.", "We summarize our contributions as follows:", "• We propose two new concepts: the weight balancing of CNN features along layers (call it inter-layer attention), and the connection from shallow CNN layers to deep CNN layers through concurrently propagating RNN.", "• We demonstrate the effectiveness of proposed RLA network for an image classification task and an object detection task on benchmark datasets.", "RLA network achieves similar or superior results compared with leading deep network while requiring small model parameters increase.", "• Ablation studies investigate the effectiveness of two proposed concepts and show the compatibility towards existing intra-attention models, and the further expandability by tuning architectural designs.", "We show and discuss how RLA network is learned to interpret images by visualizing intermediate layers and plotting layer attention values.", "• RLA network is easy to implement requiring basic operations of modern deep learning frameworks.", "In this paper, we first propose inter-layer attention mechansim to enhance the representational power of CNN.", "We structurized our mechanism as 'Recurrent Layer Attention network' by utilizing two new concepts: the weight balancing of CNN features along layers and the link from shallow CNN layers to deep CNN layers via RNN for directly conveying the feature hierarchy.", "We introduce structural derivatives of RLA network: 'IA+RLA' for proving an applicability of our work toward recent intra-layer attention mechanism, and 'RLA-vector' for distilling the impacts of proposed two new concepts.", "We also precisely select statistics for the context by focusing local patterns preserved in feature summarization procedure.", "We evaluate RLA network using CIFAR and ImageNet-1k 2012 datasets for an image classification task, and also verify it's generalization ability toward an object detection task via experiments on Microsoft COCO dataset.", "For demonstrating our hypothesis that RLA network gains additional class discriminability and semantically understanding how RLA network induce their model parameters to be learned, we visualize RLA network utilizing Grad-CAM visualization, plot the layer attention value curve, and report several interesting findings.", "For future works, we are planning to integrate our inter-layer attention mechanism to intra-layer attention mechanism with heavier experiments first, and to utilize the concept of making any kinds of arbitrary connection from earlier layer to latter layer through RNN in other domains." ]

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[ "We propose a new type of end-to-end trainable attention module, which applies global weight balances among layers by utilizing co-propagating RNN with CNN." ]

[ "We seek to auto-generate stronger input features for ML methods faced with limited training data.\n", "Biological neural nets (BNNs) excel at fast learning, implying that they extract highly informative features.", "In particular, the insect olfactory network learns new odors very rapidly, by means of three key elements: A competitive inhibition layer; randomized, sparse connectivity into a high-dimensional sparse plastic layer; and Hebbian updates of synaptic weights.", "In this work we deploy MothNet, a computational model of the moth olfactory network, as an automatic feature generator.", "Attached as a front-end pre-processor, MothNet's readout neurons provide new features, derived from the original features, for use by standard ML classifiers.", "These ``insect cyborgs'' (part BNN and part ML method) have significantly better performance than baseline ML methods alone on vectorized MNIST and Omniglot data sets, reducing test set error averages 20% to 55%.", "The MothNet feature generator also substantially out-performs other feature generating methods including PCA, PLS, and NNs.", "These results highlight the potential value of BNN-inspired feature generators in the ML context.", "Machine learning (ML) methods, especially neural nets (NNs) with backprop, often require large amounts of training data to attain their high performance.", "This creates bottlenecks to deployment, and constrains the types of problems that can be addressed [1] .", "The limited-data constraint is common for ML targets that use medical, scientific, or field-collected data, as well as AI efforts focused on rapid learning.", "We seek to improve ML methods' ability to learn from limited data by means of an architecure that automatically generates, from existing features, a new set of class-separating features.", "Biological neural nets (BNNs) are able to learn rapidly, even from just a few samples.", "Assuming that rapid learning requires effective ways to separate classes, we may look to BNNs for effective feature-generators [2] .", "One of the simplest BNNs that can learn is the insect olfactory network [3] , containing the Antennal Lobe (AL) [4] and Mushroom Body(MB) [5] , which can learn a new odor given just a few exposures.", "This simple but effective feedforward network contains three key elements that are ubiquitous in BNN designs: Competitive inhibition [6] , high-dimensional sparse layers [7; 8] , and a Hebbian update mechanism [9] .", "Synaptic connections are largely random [10] .", "MothNet is a computational model of the M. sexta moth AL-MB that demonstrated rapid learning of vectorized MNIST digits, with performance superior to standard ML methods given N ≤ 10 training samples per class [11] .", "The MothNet model includes three key elements, as follows.", "(i) Competitive inhibition in the AL: Each neural unit in the AL receives input from one feature, and outputs not only a feedforward excitatory signal to the MB, but also an inhibitory signal to other neural units in the AL that tries to dampen other features' presence in the sample's output AL signature.", "(ii) Sparsity in the MB, of two types: The projections from the AL to the MB are non-dense (≈ 15% non-zero), and the MB neurons fire sparsely in the sense that only the strongest 5% to 15% of the total population are allowed to fire (through a mechanism of global inhibition).", "(iii) Weight updates affect only MB→Readout connections (AL connections are not plastic).", "Hebbian updates occur as: ∆w ij = αf i f j if f i f j > 0 (growth), and ∆w ij = −δw ij if f i f j = 0 (decay), where f i , f j are two neural firing rates (f i ∈ MB, f j ∈ Readouts) with connection weight w ij .", "In this work we tested whether the MothNet architecture can usefully serve as a front-end feature generator for an ML classifier (our thanks to Blake Richards for this suggestion).", "We combined MothNet with a downstream ML module, so that the Readouts of the trained AL-MB model were fed into the ML module as additional features.", "From the ML perspective, the AL-MB acted as an automatic feature generator; from the biological perspective, the ML module stood in for the downstream processing in more complex BNNs.", "Our Test Case was a non-spatial, 85-feature, 10-class task derived from the downsampled, vectorized MNIST data set (hereafter \"vMNIST\").", "On this non-spatial dataset, CNNs or other spatial methods were not applicable.", "The trained Mothnet Readouts, used as features, significantly improved the accuracies of ML methods (NN, SVM, and Nearest Neighbors) on the test set in almost every case.", "That is, the original input features (pixels) contained class-relevant information unavailable to the ML methods alone, but which the AL-MB network encoded in a form that enabled the ML methods to access it.", "MothNet-generated features also significantly out-performed features generated by PCA (Principal Components Analysis), PLS (Partial Least Squares), NNs, and transfer learning (weight pretraining) in terms of their ability to improve ML accuracy.", "These results indicate that the insect-derived network generated significantly stronger features than these other methods.", "We deployed an automated feature generator based on a very simple BNN, containing three key elements rare in engineered NNs but endemic in BNNs of all complexity levels:", "(i) competitive inhibition;", "(ii) sparse projection into a high-dimensional sparse layer; and", "(iii) Hebbian weight updates for training.", "This bio-mimetic feature generator significantly improved the learning abilities of standard ML methods on both vMNIST and vOmniglot.", "Class-relevant information in the raw feature distributions, not extracted by the ML methods alone, was evidently made accessible by MothNet's pre-processing.", "In addition, MothNet features were consistently much more useful than features generated by standard methods such as PCA, PLS, NNs, and pre-training.", "The competitive inhibition layer may enhance classification by creating several attractor basins for inputs, each focused on the features that present most strongly for a given class.", "This may push otherwise similar samples (of different classes) away from each other, towards their respective class attractors, increasing the effective distance between the samples.", "The sparse connectivity from AL to MB has been analysed as an additive function, which has computational and anti-noise benefits [14] .", "The insect MB brings to mind sparse autoencoders (SAs) e.g. [15] .", "However, there are several differences: MBs do not seek to match the identity function; the sparse layers of SAs have fewer active neurons than the input dimension, while in the MB the number of active neurons is much greater than the input dimension; MBs have no pre-training step; and the MB needs very few samples to bake in structure that improves classification.", "The MB differs from Reservoir Networks [16] in that MB neurons have no recurrent connections.", "Finally, the Hebbian update mechanism appears to be quite distinct from backprop.", "It has no objective function or output-based loss that is pushed back through the network, and Hebbian weight updates, either growth or decay, occur on a local \"use it or lose it\" basis.", "We suspect that the dissimilarity of the optimizers (MothNet vs ML) was an asset in terms of increasing total encoded information." ]

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[ "Features auto-generated by the bio-mimetic MothNet model significantly improve the test accuracy of standard ML methods on vectorized MNIST. The MothNet-generated features also outperform standard feature generators." ]

[ "We present an approach for anytime predictions in deep neural networks (DNNs).", "For each test sample, an anytime predictor produces a coarse result quickly, and then continues to refine it until the test-time computational budget is depleted.", "Such predictors can address the growing computational problem of DNNs by automatically adjusting to varying test-time budgets.", "In this work, we study a \\emph{general} augmentation to feed-forward networks to form anytime neural networks (ANNs) via auxiliary predictions and losses.", "Specifically, we point out a blind-spot in recent studies in such ANNs: the importance of high final accuracy.", "In fact, we show on multiple recognition data-sets and architectures that by having near-optimal final predictions in small anytime models, we can effectively double the speed of large ones to reach corresponding accuracy level.", "We achieve such speed-up with simple weighting of anytime losses that oscillate during training.", "We also assemble a sequence of exponentially deepening ANNs, to achieve both theoretically and practically near-optimal anytime results at any budget, at the cost of a constant fraction of additional consumed budget.", "In recent years, the accuracy in visual recognition tasks has been greatly improved by increasingly complex convolutional neural networks, from AlexNet BID8 and VGG BID12 , to ResNet BID3 , ResNeXt BID14 , and DenseNet BID6 .", "However, the number of applications that require latency sensitive responses is growing rapidly.", "Furthermore, their test-time computational budget can often.", "E.g., autonomous vehicles require real-time object detection, but the required detection speed depends on the vehicle speed; web servers need to meet varying amount of data and user requests throughput through out a day.", "Thus, it can be difficult for such applications to choose between slow predictors with high accuracy and fast predictors with low accuracy.", "In many cases, this dilemma can be resolved by an anytime predictor BID4 BID0 BID16 , which, for each test sample, produces a fast and crude initial prediction and continues to refine it as budget allows, so that at any test-time budget, the anytime predictor has a valid result for the sample, and the more budget is spent, the better the prediction is.In this work 1 , we focus on the anytime prediction problem in neural networks.", "We follow the recent works BID10 BID15 BID5 to append auxiliary predictions and losses in feed-forward networks for anytime predictions, and train them jointly end-to-end.", "However, we note that the existing methods all put only a small fraction of the total weightings to the final prediction, and as a result, large anytime models are often only as accurate as much smaller non-anytime models, because the accuracy gain is so costly in DNNs, as demonstrated in FIG0 .", "We address this problem with a novel and simple oscillating weightings of the losses, and will show in Sec. 3 that our small anytime models with near-optimal final predictions can effectively speed up two times large ones without them, on multiple data-sets, including ILSVRC BID11 , and on multiple models, including the very recent Multi-ScaleDenseNets (MSDnets) BID5 .", "Observing that the proposed training techniques lead to ANNs that are near-optimal in late predictions but are not as accurate in the early predictions, we assemble ANNs of exponentially increasing depths to dedicate early predictions to smaller networks, while only delaying large networks by a constant fraction of additional test-time budgets." ]

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[ "By focusing more on the final predictions in anytime predictors (such as the very recent Multi-Scale-DenseNets), we make small anytime models to outperform large ones that don't have such focus. " ]

[ "Computational imaging systems jointly design computation and hardware to retrieve information which is not traditionally accessible with standard imaging systems.", "Recently, critical aspects such as experimental design and image priors are optimized through deep neural networks formed by the unrolled iterations of classical physics-based reconstructions (termed physics-based networks).", "However, for real-world large-scale systems, computing gradients via backpropagation restricts learning due to memory limitations of graphical processing units.", "In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network’s layers to enable data-driven design for large-scale computational imaging.", "We demonstrate our methods practicality on two large-scale systems: super-resolution optical microscopy and multi-channel magnetic resonance imaging.", "Computational imaging systems (tomographic systems, computational optics, magnetic resonance imaging, to name a few) jointly design software and hardware to retrieve information which is not traditionally accessible on standard imaging systems.", "Generally, such systems are characterized by how the information is encoded (forward process) and decoded (inverse problem) from the measurements.", "The decoding process is typically iterative in nature, alternating between enforcing data consistency and image prior knowledge.", "Recent work has demonstrated the ability to optimize computational imaging systems by unrolling the iterative decoding process to form a differentiable Physicsbased Network (PbN) (1; 2; 3) and then relying on a dataset and training to learn the system's design parameters, e.g. experimental design (3; 4;", "5) , image prior model (1; 2; 6; 7).", "PbNs are constructed from the operations of reconstruction, e.g. proximal gradient descent algorithm.", "By including known structures and quantities, such as the forward model, gradient, and proximal updates, PbNs can be efficiently parameterized by only a few learnable variables, thereby enabling an efficient use of training data (6) while still retaining robustness associated with conventional physics-based inverse problems.", "Training PbNs relies on gradient-based updates computed using backpropagation (an implementation of reverse-mode differentiation (8) ).", "Most modern imaging systems seek to decode ever-larger growing quantities of information (gigabytes to terabytes) and as this grows, memory required to perform backpropagation is limited by the memory capacity of modern graphical processing units (GPUs).", "Methods to save memory during backpropagation (e.g. forward recalculation, reverse recalculation, and checkpointing) trade off spatial and temporal complexity (8) .", "For a PbN with N layers, standard backpropagation achieves O(N ) temporal and spatial complexity.", "Forward recalculation achieves O(1) memory complexity, but has to recalculate unstored variables forward from the input of the network when needed, yielding O(N 2 ) temporal complexity.", "Forward checkpointing smoothly trades off temporal, O(N K), and spatial, O(N/K), complexity by saving variables every K layers and forward-recalculating unstored variables from the closest checkpoint.", "Reverse recalculation provides a practical solution to beat the trade off between spatial vs. temporal complexity by calculating unstored variables in reverse from the output of the network, yielding O(N ) temporal and O(1) spatial complexities.", "Recently, several reversibility schemes have been proposed for residual networks (9), learning ordinary differential equations (10) , and other specialized network architectures (11; 12) .", "In this work, we propose a memory-efficient learning procedure for backpropagation for the PbN formed from proximal gradient descent, thereby enabling learning for many large-scale computational imaging systems.", "Based on the concept of invertibility and reverse recalculation, we detail how backpropagation can be performed without the need to store intermediate variables for networks composed of gradient and proximal layers.", "We highlight practical restrictions on the layers and introduce a hybrid scheme that combines our reverse recalculation methods with checkpointing to mitigate numerical error accumulation.", "Finally, we demonstrate our method's usefulness to learn the design for two practical large-scale computational imaging systems: superresolution optical microscopy (Fourier Ptychography) and multi-channel magnetic resonance imaging.", "In this communication, we presented a practical memory-efficient learning method for large-scale computational imaging problems without dramatically increasing training time.", "Using the concept of reversibility, we implemented reverse-mode differentiation with favorable spatial and temporal complexities.", "We demonstrated our method on two representative applications: SR optical microscopy and multi-channel MRI.", "We expect other computational imaging systems to nicely fall within our framework." ]

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[ "We propose a memory-efficient learning procedure that exploits the reversibility of the network’s layers to enable data-driven design for large-scale computational imaging." ]

[ "Existing multi-agent reinforcement learning (MARL) communication methods have relied on a trusted third party (TTP) to distribute reward to agents, leaving them inapplicable in peer-to-peer environments.", "This paper proposes reward distribution using {\\em Neuron as an Agent} (NaaA) in MARL without a TTP with two key ideas:", "(i) inter-agent reward distribution and", "(ii) auction theory.", "Auction theory is introduced because inter-agent reward distribution is insufficient for optimization.", "Agents in NaaA maximize their profits (the difference between reward and cost) and, as a theoretical result, the auction mechanism is shown to have agents autonomously evaluate counterfactual returns as the values of other agents.", "NaaA enables representation trades in peer-to-peer environments, ultimately regarding unit in neural networks as agents.", "Finally, numerical experiments (a single-agent environment from OpenAI Gym and a multi-agent environment from ViZDoom) confirm that NaaA framework optimization leads to better performance in reinforcement learning." ]

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[ "Neuron as an Agent (NaaA) enable us to train multi-agent communication without a trusted third party." ]

[ "Increasing model size when pretraining natural language representations often results in improved performance on downstream tasks.", "However, at some point further model increases become harder due to GPU/TPU memory limitations, longer training times, and unexpected model degradation.", "To address these problems, we present two parameter-reduction techniques to lower memory consumption and increase the training speed of BERT.", "Comprehensive empirical evidence shows that our proposed methods lead to models that scale much better compared to the original BERT.", "We also use a self-supervised loss that focuses on modeling inter-sentence coherence, and show it consistently helps downstream tasks with multi-sentence inputs.", "As a result, our best model establishes new state-of-the-art results on the GLUE, RACE, and SQuAD benchmarks while having fewer parameters compared to BERT-large.", "Full network pre-training (Dai & Le, 2015; Radford et al., 2018; Howard & Ruder, 2018 ) has led to a series of breakthroughs in language representation learning.", "Many nontrivial NLP tasks, including those that have limited training data, have greatly benefited from these pre-trained models.", "One of the most compelling signs of these breakthroughs is the evolution of machine performance on a reading comprehension task designed for middle and high-school English exams in China, the RACE test (Lai et al., 2017) : the paper that originally describes the task and formulates the modeling challenge reports then state-of-the-art machine accuracy at 44.1%; the latest published result reports their model performance at 83.2% ; the work we present here pushes it even higher to 89.4%, a stunning 45.3% improvement that is mainly attributable to our current ability to build high-performance pretrained language representations.", "Evidence from these improvements reveals that a large network is of crucial importance for achieving state-of-the-art performance .", "It has become common practice to pre-train large models and distill them down to smaller ones (Sun et al., 2019; Turc et al., 2019) for real applications.", "Given the importance of model size, we ask: Is having better NLP models as easy as having larger models?", "An obstacle to answering this question is the memory limitations of available hardware.", "Given that current state-of-the-art models often have hundreds of millions or even billions of parameters, it is easy to hit these limitations as we try to scale our models.", "Training speed can also be significantly hampered in distributed training, as the communication overhead is directly proportional to the number of parameters in the model.", "We also observe that simply growing the hidden size of a model such as BERT-large can lead to worse performance.", "Table 1 and Fig. 1 show a typical example, where we simply increase the hidden size of BERT-large to be 2x larger and get worse results with this BERT-xlarge model.", "Model Hidden Size Parameters RACE (Accuracy) BERT-large 1024 334M 72.0% BERT-large (ours) 1024 334M 73.9% BERT-xlarge (ours) 2048 1270M 54.3% Table 1 : Increasing hidden size of BERT-large leads to worse performance on RACE.", "Existing solutions to the aforementioned problems include model parallelization (Shoeybi et al., 2019) and clever memory management (Chen et al., 2016; .", "These solutions address the memory limitation problem, but not the communication overhead and model degradation problem.", "In this paper, we address all of the aforementioned problems, by designing A Lite BERT (ALBERT) architecture that has significantly fewer parameters than a traditional BERT architecture.", "ALBERT incorporates two parameter reduction techniques that lift the major obstacles in scaling pre-trained models.", "The first one is a factorized embedding parameterization.", "By decomposing the large vocabulary embedding matrix into two small matrices, we separate the size of the hidden layers from the size of vocabulary embedding.", "This separation makes it easier to grow the hidden size without significantly increasing the parameter size of the vocabulary embeddings.", "The second technique is cross-layer parameter sharing.", "This technique prevents the parameter from growing with the depth of the network.", "Both techniques significantly reduce the number of parameters for BERT without seriously hurting performance, thus improving parameter-efficiency.", "An ALBERT configuration similar to BERT-large has 18x fewer parameters and can be trained about 1.7x faster.", "The parameter reduction techniques also act as a form of regularization that stabilizes the training and helps with generalization.", "To further improve the performance of ALBERT, we also introduce a self-supervised loss for sentence-order prediction (SOP).", "SOP primary focuses on inter-sentence coherence and is designed to address the ineffectiveness of the next sentence prediction (NSP) loss proposed in the original BERT.", "As a result of these design decisions, we are able to scale up to much larger ALBERT configurations that still have fewer parameters than BERT-large but achieve significantly better performance.", "We establish new state-of-the-art results on the well-known GLUE, SQuAD, and RACE benchmarks for natural language understanding.", "Specifically, we push the RACE accuracy to 89.4%, the GLUE benchmark to 89.4, and the F1 score of SQuAD 2.0 to 92.2.", "While ALBERT-xxlarge has less parameters than BERT-large and gets significantly better results, it is computationally more expensive due to its larger structure.", "An important next step is thus to speed up the training and inference speed of ALBERT through methods like sparse attention and block attention (Shen et al., 2018 ).", "An orthogonal line of research, which could provide additional representation power, includes hard example mining (Mikolov et al., 2013) efficient language modeling training .", "Additionally, although we have convincing evidence that sentence order prediction is a more consistently-useful learning task that leads to better language representations, we hypothesize that there could be more dimensions not yet captured by the current self-supervised training losses that could create additional representation power for the resulting representations.", "RACE RACE is a large-scale dataset for multi-choice reading comprehension, collected from English examinations in China with nearly 100,000 questions.", "Each instance in RACE has 4 candidate answers.", "Following prior work , we use the concatenation of the passage, question, and each candidate answer as the input to models.", "Then, we use the representations from the \"[CLS]\" token for predicting the probability of each answer.", "The dataset consists of two domains: middle school and high school.", "We train our models on both domains and report accuracies on both the development set and test set.", "A.2", "HYPERPARAMETERS Hyperparameters for downstream tasks are shown in Table 15 .", "We adapt these hyperparameters from , , and Yang et al. (2019" ]

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[ "A new pretraining method that establishes new state-of-the-art results on the GLUE, RACE, and SQuAD benchmarks while having fewer parameters compared to BERT-large. " ]

[ "Structured tabular data is the most commonly used form of data in industry according to a Kaggle ML and DS Survey.", "Gradient Boosting Trees, Support Vector Machine, Random Forest, and Logistic Regression are typically used for classification tasks on tabular data.", "The recent work of Super Characters method using two-dimensional word embeddings achieved state-of-the-art results in text classification tasks, showcasing the promise of this new approach.", "In this paper, we propose the SuperTML method, which borrows the idea of Super Characters method and two-dimensional embeddings to address the problem of classification on tabular data.", "For each input of tabular data, the features are first projected into two-dimensional embeddings like an image, and then this image is fed into fine-tuned ImageNet CNN models for classification.", "Experimental results have shown that the proposed SuperTML method have achieved state-of-the-art results on both large and small datasets.", "In data science, data is categorized into structured data and unstructured data.", "Structured data is also known as tabular data, and the terms will be used interchangeably.", "Anthony Goldbloom, the founder and CEO of Kaggle observed that winning techniques have been divided by whether the data was structured or unstructured BID12 .", "Currently, DNN models are widely applied for usage on unstructured data such as image, speech, and text.", "According to Anthony, \"When the data is unstructured, its definitely CNNs and RNNs that are carrying the day\" BID12 .", "The successful CNN model in the ImageNet competition BID8 has outperformed human for image classification task by ResNet BID6 since 2015.On the other side of the spectrum, machine learning models such as Support Vector Machine (SVM), Gradient Boosting Trees (GBT), Random Forest, and Logistic Regression, have been used to process structured data.", "According to a recent survey of 14,000 data scientists by Kaggle (2017) , a subdivision of structured data known as relational data is reported as the most popular type of data in industry, with at least 65% working daily with relational data.", "Regarding structured data competitions, Anthony says that currently XGBoost is winning practically every competition in the structured data category BID4 .", "XGBoost BID2 is one popular package implementing the Gradient Boosting method.Recent research has tried using one-dimensional embedding and implementing RNNs or one-dimensional CNNs to address the TML (Tabular Machine Learning) tasks, or tasks that deal with structured data processing BID7 BID11 , and also categorical embedding for tabular data with categorical features BID5 .", "However, this reliance upon onedimensional embeddings may soon come to change.", "Recent NLP research has shown that the two-dimensional embedding of the Super Characters method BID9 is capable of achieving state-of-the-art results on large dataset benchmarks.", "The Super Characters method is a two-step method that was initially designed for text classification problems.", "In the first step, the characters of the input text are drawn onto a blank image.", "In the second step, the image is fed into two-dimensional CNN models for classification.", "The two-dimensional CNN models are trained by fine-tuning from pretrained models on large image dataset, e.g. ImageNet.In this paper, we propose the SuperTML method, which borrows the concept of the Super Characters method to address TML problems.", "For each input, tabular features are first projected onto a two-dimensional embedding and fed into fine-tuned two-dimensional CNN models for classification.", "The proposed SuperTML method handles the categorical type and missing values in tabular data automatically, without need for explicit conversion into numerical type values.", "The proposed SuperTML method borrows the idea of twodimensional embedding from Super Characters and transfers the knowledge learned from computer vision to the structured tabular data.", "Experimental results shows that the proposed SuperTML method has achieved state-of-the-art results on both large and small tabular dataset." ]

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[ "Deep learning on structured tabular data using two-dimensional word embedding with fine-tuned ImageNet pre-trained CNN model." ]

[ "Predictive coding, within theoretical neuroscience, and variational autoencoders, within machine learning, both involve latent Gaussian models and variational inference.", "While these areas share a common origin, they have evolved largely independently.", "We outline connections and contrasts between these areas, using their relationships to identify new parallels between machine learning and neuroscience.", "We then discuss specific frontiers at this intersection: backpropagation, normalizing flows, and attention, with mutual benefits for both fields.", "Perception has been conventionally formulated as hierarchical feature detection [52] , similar to discriminative deep networks [34] .", "In contrast, predictive coding [48, 14] and variational autoencoders (VAEs) [31, 51] frame perception as a generative process, modeling data observations to learn and infer aspects of the external environment.", "Specifically, both areas model observations, x, using latent variables, z, through a probabilistic model, p θ (x, z) = p θ (x|z)p θ (z).", "Both areas also use variational inference, introducing an approximate posterior, q(z|x), to infer z and learn the model parameters, θ.", "These similarities are the result of a common origin, with Mumford [45] , Dayan et al. [9] , and others [46] formalizing earlier ideas [59, 38] .", "However, since their inception, these areas have developed largely independently.", "We explore their relationships (see also [58, 37] ) and highlight opportunities for the transfer of ideas.", "In identifying these ties, we hope to strengthen this promising, close connection between neuroscience and machine learning, prompting further investigation.", "We have identified commonalities between predictive coding and VAEs, discussing new frontiers resulting from this perspective.", "Reuniting these areas may strengthen the connection between neuroscience and machine learning.", "Further refining this connection could lead to mutual benefits: neuroscience can offer inspiration for investigation in machine learning, and machine learning can evaluate ideas on real-world datasets and environments.", "Indeed, despite some push back [17] , if predictive coding and related theories [18] are to become validated descriptions of the brain and overcome their apparent generality, they will likely require the computational tools and ideas of modern machine learning to pin down and empirically compare design choices." ]

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[ "connections between predictive coding and VAEs + new frontiers" ]

[ "Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates.", "Though prevailing, they are observed to generalize poorly compared with SGD or even fail to converge due to unstable and extreme learning rates.", "Recent work has put forward some algorithms such as AMSGrad to tackle this issue but they failed to achieve considerable improvement over existing methods.", "In our paper, we demonstrate that extreme learning rates can lead to poor performance.", "We provide new variants of Adam and AMSGrad, called AdaBound and AMSBound respectively, which employ dynamic bounds on learning rates to achieve a gradual and smooth transition from adaptive methods to SGD and give a theoretical proof of convergence.", "We further conduct experiments on various popular tasks and models, which is often insufficient in previous work.", "Experimental results show that new variants can eliminate the generalization gap between adaptive methods and SGD and maintain higher learning speed early in training at the same time.", "Moreover, they can bring significant improvement over their prototypes, especially on complex deep networks.", "The implementation of the algorithm can be found at https://github.com/Luolc/AdaBound .", "There has been tremendous progress in first-order optimization algorithms for training deep neural networks.", "One of the most dominant algorithms is stochastic gradient descent (SGD) BID15 , which performs well across many applications in spite of its simplicity.", "However, there is a disadvantage of SGD that it scales the gradient uniformly in all directions.", "This may lead to poor performance as well as limited training speed when the training data are sparse.", "To address this problem, recent work has proposed a variety of adaptive methods that scale the gradient by square roots of some form of the average of the squared values of past gradients.", "Examples of such methods include ADAM BID7 , ADAGRAD BID2 and RMSPROP BID16 .", "ADAM in particular has become the default algorithm leveraged across many deep learning frameworks due to its rapid training speed BID17 .Despite", "their popularity, the generalization ability and out-of-sample behavior of these adaptive methods are likely worse than their non-adaptive counterparts. Adaptive", "methods often display faster progress in the initial portion of the training, but their performance quickly plateaus on the unseen data (development/test set) BID17 . Indeed,", "the optimizer is chosen as SGD (or with momentum) in several recent state-of-the-art works in natural language processing and computer vision BID11 BID18 , wherein these instances SGD does perform better than adaptive methods. BID14 have", "recently proposed a variant of ADAM called AMSGRAD, hoping to solve this problem. The authors", "provide a theoretical guarantee of convergence but only illustrate its better performance on training data. However, the", "generalization ability of AMSGRAD on unseen data is found to be similar to that of ADAM while a considerable performance gap still exists between AMSGRAD and SGD BID6 BID1 .In this paper", ", we first conduct an empirical study on ADAM and illustrate that both extremely large and small learning rates exist by the end of training. The results", "correspond with the perspective pointed out by BID17 that the lack of generalization performance of adaptive methods may stem from unstable and extreme learning rates. In fact, introducing", "non-increasing learning rates, the key point in AMSGRAD, may help abate the impact of huge learning rates, while it neglects possible effects of small ones. We further provide an", "example of a simple convex optimization problem to elucidate how tiny learning rates of adaptive methods can lead to undesirable non-convergence. In such settings, RMSPROP", "and ADAM provably do not converge to an optimal solution, and furthermore, however large the initial step size α is, it is impossible for ADAM to fight against the scale-down term.Based on the above analysis, we propose new variants of ADAM and AMSGRAD, named AD-ABOUND and AMSBOUND, which do not suffer from the negative impact of extreme learning rates. We employ dynamic bounds", "on learning rates in these adaptive methods, where the lower and upper bound are initialized as zero and infinity respectively, and they both smoothly converge to a constant final step size. The new variants can be", "regarded as adaptive methods at the beginning of training, and they gradually and smoothly transform to SGD (or with momentum) as time step increases. In this framework, we can", "enjoy a rapid initial training process as well as good final generalization ability. We provide a convergence", "analysis for the new variants in the convex setting.We finally turn to an empirical study of the proposed methods on various popular tasks and models in computer vision and natural language processing. Experimental results demonstrate", "that our methods have higher learning speed early in training and in the meantime guarantee strong generalization performance compared to several adaptive and non-adaptive methods. Moreover, they can bring considerable", "improvement over their prototypes especially on complex deep networks.", "We investigate existing adaptive algorithms and find that extremely large or small learning rates can result in the poor convergence behavior.", "A rigorous proof of non-convergence for ADAM is provided to demonstrate the above problem.Motivated by the strong generalization ability of SGD, we design a strategy to constrain the learning rates of ADAM and AMSGRAD to avoid a violent oscillation.", "Our proposed algorithms, AD-ABOUND and AMSBOUND, which employ dynamic bounds on their learning rates, achieve a smooth transition to SGD.", "They show the great efficacy on several standard benchmarks while maintaining advantageous properties of adaptive methods such as rapid initial progress and hyperparameter insensitivity." ]

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[ "Novel variants of optimization methods that combine the benefits of both adaptive and non-adaptive methods." ]

[ "An important problem that arises in reinforcement learning and Monte Carlo methods is estimating quantities defined by the stationary distribution of a Markov chain.", "In many real-world applications, access to the underlying transition operator is limited to a fixed set of data that has already been collected, without additional interaction with the environment being available.", "We show that consistent estimation remains possible in this scenario, and that effective estimation can still be achieved in important applications.", "Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions, derived from fundamental properties of the stationary distribution, and exploiting constraint reformulations based on variational divergence minimization.", "The resulting algorithm, GenDICE, is straightforward and effective.", "We prove the consistency of the method under general conditions, provide a detailed error analysis, and demonstrate strong empirical performance on benchmark tasks, including off-line PageRank and off-policy policy evaluation.", "Estimation of quantities defined by the stationary distribution of a Markov chain lies at the heart of many scientific and engineering problems.", "Famously, the steady-state distribution of a random walk on the World Wide Web provides the foundation of the PageRank algorithm (Langville & Meyer, 2004) .", "In many areas of machine learning, Markov chain Monte Carlo (MCMC) methods are used to conduct approximate Bayesian inference by considering Markov chains whose equilibrium distribution is a desired posterior (Andrieu et al., 2002 ).", "An example from engineering is queueing theory, where the queue lengths and waiting time under the limiting distribution have been extensively studied (Gross et al., 2018) .", "As we will also see below, stationary distribution quantities are of fundamental importance in reinforcement learning (RL) (e.g., Tsitsiklis & Van Roy, 1997) .", "Classical algorithms for estimating stationary distribution quantities rely on the ability to sample next states from the current state by directly interacting with the environment (as in on-line RL or MCMC), or even require the transition probability distribution to be given explicitly (as in PageRank).", "Unfortunately, these classical approaches are inapplicable when direct access to the environment is not available, which is often the case in practice.", "There are many practical scenarios where a collection of sampled trajectories is available, having been collected off-line by an external mechanism that chose states and recorded the subsequent next states.", "Given such data, we still wish to estimate a stationary quantity.", "One important example is off-policy policy evaluation in RL, where we wish to estimate the value of a policy different from that used to collect experience.", "Another example is off-line PageRank (OPR), where we seek to estimate the relative importance of webpages given a sample of the web graph.", "Motivated by the importance of these off-line scenarios, and by the inapplicability of classical methods, we study the problem of off-line estimation of stationary values via a stationary distribution corrector.", "Instead of having access to the transition probabilities or a next-state sampler, we assume only access to a fixed sample of state transitions, where states have been sampled from an unknown distribution and next-states are sampled according to the Markov chain's transition operator.", "This off-line setting is distinct from that considered by most MCMC or on-line RL methods, where it is assumed that new observations can be continually sampled by demand from the environment.", "The off-line setting is indeed more challenging than its more traditional on-line counterpart, given that one must infer an asymptotic quantity from finite data.", "Nevertheless, we develop techniques that still allow consistent estimation under general conditions, and provide effective estimates in practice.", "The main contributions of this work are:", "• We formalize the problem of off-line estimation of stationary quantities, which captures a wide range of practical applications.", "• We propose a novel stationary distribution estimator, GenDICE, for this task.", "The resulting algorithm is based on a new dual embedding formulation for divergence minimization, with a carefully designed mechanism that explicitly eliminates degenerate solutions.", "• We theoretically establish consistency and other statistical properties of GenDICE, and empirically demonstrate that it achieves significant improvements on several behavior-agnostic offpolicy evaluation benchmarks and an off-line version of PageRank.", "The methods we develop in this paper fundamentally extend recent work in off-policy policy evaluation (Liu et al., 2018; Nachum et al., 2019) by introducing a new formulation that leads to a more general, and as we will show, more effective estimation method.", "In this paper, we proposed a novel algorithm GenDICE for general stationary distribution correction estimation, which can handle both the discounted and average stationary distribution given multiple behavior-agnostic samples.", "Empirical results on off-policy evaluation and offline PageRank show the superiority of proposed method over the existing state-of-the-art methods.", "the existence of the stationary distribution.", "Our discussion is all based on this assumption.", "Assumption 1 Under the target policy, the resulted state-action transition operator T has a unique stationary distribution in terms of the divergence D (·||·).", "If the total variation divergence is selected, the Assumption 1 requires the transition operator should be ergodic, as discussed in Meyn & Tweedie (2012)." ]

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[ "In this paper, we proposed a novel algorithm, GenDICE, for general stationary distribution correction estimation, which can handle both discounted and average off-policy evaluation on multiple behavior-agnostic samples." ]

[ "The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive.", "Numerous rigorous attempts have been made to explain generalization, but available bounds are still quite loose, and analysis does not always lead to true understanding.", "The goal of this work is to make generalization more intuitive.", "Using visualization methods, we discuss the mystery of generalization, the geometry of loss landscapes, and how the curse (or, rather, the blessing) of dimensionality causes optimizers to settle into minima that generalize well.", "Neural networks are a powerful tool for solving classification problems.", "The power of these models is due in part to their expressiveness; they have many parameters that can be efficiently optimized to fit nearly any finite training set.", "However, the real power of neural network models comes from their ability to generalize; they often make accurate predictions on test data that were not seen during training, provided the test data is sampled from the same distribution as the training data.", "The generalization ability of neural networks is seemingly at odds with their expressiveness.", "Neural network training algorithms work by minimizing a loss function that measures model performance using only training data.", "Because of their flexibility, it is possible to find parameter configurations Figure 1: A minefield of bad minima: we train a neural net classifier and plot the iterates of SGD after each tenth epoch (red dots).", "We also plot locations of nearby \"bad\" minima with poor generalization (blue dots).", "We visualize these using t-SNE embedding.", "All blue dots achieve near perfect train accuracy, but with test accuracy below 53% (random chance is 50%).", "The final iterate of SGD (yellow star) also achieves perfect train accuracy, but with 98.5% test accuracy.", "Miraculously, SGD always finds its way through a landscape full of bad minima, and lands at a minimizer with excellent generalization.", "for neural networks that perfectly fit the training data and minimize the loss function while making mostly incorrect predictions on test data.", "Miraculously, commonly used optimizers reliably avoid such \"bad\" minima of the loss function, and succeed at finding \"good\" minima that generalize well.", "Our goal here is to develop an intuitive understanding of neural network generalization using visualizations and experiments rather than analysis.", "We begin with some experiments to understand why generalization is puzzling, and how over-parameterization impacts model behavior.", "Then, we explore how the \"flatness\" of minima correlates with generalization, and in particular try to understand why this correlation exists.", "We explore how the high dimensionality of parameter spaces biases optimizers towards landing in flat minima that generalize well.", "Finally, we present some counterfactual experiments to validate the intuition we develop.", "Code to reproduce experiments is available at https://github.com/genviz2019/genviz.", "We explored the connection between generalization and loss function geometry using visualizations and experiments on classification margin and loss basin volumes, the latter of which does not appear in the literature.", "While experiments can provide useful insights, they sometimes raise more questions than they answer.", "We explored why the \"large margin\" properties of flat minima promote generalization.", "But what is the precise metric for \"margin\" that neural networks respect?", "Experiments suggest that the small volume of bad minima prevents optimizers from landing in them.", "But what is a correct definition of \"volume\" in a space that is invariant to parameter re-scaling and other transforms, and how do we correctly identify the attraction basins for good minima?", "Finally and most importantly: how do we connect these observations back to a rigorous PAC learning framework?", "The goal of this study is to foster appreciation for the complex behaviors of neural networks, and to provide some intuitions for why neural networks generalize.", "We hope that the experiments contained here will provide inspiration for theoretical progress that leads us to rigorous and definitive answers to the deep questions raised by generalization." ]

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[ "An intuitive empirical and visual exploration of the generalization properties of deep neural networks." ]

[ "We argue that symmetry is an important consideration in addressing the problem\n", "of systematicity and investigate two forms of symmetry relevant to symbolic processes. \n", "We implement this approach in terms of convolution and show that it can\n", "be used to achieve effective generalisation in three toy problems: rule learning,\n", "composition and grammar learning.", "Convolution (LeCun & Bengio, 1998) has been an incredibly effective element in making Deep Learning successful.", "Applying the same set of filters across all positions in an image captures an important characteristic of the processes that generate the objects depicted in them, namely the translational symmetry of the underlying laws of nature.", "Given the impact of these architectures, researchers are increasingly interested in finding approaches that can be used to exploit further symmetries (Cohen & Welling, 2016; Higgins et al., 2018) , such as rotation or scale.", "Here, we will investigate symmetries relevant to symbolic processing.", "We show that incorporating symmetries derived from symbolic processes into neural architectures allows them to generalise more robustly on tasks that require handling elements and structures that were not seen at training time.", "Specifically, we construct convolution-based models that outperform standard approaches on the rule learning task of Marcus et al. (1999) , a simplified form of the SCAN task (Lake & Baroni, 2018 ) and a simple context free language learning task.", "Symbolic architectures form the main alternative to conventional neural networks as models of intelligent behaviour, and have distinct characteristics and abilities.", "Specifically, they form representations in terms of structured combinations of atomic symbols.", "Their power comes not from the atomic symbols themselves, which are essentially arbitrary, but from the ability to construct and transform complex structures.", "This allows symbolic processing to happen without regard to the meaning of the symbols themselves, expressed in the formalist's motto as If you take care of the syntax, the semantics will take care of itself (Haugeland, 1985) .", "From this point of view, thought is a form of algebra (James, 1890; Boole, 1854) in which formal rules operate over symbolic expressions, without regard to the values of the variables they contain (Marcus, 2001) .", "As a consequence, those values can be processed systematically across all the contexts they occur in.", "So, for example, we do not need to know who Socrates is or even what mortal means in order to draw a valid conclusion from All men are mortal and Socrates is a man.", "However, connectionist approaches have been criticised as lacking this systematicity.", "Fodor & Pylyshyn (1988) claimed that neural networks lack the inherent ability to model the fact that cognitive capacities always exhibit certain symmetries, so that the ability to entertain a given thought implies the ability to entertain thoughts with semantically related contents.", "Thus, understanding these symmetries and designing neural architectures around them may enable us to build systems that demonstrate this systematicity.", "However, the concept of systematicity has itself drawn scrutiny and criticism from a range of researchers interested in real human cognition and behaviour.", "Pullum & Scholz (2007) argue that the definition is too vague.", "Nonetheless, understanding the symmetries of symbolic processes is likely to be fruitful in itself, even where human cognition fails to fully embody that idealisation.", "We investigate two kinds of symmetry, relating to permutations of symbols and to equivalence between memory slots.", "The relation between symbols and their referents is, in principle, arbitrary, and any permutation of this correspondence is therefore a symmetry of the system.", "More simply, the names we give to things do not matter, and we should be able to get equivalent results whether we call it rose or trandafir, as long as we do so consistently.", "Following on from that, a given symbol should be treated consistently wherever we find it.", "This can be thought of as a form of symmetry over the various slots within the data structures, such as stacks and queues, where symbols can be stored.", "We explore these questions using a number of small toy problems and compare the performance of architectures with and without the relevant symmetries.", "In each case, we use convolution as the means of implementing the symmetry, which, in practical terms, allows us to rely only on standard deep learning components.", "In addition, this approach opens up novel uses for convolutional architectures, and suggests connections between symbolic processes and spatial representations.", "One way to address the criticisms of distributed approaches raised by Fodor & Pylyshyn (1988) has been to focus on methods for binding and combining multiple representations (Smolensky, 1990; Hinton, 1990; Plate, 1991; Pollack, 1990; Hummel & Holyoak, 1997) in order to handle constituent structure more effectively.", "Here, we instead examined the role of symmetry in the systematicity of how those representations are processed, using a few simple proof-of-concept problems.", "We showed that imposing a symmetry on the architecture was effective in obtaining the desired form of generalisation when learning simple rules, composing representations and learning grammars.", "In particular, we discussed two forms of symmetry relevant to the processing of symbols, corresponding respectively to the fact that all atomic symbols are essentially equivalent and the fact that any given symbol can be represented in multiple places, yet retain the same meaning.", "The first of these gives rise to a symmetry under permutations of these symbols, which allows generalisation to occur from one symbol to another.", "The second gives rise to a symmetry across memory locations, which allows generalisation from simple structures to more complex ones.", "On all the problems, we implemented the symmetries using convolution.", "From a practical point of view, this allowed us to build networks using only long-accepted components from the standard neural toolkit.", "From a theoretical point of view, however, this implementation decision draws a connection between the cognition of space and the cognition of symbols.", "The translational invariance of space is probably the most significant and familiar example of symmetry we encounter in our natural environment.", "As such it forms a sensible foundation on which to build an understanding of other symmetries.", "In fact, Corcoran & Tarski (1986) use invariances under various spatial transformations within geometry as a starting point for their definition of logical notion in terms of invariance under all permutations.", "Moreover, from an evolutionary perspective, it is also plausible that there are common origins behind the mechanisms that support the exploitation of a variety of different symmetries, including potentially spatial and symbolic.", "In addition, recent research supports the idea that cerebral structures historically associated with the representation of spatial structure, such as the hippocampus and entorhinal cortex, also play a role in representing more general relational structures (Behrens et al., 2018; Duff & Brown-Schmidt, 2012) .", "Thus, our use of convolution is not merely a detail of implementation, but also an illustration of how spatial symmetries might relate to more abstract domains.", "In particular, the recursive push down automata, discussed in Section 4, utilises push and pop operations that relate fairly transparently to spatial translations.", "Of course, a variety of other symmetries, beyond translations, are likely to be important in human cognition, and an important challenge for future research will be to understand how symmetries are discovered and learned empirically, rather than being innately specified.", "A common theme in our exploration of symmetry, was the ability it conferred to separate content from structure.", "Imposing a symmetry across symbols or memory locations, allowed us to abstract away from the particular content represented to represent the structure containing it.", "So, for example the grammar rule learned by our network on the syllable sequences of Marcus et al. (1999) was able to generalise from seen to unseen syllables because it represented the abstract structure of ABB and ABA sequences, without reference to the particular syllables involved.", "We explored how this ability could also be exploited on composition and grammar learning tasks, but it is likely that there are many other situations where such a mechanism would be useful." ]

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[ "We use convolution to make neural networks behave more like symbolic systems." ]

[ "Key equatorial climate phenomena such as QBO and ENSO have never been adequately explained as deterministic processes.", "This in spite of recent research showing growing evidence of predictable behavior.", "This study applies the fundamental Laplace tidal equations with simplifying assumptions along the equator — i.e. no Coriolis force and a small angle approximation.", "The solutions to the partial differential equations are highly non-linear related to Navier-Stokes and only search approaches can be used to fit to the data." ]

[ 1, 0, 0, 0 ]

[ 0.2142857164144516, 0.08695651590824127, 0.0555555522441864, 0.12121211737394333 ]

[ "Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO" ]

[ "In the field of Continual Learning, the objective is to learn several tasks one after the other without access to the data from previous tasks.", "Several solutions have been proposed to tackle this problem but they usually assume that the user knows which of the tasks to perform at test time on a particular sample, or rely on small samples from previous data and most of them suffer of a substantial drop in accuracy when updated with batches of only one class at a time.", "In this article, we propose a new method, OvA-INN, which is able to learn one class at a time and without storing any of the previous data.", "To achieve this, for each class, we train a specific Invertible Neural Network to output the zero vector for its class.", "At test time, we can predict the class of a sample by identifying which network outputs the vector with the smallest norm.", "With this method, we show that we can take advantage of pretrained models by stacking an invertible network on top of a features extractor.", "This way, we are able to outperform state-of-the-art approaches that rely on features learning for the Continual Learning of MNIST and CIFAR-100 datasets.", "In our experiments, we are reaching 72% accuracy on CIFAR-100 after training our model one class at a time.", "A typical Deep Learning workflow consists in gathering data, training a model on this data and finally deploying the model in the real world (Goodfellow et al., 2016) .", "If one would need to update the model with new data, it would require to merge the old and new data and process a training from scratch on this new dataset.", "Nevertheless, there are circumstances where this method may not apply.", "For example, it may not be possible to store the old data because of privacy issues (health records, sensible data) or memory limitations (embedded systems, very large datasets).", "In order to address those limitations, recent works propose a variety of approaches in a setting called Continual Learning (Parisi et al., 2018) .", "In Continual Learning, we aim to learn the parameters w of a model on a sequence of datasets", "with the inputs x j i ∈ X i and the labels y j i ∈ Y i , to predict p(y * |w, x * ) for an unseen pair (x * , y * ).", "The training has to be done on each dataset, one after the other, without the possibility to reuse previous datasets.", "The performance of a Continual Learning algorithm can then be measured with two protocols : multi-head or single-head.", "In the multi-head scenario, the task identifier i is known at test time.", "For evaluating performances on task i, the set of all possible labels is then Y = Y i .", "Whilst in the single-head scenario, the task identifier is unknown, in that case we have Y = ∪ N i=1 Y i with N the number of tasks learned so far.", "For example, let us say that the goal is to learn MNIST sequentially with two batches: using only the data from the first five classes and then only the data from the remaining five other classes.", "In multi-head learning, one asks at test time to be able to recognize samples of 0-4 among the classes 0-4 and samples of 5-9 among classes 5-9.", "On the other hand, in single-head learning, one can not assume from which batch a sample is coming from, hence the need to be able to recognize any samples of 0-9 among classes 0-9.", "Although the former one has received the most attention from researchers, the last one fits better to the desiderata of a Continual Learning system as expressed in Farquhar & Gal (2018) and (van de Ven & Tolias, 2019) .", "The single-head scenario is also notoriously harder than its multi-head counterpart (Chaudhry et al., 2018) and is the focus of the present work.", "Updating the parameters with data from a new dataset exposes the model to drastically deteriorate its performance on previous data, a phenomenon known as catastrophic forgetting (McCloskey & Cohen, 1989) .", "To alleviate this problem, researchers have proposed a variety of approaches such as storing a few samples from previous datasets (Rebuffi et al., 2017) , adding distillation regularization (Li & Hoiem, 2018) , updating the parameters according to their usefulness on previous datasets (Kirkpatrick et al., 2017) , using a generative model to produce samples from previous datasets (Kemker & Kanan, 2017) .", "Despite those efforts toward a more realistic setting of Continual Learning, one can notice that, most of the time, results are proposed in the case of a sequence of batches of multiple classes.", "This scenario often ends up with better accuracy (because the learning procedure highly benefits of the diversity of classes to find the best tuning of parameters) but it does not illustrate the behavior of those methods in the worst case scenario.", "In fact, Continual Learning algorithms should be robust in the size of the batch of classes.", "In this work, we propose to implement a method specially designed to handle the case where each task consists of only one class.", "It will therefore be evaluated in the single-head scenario.", "Our approach, named One-versus-All Invertible Neural Networks (OvA-INN), is based on an invertible neural network architecture proposed by Dinh et al. (2014) .", "We use it in a One-versus-All strategy : each network is trained to make a prediction of a class and the most confident one on a sample is used to identify the class of the sample.", "In contrast to most other methods, the training phase of each class can be independently executed from one another.", "The contributions of our work are :", "(i) a new approach for Continual Learning with one class per batch;", "(ii) a neural architecture based on Invertible Networks that does not require to store any of the previous data;", "(iii) state-of-the-art results on several tasks of Continual Learning for Computer Vision (CIFAR-100, MNIST) in this setting.", "We start by reviewing the closest methods to our approach in Section 2, then explain our method in Section 3, analyse its performances in Section 4 and identify limitations and possible extensions in Section 5.", "A limiting factor in our approach is the necessity to add a new network each time one wants to learn a new class.", "This makes the memory and computational cost of OvA-INN linear with the number of classes.", "Recent works in networks merging could alleviate the memory issue by sharing weights (Chou et al., 2018) or relying on weights superposition (Cheung et al., 2019) .", "This being said, we showed that Ova-INN was able to achieve superior accuracy on CIFAR-100 class-by-class training than approaches reported in the literature, while using less parameters.", "Another constraint of using Invertible Networks is to keep the size of the output equal to the size of the input.", "When one wants to apply a features extractor with a high number of output channels, it can have a very negative impact on the memory consumption of the invertible layers.", "Feature Selection or Feature Aggregation techniques may help to alleviate this issue (Tang et al., 2014) .", "Finally, we can notice that our approach is highly dependent on the quality of the pretrained features extractor.", "In our CIFAR-100, we had to rescale the input to make it compatible with ResNet.", "Nonetheless, recent research works show promising results in training features extractors in very efficient ways (Asano et al., 2019) .", "Because it does not require to retrain its features extractor, we can foresee better performance in class-by-class learning with OvA-INN as new and more efficient features extractors are discovered.", "As a future research direction, one could try to incorporate our method in a Reinforcement Learning scenario where various situations can be learned separately in a first phase (each situation with its own Invertible Network).", "Then during a second phase where any situation can appear without the agent explicitly told in which situation it is in, the agent could rely on previously trained Invertible Networks to improve its policy.", "This setting is closely related to Options in Reinforcement Learning.", "Also, in a regression setting, one can add a fully connected layer after an intermediate layer of an Invertible Network and use it to predict the output for the trained class.", "At test time, one only need to read the output from the regression layer of the Invertible Network that had the highest confidence.", "In this paper, we proposed a new approach for the challenging problem of single-head Continual Learning without storing any of the previous data.", "On top of a fixed pretrained neural network, we trained for each class an Invertible Network to refine the extracted features and maximize the loglikelihood on samples from its class.", "This way, we show that we can predict the class of a sample by running each Invertible Network and identifying the one with the highest log-likelihood.", "This setting allows us to take full benefit of pretrained models, which results in very good performances on the class-by-class training of CIFAR-100 compared to prior works.", "channels with 5 × 5 kernel, a fully-connected layer with 100 channels applied on an input of size 7 × 7 and a final layer of 10 channels :", "S iCaRL,MNIST = 28 × 28 × 800 + (5 × 5 + 1) × 32 + (5 × 5 + 1) × 64 + (7 × 7 × 64 + 1) × 100 + (100 + 1) × 10 = 944406" ]

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[ "We propose to train an Invertible Neural Network for each class to perform class-by-class Continual Learning." ]

[ "Human-computer conversation systems have attracted much attention in Natural Language Processing.", "Conversation systems can be roughly divided into two categories: retrieval-based and generation-based systems.", "Retrieval systems search a user-issued utterance (namely a query) in a large conversational repository and return a reply that best matches the query.", "Generative approaches synthesize new replies.", "Both ways have certain advantages but suffer from their own disadvantages.", "We propose a novel ensemble of retrieval-based and generation-based conversation system.", "The retrieved candidates, in addition to the original query, are fed to a reply generator via a neural network, so that the model is aware of more information.", "The generated reply together with the retrieved ones then participates in a re-ranking process to find the final reply to output.", "Experimental results show that such an ensemble system outperforms each single module by a large margin.\n", "Automatic human-computer conversation systems have long served humans in domain-specific scenarios.", "A typical approach for such systems is built by human engineering, for example, using manually constructed ontologies ), natural language templates ), and even predefined dialogue state tracking BID29 ).Recently", ", researchers have paid increasing attention to open-domain, chatbot-style human-computer conversations such as XiaoIce 1 and Duer 2 due to their important commercial values. For opendomain", "conversations, rules and templates would probably fail since they hardly can handle the great diversity of conversation topics and flexible representations of natural language sentences. With the increasing", "popularity of on-line social media and community question-answering platforms, a huge number of human-human conversation utterances are available on the public Web BID32 ; BID13 ). Previous studies begin", "to develop data-oriented approaches, which can be roughly categorized into two groups: retrieval systems and generative systems.When a user issues an utterance (called a query), the retrieval-based conversation systems search a corresponding utterance (called a reply) that best matches the query in a pre-constructed conversational repository BID10 ; BID11 ). Owing to the abundant", "web resources, the retrieval mechanism will always find a candidate reply given a query using semantic matching. The retrieved replies", "usually have various expressions with rich information. However, the retrieved", "replies are limited by the capacity of the pre-constructed repository. Even the best matched", "reply from the conversational repository is not guaranteed to be a good response since most cases are not tailored for the issued query.To make a reply tailored appropriately for the query, a better way is to generate a new one accordingly. With the prosperity of", "neural networks powered by deep learning, generation-based conversation systems are developing fast. Generation-based conversation", "systems can synthesize a new sentence as the reply, and thus bring the results of good flexibility and quality. A typical generationbased conversation", "model is seq2seq BID23 ; BID22 ; BID20 ), in which two recurrent neural networks (RNNs) are used as the encoder and the decoder. The encoder is to capture the semantics", "of the query with one or a few distributed and real-valued vectors (also known as embeddings); the decoder aims at decoding the query embeddings to a reply. Long short term memory (LSTM) BID8 Table", "1 : Characteristics of retrieved and generated replies in two different conversational systems.(GRUs) BID3 ) could further enhance the RNNs", "to model", "longer sentences. The advantage of generation-based conversation", "systems is that they can produce flexible and tailored replies. A well known problem for the generation conversation", "systems based on \"Seq2Seq\" is that they are prone to choose universal and common generations. These generated replies such as \"I don't know\" and \"", "Me too\" suit many queries BID20 ), but they contain insufficient semantics and information. Such insufficiency leads to non-informative conversations", "in real applications.Previously, the retrieval-based and generation-based systems with their own characteristics, as listed in Table 1 , have been developed separately. We are seeking to absorb their merits. Hence, we propose", "an ensemble of retrieval-based and generation-based", "conversation systems. Specifically, given a query, we first apply the retrieval module to search", "for k candidate replies. We then propose a \"multi sequence to sequence\" (multi-seq2seq) model to integrate", "each retrieved reply into the Seq2Seq generation process so as to enrich the meaning of generated replies to respond the query. We generate a reply via the multi-seq2seq generator based on the query and k retrieved", "replies. Afterwards, we construct a re-ranker to re-evaluate the retrieved replies and the newly", "generated reply so that more meaningful replies with abundant information would stand out. The highest ranked candidate (either retrieved or generated) is returned to the user as", "the final reply. To the best of our knowledge, we are the first to build a bridge over retrieval-based and", "generation-based modules to work out a solution for an ensemble of conversation system.Experimental results show that our ensemble system consistently outperforms each single component in terms of subjective and objective metrics, and both retrieval-based and generation-based methods contribute to the overall approach. This also confirms the rationale for building model ensembles for conversation systems.", "Having verified that our model achieves the best performance, we are further curious how each gadget contributes to our final system.", "Specifically, we focus on the following research questions.", "In this paper, we propose a novel ensemble of retrieval-based and generation-based open-domain conversation systems.", "The retrieval part searches the k best-matched candidate replies, which are, along with the original query, fed to an RNN-based multi-seq2seq reply generator.", "Then the generated replies and retrieved ones are re-evaluated by a re-ranker to find the final result.", "Although traditional generation-based and retrieval-based conversation systems are isolated, we have designed a novel mechanism to connect both modules.", "The proposed ensemble model clearly outperforms state-of-the-art conversion systems in the constructed large-scale conversation dataset." ]

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[ "A novel ensemble of retrieval-based and generation-based for open-domain conversation systems." ]

[ "Deep neural networks trained on a wide range of datasets demonstrate impressive transferability.", "Deep features appear general in that they are applicable to many datasets and tasks.", "Such property is in prevalent use in real-world applications.", "A neural network pretrained on large datasets, such as ImageNet, can significantly boost generalization and accelerate training if fine-tuned to a smaller target dataset.", "Despite its pervasiveness, few effort has been devoted to uncovering the reason of transferability in deep feature representations.", "This paper tries to understand transferability from the perspectives of improved generalization, optimization and the feasibility of transferability.", "We demonstrate that", "1) Transferred models tend to find flatter minima, since their weight matrices stay close to the original flat region of pretrained parameters when transferred to a similar target dataset;", "2) Transferred representations make the loss landscape more favorable with improved Lipschitzness, which accelerates and stabilizes training substantially.", "The improvement largely attributes to the fact that the principal component of gradient is suppressed in the pretrained parameters, thus stabilizing the magnitude of gradient in back-propagation.", "3) The feasibility of transferability is related to the similarity of both input and label.", "And a surprising discovery is that the feasibility is also impacted by the training stages in that the transferability first increases during training, and then declines.", "We further provide a theoretical analysis to verify our observations.", "The last decade has witnessed the enormous success of deep neural networks in a wide range of applications.", "Deep learning has made unprecedented advances in many research fields, including computer vision, natural language processing, and robotics.", "Such great achievement largely attributes to several desirable properties of deep neural networks.", "One of the most prominent properties is the transferability of deep feature representations.", "Transferability is basically the desirable phenomenon that deep feature representations learned from one dataset can benefit optimization and generalization on different datasets or even different tasks, e.g. from real images to synthesized images, and from image recognition to object detection (Yosinski et al., 2014) .", "This is essentially different from traditional learning techniques and is often regarded as one of the parallels between deep neural networks and human learning mechanisms.", "In real-world applications, practitioners harness transferability to overcome various difficulties.", "Deep networks pretrained on large datasets are in prevalent use as general-purpose feature extractors for downstream tasks (Donahue et al., 2014) .", "For small datasets, a standard practice is to fine-tune a model transferred from large-scale dataset such as ImageNet (Russakovsky et al., 2015) to avoid over-fitting.", "For complicated tasks such as object detection, semantic segmentation and landmark localization, ImageNet pretrained networks accelerate training process substantially (Oquab et al., 2014; He et al., 2018) .", "In the NLP field, advances in unsupervised pretrained representations have enabled remarkable improvement in downstream tasks (Vaswani et al., 2017; Devlin et al., 2019) .", "Despite its practical success, few efforts have been devoted to uncovering the underlying mechanism of transferability.", "Intuitively, deep neural networks are capable of preserving the knowledge learned on one dataset after training on another similar dataset (Yosinski et al., 2014; Li et al., 2018b; 2019) .", "This is even true for notably different datasets or apparently different tasks.", "Another line of works have observed several detailed phenomena in the transfer learning of deep networks (Kirkpatrick et al., 2016; Kornblith et al., 2019 ), yet it remains unclear why and how the transferred representations are beneficial to the generalization and optimization perspectives of deep networks.", "The present study addresses this important problem from several new perspectives.", "We first probe into how pretrained knowledge benefits generalization.", "Results indicate that models fine-tuned on target datasets similar to the pretrained dataset tend to stay close to the transferred parameters.", "In this sense, transferring from a similar dataset makes fine-tuned parameters stay in the flat region around the pretrained parameters, leading to flatter minima than training from scratch.", "Another key to transferability is that transferred features make the optimization landscape significantly improved with better Lipschitzness, which eases optimization.", "Results show that the landscapes with transferred features are smoother and more predictable, fundamentally stabilizing and accelerating training especially at the early stages of training.", "This is further enhanced by the proper scaling of gradient in back-propagation.", "The principal component of gradient is suppressed in the transferred weight matrices, controlling the magnitude of gradient and smoothing the loss landscapes.", "We also investigate a common concern raised by practitioners: when is transfer learning helpful to target tasks?", "We test the transferability of pretrained networks with varying inputs and labels.", "Instead of the similarity between pretrained and target inputs, what really matters is the similarity between the pretrained and target tasks, i.e. both inputs and labels are required to be sufficiently similar.", "We also investigate the relationship between pretraining epoch and transferability.", "Surprisingly, although accuracy on the pretrained dataset increases throughout training, transferability first increases at the beginning and then decreases significantly as pretraining proceeds.", "Finally, this paper gives a theoretical analysis based on two-layer fully connected networks.", "Theoretical results consistently justify our empirical discoveries.", "The analysis here also casts light on deeper networks.", "We believe the mechanism of transferability is the fundamental property of deep neural networks and the in-depth understanding presented here may stimulate further algorithmic advances.", "Why are deep representations pretrained from modern neural networks generally transferable to novel tasks?", "When is transfer learning feasible enough to consistently improve the target task performance?", "These are the key questions in the way of understanding modern neural networks and applying them to a variety of real tasks.", "This paper performs the first in-depth analysis of the transferability of deep representations from both empirical and theoretical perspectives.", "The results reveal that pretrained representations will improve both generalization and optimization performance of a target network provided that the pretrained and target datasets are sufficiently similar in both input and labels.", "With this paper, we show that transfer learning, as an initialization technique of neural networks, exerts implicit regularization to restrict the networks from escaping the flat region of pretrained landscape." ]

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[ "Understand transferability from the perspectives of improved generalization, optimization and the feasibility of transferability." ]

[ "We address the following question: How redundant is the parameterisation of ReLU networks?", "Specifically, we consider transformations of the weight space which leave the function implemented by the network intact.", "Two such transformations are known for feed-forward architectures: permutation of neurons within a layer, and positive scaling of all incoming weights of a neuron coupled with inverse scaling of its outgoing weights.", "In this work, we show for architectures with non-increasing widths that permutation and scaling are in fact the only function-preserving weight transformations.", "For any eligible architecture we give an explicit construction of a neural network such that any other network that implements the same function can be obtained from the original one by the application of permutations and rescaling.", "The proof relies on a geometric understanding of boundaries between linear regions of ReLU networks, and we hope the developed mathematical tools are of independent interest.\n", "Ever since its early successes, deep learning has been a puzzle for machine learning theorists.", "Multiple aspects of deep learning seem at first sight to contradict common sense: single-hidden-layer networks suffice to approximate any continuous function (Cybenko, 1989; Hornik et al., 1989 ), yet in practice deeper is better; the loss surface is highly non-convex, yet it can be minimised by first-order methods; the capacity of the model class is immense, yet deep networks tend not to overfit (Zhang et al., 2017) .", "Recent investigations into these and other questions have emphasised the role of overparameterisation, or highly redundant function representation.", "It is now known that overparameterised networks enjoy both easier training (Allen-Zhu et al., 2019; Du et al., 2019; Frankle & Carbin, 2019) , and better generalisation (Belkin et al., 2019; Neyshabur et al., 2019; Novak et al., 2018) .", "However, the specific mechanism by which over-parameterisation operates is still largely a mystery.", "In this work, we study one particular aspect of over-parameterisation, namely the ability of neural networks to represent a target function in many different ways.", "In other words, we ask whether many different parameter configurations can give rise to the same function.", "Such a notion of parameterisation redundancy has so far remained unexplored, despite its potential connections to the structure of the loss landscape, as well as to the literature on neural network capacity in general.", "Specifically, we consider feed-forward ReLU networks, with weight matrices W 1 , . . . , W L , and biases b 1 , . . . , b L ,.", "We study parameter transformations which preserve the output behaviour of the network h(z) = W L σ(W L−1 σ(. . . W 1 z + b 1 . . . ) + b L−1 ) + b L for all inputs z in some domain Z. Two such transformations are known for feed-forward ReLU architectures:", "1. Permutation of units (neurons) within a layer, i.e. for some permutation matrix P,", "2. Positive scaling of all incoming weights of a unit coupled with inverse scaling of its outgoing weights.", "Applied to a whole layer, with potentially different scaling factors arranged into a diagonal matrix M, this can be written as", "Our main theorem applies to architectures with non-increasing widths, and shows that there are no other function-preserving parameter transformations besides permutation and scaling.", "Stated formally:", "Theorem 1.", "Consider a bounded open nonempty domain Z ⊆ R d0 and any architecture", "For this architecture, there exists a ReLU network h θ : Z → R, or equivalently a setting of the weights θ (W 1 , b 1 , . . . , W L , b L ), such that for any 'general' ReLU network h η : Z → R (with the same architecture) satisfying h θ (z) = h η (z) for all z ∈ Z, there exist permutation matrices P 1 , . . . P L−1 , and positive diagonal matrices M 1 , . . . , M L−1 , such that", "where η (W 1 , b 1 , . . . , W L , b L ) are the parameters of h η .", "In the above, 'general' networks is a class of networks meant to exclude degenerate cases.", "We give a more precise definition in Section 3; for now it suffices to note that almost all networks are general.", "The proof of the result relies on a geometric understanding of prediction surfaces of ReLU networks.", "These surfaces are piece-wise linear functions, with non-differentiabilities or 'folds' between linear regions.", "It turns out that folds carry a lot of information about the parameters of a network, so much in fact, that some networks are uniquely identified (up to permutation and scaling) by the function they implement.", "This is the main insight of the theorem.", "In the following sections, we introduce in more detail the concept of a fold-set, and describe its geometric structure for a subclass of ReLU networks.", "The paper culminates in a proof sketch of the main result.", "The full proof, including proofs of intermediate results, is included in the Appendix.", "In this work, we have shown that for architectures with non-increasing widths, certain ReLU networks are almost uniquely identified by the function they implement.", "The result suggests that the function-equivalence classes of ReLU networks are surprisingly small, i.e. there may be only little redundancy in the way ReLU networks are parameterised, contrary to what is commonly believed.", "This apparent contradiction could be explained in a number of ways:", "• It could be the case that even though exact equivalence classes are small, approximate equivalence is much easier to achieve.", "That is, it could be that h θ − h η ≤ is satisfied by a disproportionately larger class of parameters η than h θ − h η = 0.", "This issue is related to the so-called inverse stability of the realisation map of neural nets, which is not yet well understood.", "• Another possibility is that the kind of networks we consider in this paper is not representative of networks typically encountered in practice, i.e. it could be that 'typical networks' do not have well connected dependency graphs, and are therefore not easily identifiable.", "• Finally, we have considered only architectures with non-increasing widths, whereas some previous theoretical work has assumed much wider intermediate layers compared to the input dimension.", "It is possible that parameterisation redundancy is much larger in such a regime compared to ours.", "However, gains from over-parameterisation have also been observed in practical settings with architectures not unlike those considered here.", "We consider these questions important directions for further research.", "We also hypothesise that our analysis could be extended to convolutional and recurrent networks, and to other piece-wise linear activation functions such as leaky ReLU.", "Definition A.1 (Partition).", "Let S ⊆ Z. We define the partition of Z induced by S, denoted P Z (S), as the set of connected components of Z \\ S. Definition A.2 (Piece-wise hyperplane).", "Let P be a partition of Z. We say H ⊆ Z is a piece-wise hyperplane with respect to partition P, if H = ∅ and there exist (w, b) = (0, 0) and P ∈ P such that H = {z ∈ P | w z + b = 0}.", "Definition A.3 (Piece-wise linear surface / pwl. surface).", "A set S ⊆ Z is called a piece-wise linear surface on Z of order κ if it can be written as", ", and no number smaller than κ admits such a representation.", "Lemma A.1.", "If S 1 , S 2 are piece-wise linear surfaces on Z of order k 1 and k 2 , then S 1 ∪ S 2 is a piece-wise linear surface on Z of order at most max {k 1 , k 2 }.", "We can write H", "Given sets Z and S ⊆ Z, we introduce the notation", "(The dependence on Z is suppressed.)", "By Lemma A.1, i S is itself a pwl.", "surface on Z of order at most i.", "Lemma A.2.", "For i ≤ j and any set S, we have i j S = j i S = i S.", "Proof.", "We will need these definitions:", "j S = {S ⊆ S | S is a pwl.", "surface of order at most j},", "i j S = {S ⊆ j S | S is a pwl.", "surface of order at most i},", "surface of order at most j}.", "Consider first the equality j i S = i S. We know that j i S ⊆ i S because the square operator always yields a subset.", "At the same time, i S ⊆ j i S, because i S satisfies the condition for membership in (6).", "To prove the equality i j S = i S, we use the inclusion j S ⊆ S to deduce i j S ⊆ i S. Now let S ⊆ S be one of the sets under the union in (3), i.e. it is a pwl.", "surface of order at most i.", "Then it is also a pwl.", "surface of order at most j, implying S ⊆ j S. This means S is also one of the sets under the union in (5), proving that i S ⊆ i j S.", "Lemma A.3.", "Let Z and S ⊆ Z be sets.", "Then one can write k+1 S = k S ∪ i H i where H i are piece-wise hyperplanes wrt.", "P Z ( k S).", "Proof.", "At the same time,", "is a pwl.", "surface of order at most k + 1 because k S is a pwl.", "surface of order at most k and H k+1 i", "can be decomposed into piece-wise hyperplanes wrt.", "Definition A.4 (Canonical representation of a pwl. surface).", "Let S be a pwl.", "surface on Z. The pwl.", "is a pwl.", "surface in canonical form, then κ is the order of S.", "Proof.", "Denote the order of S by λ.", "By the definition of order, λ ≤ κ, and S = λ S. Then, since", "It follows that κ = λ.", "Lemma A.5.", "Every pwl.", "surface has a canonical representation.", "Proof.", "The inclusion l∈[k],i∈[n l ] H l i ⊆ k S holds for any representation.", "We will show the other inclusion by induction in the order of S. If S is order one, 1 S ⊆ S = i∈[n1] H 1 i holds for any representation and we are done.", "Now assume the lemma holds up to order κ − 1, and let S be order κ.", "Then by Lemma A.3, S = κ S = κ−1 S ∪ i H κ i , where H κ i are piece-wise hyperplanes wrt.", "P Z ( κ−1 S).", "By the inductive assumption, κ−1 S has a canonical representation, Proof.", "Let k ∈ [κ].", "Because both representations are canonical, we have", "where H k i and G k j are piece-wise hyperplanes wrt.", "where on both sides above we have a union of hyperplanes on an open set.", "The claim follows.", "Definition A.5 (Dependency graph of a pwl. surface).", "Let S be a piece-wise linear surface on Z, and let S = l∈[κ],i∈[n l ] H l i be its canonical representation.", "We define the dependency graph of S as the directed graph that has the piece-wise hyperplanes H l i l,i as vertices, and has an edge" ]

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[ "We prove that there exist ReLU networks whose parameters are almost uniquely determined by the function they implement." ]

[ "A general problem that received considerable recent attention is how to perform multiple tasks in the same network, maximizing both efficiency and prediction accuracy.", "A popular approach consists of a multi-branch architecture on top of a\n", "shared backbone, jointly trained on a weighted sum of losses.", "However, in many cases, the shared representation results in non-optimal performance, mainly due to an interference between conflicting gradients of uncorrelated tasks.", "Recent approaches address this problem by a channel-wise modulation of the feature-maps along the shared backbone, with task specific vectors, manually or dynamically tuned.", "Taking this approach a step further, we propose a novel architecture which\n", "modulate the recognition network channel-wise, as well as spatial-wise, with an efficient top-down image-dependent computation scheme.", "Our architecture uses no task-specific branches, nor task specific modules.", "Instead, it uses a top-down modulation network that is shared between all of the tasks.", "We show the effectiveness of our scheme by achieving on par or better results than alternative approaches on both correlated and uncorrelated sets of tasks.", "We also demonstrate our advantages in terms of model size, the addition of novel tasks and interpretability. \n", "Code will be released.", "The goal of multi-task learning is to improve the learning efficiency and increase the prediction accuracy of multiple tasks learned and performed together in a shared network.", "Over the years, several types of architectures have been proposed to combine multiple tasks training and evaluation.", "Most current schemes assume task-specific branches, on top of a shared backbone (Figure 1a) and use a weighted sum of tasks losses, fixed or dynamically tuned, to train them (Chen et al., 2017; Kendall et al., 2018; Sener & Koltun, 2018) .", "Having a shared representation is more efficient from the standpoint of memory and sample complexity and can also be beneficial in cases where the tasks are correlated to each other (Maninis et al., 2019) .", "However, in many other cases, the shared representation can also result in worse performance due to the limited capacity of the shared backbone and interference between conflicting gradients of uncorrelated tasks (Zhao et al., 2018) .", "The performance of the multi-branch architecture is highly dependent on the relative losses weights and the task correlations, and cannot be easily determined without a \"trial and error\" phase search (Kendall et al., 2018) .", "Another type of architecture (Maninis et al., 2019 ) that has been recently proposed uses task specific modules, integrated along a feed-forward backbone and producing task-specific vectors to modulate the feature-maps along it (Figure 1b) .", "Here, both training and evaluation use a single tasking paradigm: executing one task at a time, rather than getting all the task responses in a single forward pass of the network.", "A possible disadvantage of using task-specific modules and of using a fixed number of branches, is that it may become difficult to add additional tasks at a later time during the system life-time.", "Modulation-based architectures have been also proposed by Strezoski et al. (2019) and Zhao et al. (2018) (Figure 1c ).", "However, all of these works modulate the recognition network channel-wise, using the same modulation vector for all the spatial dimension of the feature-maps.", "We propose a new type of architecture with no branching, which performs single task at a time but with no task-specific modules (Figure 1d ).", "The core component of our approach is a top-down (TD)", "(a)", "(b)", "(c)", "(d) Figure 1:", "(a) Multi branched architecture, task specific branches on a top of a shared backbone, induces capacity and destructive interference problems, force careful tuning.", "Recently proposed architectures:", "(b) using tasks specific modules and", "(c) using channel-wise modulation modules.", "(d) Our architecture: a top-down image-aware full tensor modulation network with no task specific modules.", "modulation network, which carries the task information in combination with the image information, obtained from a first bottom-up (BU1) network, and modulates a second bottom-up (BU2) network common for all the tasks.", "In our approach, the modulation is channel-wise as well as spatial-wise (a full tensor modulation), calculated sequentially along the TD stream.", "This allows us, for example, to modulate only specific spatial locations of the image depending on the current task, and get interpretability properties by visualizing the activations in the lowest feature-map of the TD stream.", "In contrast to previous works, our modulation mechanism is also \"image-aware\" in the sense that information from the image, extracted by the BU1 stream, is accumulated by the TD stream, and affects the modulation process.", "The main differences between our approach and previous approaches are the following: First, as mentioned, our approach does not use multiple branches or task-specific modules.", "We can scale the number of tasks with no additional layers.", "Second, our modulation scheme includes a spatial component, which allows attention to specific locations in the image, as illustrated in figure 2a for the Multi-MNIST tasks (Sabour et al., 2017) .", "Third, the modulation in our scheme is also image dependent and can modulate regions of the image based on their content rather than location (relevant examples are demonstrated in figures 2b and 2c).", "We empirically evaluated the proposed approach on three different datasets.", "First, we demonstrated on par accuracies with the single task baseline on an uncorrelated set of tasks with MultiMNIST while using less parameters.", "Second, we examined the case of correlated tasks and outperformed all baselines on the CLEVR (Johnson et al., 2017) dataset.", "Third, we scaled the number of tasks and demonstrated our inherent attention mechanism on the CUB200 (Welinder et al., 2010) dataset.", "The choice of datasets includes cases where the tasks are uncorrelated (Multi-MNIST) and cases where the tasks are relatively correlated (CLEVR and CUB200).", "The results demonstrate that our proposed scheme can successfully handle both cases and shows distinct advantages over the channel-wise modulation approach." ]

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[ "We propose a top-down modulation network for multi-task learning applications with several advantages over current schemes. " ]

[ "Clustering algorithms have wide applications and play an important role in data analysis fields including time series data analysis.", "The performance of a clustering algorithm depends on the features extracted from the data.", "However, in time series analysis, there has been a problem that the conventional methods based on the signal shape are unstable for phase shift, amplitude and signal length variations.\n", "In this paper, we propose a new clustering algorithm focused on the dynamical system aspect of the signal using recurrent neural network and variational Bayes method.", "Our experiments show that our proposed algorithm has a robustness against above variations and boost the classification performance.", "The rapid progress of IoT technology has brought huge data in wide fields such as traffic, industries, medical research and so on.", "Most of these data are gathered continuously and accumulated as time series data, and the extraction of features from a time series have been studied intensively in recent years.", "The difficulty of time series analysis is the variation of the signal in time which gives rise to phase shift, compress/stretch and length variation.", "Many methods have been proposed to solve these problems.", "Dynamic Time Warping (DTW) was designed to measure the distance between warping signals (Rabiner & Juang, 1993) .", "This method solved the compress/stretch problem by applying a dynamic planning method.", "Fourier transfer or wavelet transfer can extract the features based on the frequency components of signals.", "The phase shift independent features are obtained by calculating the power spectrum of the transform result.", "In recent years, the recurrent neural network (RNN), which has recursive neural network structure, has been widely used in time series analysis (Elman, 1990; 1991) .", "This recursive network structure makes it possible to retain the past information of time series.", "Furthermore, this architecture enables us to apply this algorithm to signals with different lengths.", "Although the methods mentioned above are effective solutions for the compress/stretch, phase shift and signal length variation issues respectively, little has been studied about these problems comprehensively.", "Let us turn our attention to feature extraction again.", "Unsupervised learning using a neural network architecture autoencoder (AE) has been studied as a feature extraction method (Hinton & Salakhutdinov, 2006; Vincent et al., 2008; Rifai et al., 2011) .", "AE using RNN structure (RNN-AE) has also been proposed (Srivastava et al., 2015) and it has been applied to real data such as driving data (Dong et al., 2017) and others.", "RNN-AE can be also interpreted as the discrete dynamical system: chaotic behavior and the deterrent method have been studied from this point of view (Zerroug et al., 2013; Laurent & von Brecht, 2016) .", "In this paper, we propose a new clustering algorithm for feature extraction focused on the dynamical system aspect of RNN-AE.", "In order to achieve this, we employed a multi-decoder autoencoder with multiple decoders to describe different dynamical systems.", "We also applied the variational Bayes method (Attias, 1999; Ghahramani & Beal, 2001; Kaji & Watanabe, 2011) as the clustering algorithm.", "This paper is composed as follows: in Section 4, we explain AE from a dynamical system view, then we define our model and from this, derive its learning algorithm.", "In Section 5, we describe the application of our algorithm to an actual time series to show its robustness, including running two experiments using periodic data and driving data.", "Finally we summarize our study and describe our future work in Section 7.", "We verified the feature extraction peformance of the MDRA using actual time series data.", "In Section 5.1, we saw that the periodic signals are completely classified by the frequency using clustering weight r n .", "In this experiment, the average clustering weights, the elements of are (3.31e-01, 8.31e-47, 8.31e-47, 3.46e-01, 8.31e-47, 3.19e-01, 8.31e-47) , with only three components having effective weights.", "This weight narrowing-down is one of the advantages of VB learning.", "The left of Fig. 9 shows an enlarged view of around \"freq 4\" in Fig. 7 (right) .", "We found that the distribution of \"freq 4\" is in fact spread linearly.", "The right of Fig. 9 is the result Hinton, 2008) .", "We found that each frequency data formed several spreading clusters without overlapping.", "As we saw earlier, the distribution of r n has a spreading distribution compared to that of h n .", "We inferred that the spreading of the distribution r n was caused by extracting the diversity on the driving scenes.", "In addition, the identification result shows that the combination of the features given by r n and h n can improve the performance.", "Dong et al. (2017) , which studied a driver identify algorithm using the AE, proposed the minimization of the error integrating the reconstruction error of AE and the classification error of deep neural network.", "This algorithm can avoid the over-fitting by using unlabeled data whose data collection cost is smaller than labeled data.", "From these results, we can expect that the MDRA can contribute to not only boost identification performance but also restrain the over-fitting.", "In this paper, we proposed a new algorithm MDRA that can extract dynamical system features of a time series data.", "We conducted experiments using periodic signals and actual driving data to verify the advantages of MDRA.", "The results show that our algorithm not only has robustness for the phase shift, amplitude and signal length variation, but also can boost classification performance." ]

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[ "Novel time series data clustring algorithm based on dynamical system features." ]

[ "Two important topics in deep learning both involve incorporating humans into the modeling process: Model priors transfer information from humans to a model by regularizing the model's parameters; Model attributions transfer information from a model to humans by explaining the model's behavior.", "Previous work has taken important steps to connect these topics through various forms of gradient regularization.", "We find, however, that existing methods that use attributions to align a model's behavior with human intuition are ineffective.", "We develop an efficient and theoretically grounded feature attribution method, expected gradients, and a novel framework, attribution priors, to enforce prior expectations about a model's behavior during training.", "We demonstrate that attribution priors are broadly applicable by instantiating them on three different types of data: image data, gene expression data, and health care data.", "Our experiments show that models trained with attribution priors are more intuitive and achieve better generalization performance than both equivalent baselines and existing methods to regularize model behavior.", "Recent work on interpreting machine learning models has focused on feature attribution methods.", "Given an input feature, a model, and a prediction on a particular sample, such methods assign a number to the input feature that represents how important the input feature was for making the prediction.", "Previous literature about such methods has focused on the axioms they should satisfy (Lundberg and Lee, 2017; Sundararajan et al., 2017; Štrumbelj and Kononenko, 2014; Datta et al., 2016) , and how attribution methods can give us insight into model behavior (Lundberg et al., 2018a; Sayres et al., 2019; Zech et al., 2018) .", "These methods can be an effective way of revealing problems in a model or a dataset.", "For example, a model may place too much importance on undesirable features, rely on many features when sparsity is desired, or be sensitive to high frequency noise.", "In such cases, we often have a prior belief about how a model should treat input features, but for neural networks it can be difficult to mathematically encode this prior in terms of the original model parameters.", "Ross et al. (2017b) introduce the idea of regularizing explanations to train models that better agree with domain knowledge.", "Given a binary variable indicating whether each feature should or should not be important for predicting on each sample in the dataset, their method penalizes the gradients of unimportant features.", "However, two drawbacks limit the method's applicability to real-world problems.", "First, gradients don't satisfy the theoretical guarantees that modern feature attribution methods do (Sundararajan et al., 2017) .", "Second, it is often difficult to specify which features should be important in a binary manner.", "More recent work has stressed that incorporating intuitive, human priors will be necessary for developing robust and interpretable models (Ilyas et al., 2019) .", "Still, it remains challenging to encode meaningful, human priors like \"have smoother attribution maps\" or \"treat this group of features similarly\" by penalizing the gradients or parameters of a model.", "In this work, we propose an expanded framework for encoding abstract priors, called attribution priors, in which we directly regularize differentiable functions of a model's axiomatic feature attributions during training.", "This framework, which can be seen as a generalization of gradient-based regularization (LeCun et al., 2010; Ross et al., 2017b; Yu et al., 2018; Jakubovitz and Giryes, 2018; Roth et al., 2018) , can be used to encode meaningful domain knowledge more effectively than existing methods.", "Furthermore, we introduce a novel feature attribution method -expected gradientswhich extends integrated gradients (Sundararajan et al., 2017) , is naturally suited to being regularized under an attribution prior, and avoids hyperparameter choices required by previous methods.", "Using attribution priors, we build improved deep models for three different prediction tasks.", "On images, we use our framework to train a deep model that is more interpretable and generalizes better to noisy data by encouraging the model to have piecewise smooth attribution maps over pixels.", "On gene expression data, we show how to both reduce prediction error and better capture biological signal by encouraging similarity among gene expression features using a graph prior.", "Finally, on a patient mortality prediction task, we develop a sparser model and improve performance when learning from limited training data by encouraging a skewed distribution of the feature attributions.", "The immense popularity of deep learning has driven its application in many domains with diverse, complicated prior knowledge.", "While it is in principle possible to hand-design network architectures to encode this knowledge, we propose a simpler approach.", "Using attribution priors, any knowledge that can be encoded as a differentiable function of feature attributions can be used to encourage a model to act in a particular way in a particular domain.", "We also introduce expected gradients, a feature attribution method that is theoretically justified and removes the choice of a single reference value that many existing feature attribution methods require.", "We further demonstrate that expected gradients naturally integrates with attribution priors via sampling during SGD.", "The combination allows us to improve model performance by encoding prior knowledge across several different domains.", "It leads to smoother and more interpretable image models, biological predictive models that incorporate graph-based prior knowledge, and sparser health care models that can perform better in data-scarce scenarios.", "Attribution priors provide a broadly applicable framework for encoding domain knowledge, and we believe they will be valuable across a wide array of domains in the future.", "Normally, training with a penalty on any function of the gradients would require solving a differential equation.", "To avoid this, we adopt a double back-propagation scheme in which the gradients are first calculated with respect to the training loss, and alternately calculated with the loss with respect to the attributions (Yu et al., 2018; Drucker and Le Cun, 1992) .", "Our attribution method, expected gradients, requires background reference samples to be drawn from the training data.", "More specifically, for each input in a batch of inputs, we need k additional inputs to calculate expected gradients for that input batch.", "As long as k is smaller than the batch size, we can avoid any additional data reading by re-using the same batch of input data as a reference batch, as in Zhang et al. (2017) .", "We accomplish this by shifting the batch of input k times, such that each input in the batch uses k other inputs from the batch as its reference values." ]

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[ "A method for encouraging axiomatic feature attributions of a deep model to match human intuition." ]

[ "Recurrent neural networks (RNNs) have shown excellent performance in processing sequence data.", "However, they are both complex and memory intensive due to their recursive nature.", "These limitations make RNNs difficult to embed on mobile devices requiring real-time processes with limited hardware resources.", "To address the above issues, we introduce a method that can learn binary and ternary weights during the training phase to facilitate hardware implementations of RNNs.", "As a result, using this approach replaces all multiply-accumulate operations by simple accumulations, bringing significant benefits to custom hardware in terms of silicon area and power consumption.", "On the software side, we evaluate the performance (in terms of accuracy) of our method using long short-term memories (LSTMs) and gated recurrent units (GRUs) on various sequential models including sequence classification and language modeling.", "We demonstrate that our method achieves competitive results on the aforementioned tasks while using binary/ternary weights during the runtime.", "On the hardware side, we present custom hardware for accelerating the recurrent computations of LSTMs with binary/ternary weights.", "Ultimately, we show that LSTMs with binary/ternary weights can achieve up to 12x memory saving and 10x inference speedup compared to the full-precision hardware implementation design.", "Convolutional neural networks (CNNs) have surpassed human-level accuracy in various complex tasks by obtaining a hierarchical representation with increasing levels of abstraction BID3 ; BID31 ).", "As a result, they have been adopted in many applications for learning hierarchical representation of spatial data.", "CNNs are constructed by stacking multiple convolutional layers often followed by fully-connected layers BID30 ).", "While the vast majority of network parameters (i.e. weights) are usually found in fully-connected layers, the computational complexity of CNNs is dominated by the multiply-accumulate operations required by convolutional layers BID46 ).", "Recurrent neural networks (RNNs), on the other hand, have shown remarkable success in modeling temporal data BID36 ; BID12 ; BID6 ; ; ).", "Similar to CNNs, RNNs are typically over-parameterized since they build on high-dimensional input/output/state vectors and suffer from high computational complexity due to their recursive nature BID45 ; BID14 ).", "As a result, the aforementioned limitations make the deployment of CNNs and RNNs difficult on mobile devices that require real-time inference processes with limited hardware resources.Several techniques have been introduced in literature to address the above issues.", "In BID40 ; BID22 ; BID29 ; BID42 ), it was shown that the weight matrix can be approximated using a lower rank matrix.", "In BID34 ; BID14 ; ; BID1 ), it was shown that a significant number of parameters in DNNs are noncontributory and can be pruned without any performance degradation in the final accuracy performance.", "Finally, quantization approaches were introduced in ; BID33 ; BID9 ; BID26 ; BID20 ; BID39 ; BID19 ; BID49 ; ; ) to reduce the required bitwidth of weights/activations.", "In this way, power-hungry multiply-accumulate operations are replaced by simple accumulations while also reducing the number of memory accesses to the off-chip memory.Considering the improvement factor of each of the above approaches in terms of energy and power reductions, quantization has proven to be the most beneficial for hardware implementations.", "However, all of the aforementioned quantization approaches focused on optimizing CNNs or fully-connected networks only.", "As a result, despite the remarkable success of RNNs in processing sequential data, RNNs have received the least attention for hardware implementations, when compared to CNNs and fully-connected networks.", "In fact, the recursive nature of RNNs makes their quantization difficult.", "In BID18 ), for example, it was shown that the well-known BinaryConnect technique fails to binarize the parameters of RNNs due to the exploding gradient problem ).", "As a result, a binarized RNN was introduced in BID18 ), with promising results on simple tasks and datasets.", "However it does not generalize well on tasks requiring large inputs/outputs BID45 ).", "In BID45 ; BID20 ), multi-bit quantized RNNs were introduced.", "These works managed to match their accuracy performance with their full-precision counterparts while using up to 4 bits for data representations.In this paper, we propose a method that learns recurrent binary and ternary weights in RNNs during the training phase and eliminates the need for full-precision multiplications during the inference time.", "In this way, all weights are constrained to {+1, −1} or {+1, 0, −1} in binary or ternary representations, respectively.", "Using the proposed approach, RNNs with binary and ternary weights can achieve the performance accuracy of their full-precision counterparts.", "In summary, this paper makes the following contributions:• We introduce a method for learning recurrent binary and ternary weights during both forward and backward propagation phases, reducing both the computation time and memory footprint required to store the extracted weights during the inference.•", "We perform a set of experiments on various sequential tasks, such as sequence classification, language modeling, and reading comprehension. We", "then demonstrate that our binary/ternary models can achieve near state-of-the-art results with greatly reduced computational complexity.", "In this section, we evaluate the performance of the proposed LSTMs with binary/ternary weights on different temporal tasks to show the generality of our method.", "We defer hyperparameters and tasks details for each dataset to Appendix C due to the limited space.", "As discussed in Section 4, the training models ignoring the quantization loss fail to quantize the weights in LSTM while they perform well on CNNs and fully-connected networks.", "To address this problem, we proposed the use of batch normalization during the quantization process.", "To justify the importance of such a decision, we have performed different experiments over a wide range of temporal tasks and compared the accuracy performance of our binarization/ternarization method with binaryconnect as a method that ignores the quantization loss.", "The experimental results showed that binaryconnect method fails to learn binary/ternary weights.", "On the other hand, our method not only learns recurrent binary/ternary weights but also outperforms all the existing quantization methods in literature.", "It is also worth mentioning that the models trained with our method achieve a comparable accuracy performance w.r.t. their full-precision counterpart.Figure 1(a", ") shows a histogram of the binary/ternary weights of the LSTM layer used for characterlevel language modeling task on the Penn Treebank corpus. In", "fact, our model learns to use binary or ternary weights by steering the weights into the deterministic values of -1, 0 or 1. Despite", "the CNNs or fully-connected networks trained with binary/ternary weights that can use either real-valued or binary/ternary weights, the proposed LSTMs trained with binary/ternary can only perform the inference computations with binary/ternary weights. Moreover", ", the distribution of the weights is dominated by non-zero values for the model with ternary weights.To show the effect of the probabilistic quantization on the prediction accuracy of temporal tasks, we adopted the ternarized network trained for the character-level language modeling tasks on the Penn Treebank corpus (see Section 5.1). We measured", "the prediction accuracy of this network on the test set over 10000 samples and reported the distribution of the prediction accuracy in FIG0 . FIG0 (b) shows", "that", "the variance imposed by the stochastic ternarization on the prediction accuracy is very small and can be ignored. It is worth mentioning", "that we also have observed a similar behavior for other temporal tasks used in this paper. FIG1 illustrates the learning", "curves and generalization of our method to longer sequences on the validation set of the Penn Treebank corpus. In fact, the proposed training", "algorithm also tries to retains the main features of using batch normalization, i.e., fast convergence and good generalization over long sequences. FIG1 (a) shows that our model", "converges", "faster than the full-precision LSTM for the first few epochs. After a certain point, the convergence", "rate of our method decreases, that prevents the model from early overfitting. FIG1 (b) also shows that our training", "method", "generalizes well over longer sequences than those seen during training. Similar to the full-precision baseline,", "our binary/ternary models learn to focus only on information relevant to the generation of the next target character. In fact, the prediction accuracy of our", "models improves as the sequence length increases since longer sequences provides more information from past for generation of the next target character.While we have only applied our binarization/ternarization method on LSTMs, our method can be used to binarize/ternarize other recurrent architectures such as GRUs. To show the versatility of our method,", "we repeat the character-level language modeling task performed in Section 5.1 using GRUs on the Penn Treebank, War & Peace and Linux Kernel corpora. We also adopted the same network configurations", "and settings used in Section 5.1 for each of the aforementioned corpora. TAB4 6 summarizes the performance of our binarized/ternarized", "models. The simulation results show that our method can successfully", "binarize/ternarize the recurrent weights of GRUs.As a final note, we have investigated the effect of using different batch sizes on the prediction accuracy of our binarized/ternarized models. To this end, we trained an LSTM of size 1000 over a sequence", "length of 100 and different batch sizes to perform the character-level language modeling task on the Penn Treebank corpus. Batch normalization cannot be used for the batch size of 1 as", "the output vector will be all zeros. Moreover, using a small batch size leads to a high variance when", "estimating the statistics of the unnormalized vector, and consequently a lower prediction accuracy than the baseline model without bath normalization, as shown in Figure 3 . On the other hand, the prediction accuracy of our binarization/ternarization", "models improves as the batch size increases, while the prediction accuracy of the baseline model decreases. Figure 3 : Effect of different batch sizes on the prediction accuracy of the", "character-level language modeling task on the Penn Treebank corpus. The introduced binarized/ternarized recurrent models can be exploited by various", "dataflows such as DaDianNao (Chen et al. (2014) ) and TPU (Jouppi et al. (2017) ). In order to evaluate the effectiveness of LSTMs with recurrent binary/ternary weights", ", we build our binary/ternary architecture over DaDianNao as a baseline which has proven to be the most efficient dataflow for DNNs with sigmoid/tanh functions. In fact, DaDianNao achieves a speedup of 656× and reduces the energy by 184× over a", "GPU (Chen et al. (2014) ). Moreover, some hardware techniques can be adopted on top of DaDianNao to further speed", "up the computations. For instance, showed that ineffectual computations of zero-valued weights can be skipped", "to improve the run-time performance of DaDianNao. In DaDianNao, a DRAM is used to store all the weights/activations and provide the required", "memory bandwidth for each multiply-accumulate (MAC) unit. For evaluation purposes, we consider two different application-specific integrated circuit", "(ASIC) architectures implementing Eq. (2): low-power implementation and high-speed inference engine. We build these two architectures based on the aforementioned dataflow. For the low-power implementation", ", we use 100 MAC units. We also use a 12-bit fixed-point representation", "for both weights and activations of the full-precision", "model as a baseline architecture. As a result, 12-bit multipliers are required to perform the recurrent computations. Note that using the", "12-bit fixed-point representation for weights and activations guarantees no prediction", "accuracy loss in the full-precision models. For the LSTMs with recurrent binary/ternary weights, a 12-bit fixed-point representation is only used for", "activations and multipliers in the MAC units are replaced with low-cost multiplexers. Similarly, using 12-bit fixed-point representation for activations guarantees no prediction accuracy loss", "in the introduced binary/ternary models. We implemented our low-power inference engine for both the full-precision and binary/ternary-precision models", "in TSMC 65-nm CMOS technology. The synthesis results excluding the implementation cost of the DRAM are summarized in TAB7 . They show that using", "recurrent binary/ternary weights results in up to 9× lower power and 10.6× lower silicon area", "compared to the baseline when performing the inference computations at 400 MHz.For the high-speed design, we consider the same silicon area and power consumption for both the fullprecision and binary/ternary-precision models. Since the MAC units of the binary/ternary-precision model require less silicon area and power consumption as a result", "of using multiplexers instead of multipliers, we can instantiate up to 10× more MAC units, resulting in up to 10× speedup compared to the full-precision model (see TAB7 ). It is also worth noting that the models using recurrent binary/ternary weights also require up to 12× less memory bandwidth", "than the full-precision models. More details on the proposed architecture are provided in Appendix D.", "In this paper, we introduced a method that learns recurrent binary/ternary weights and eliminates most of the full-precision multiplications of the recurrent computations during the inference.", "We showed that the proposed training method generalizes well over long sequences and across a wide range of temporal tasks such as word/character language modeling and pixel by pixel classification tasks.", "We also showed that learning recurrent binary/ternary weights brings a major benefit to custom hardware implementations by replacing full-precision multipliers with hardware-friendly multiplexers and reducing the memory bandwidth.", "For this purpose, we introduced two ASIC implementations: low-power and high-throughput implementations.", "The former architecture can save up to 9× power consumption and the latter speeds up the recurrent computations by a factor of 10.", "Figure 4: Probability density of states/gates for the BinaryConnect LSTM compared to its fullprecision counterpart on the Penn Treebank character-level modeling task.", "Both models were trained for 50 epochs.", "The vertical axis denotes the time steps.", "Figure 4 shows the probability density of the gates and hidden states of the BinaryConnect LSTM and its full-precision counterpart both trained with 1000 units and a sequence length of 100 on Penn Treebank corpus BID35 for 50 epochs.", "The probability density curves show that the gates in the binarized LSTM fail to control the flow of information.", "More specifically, the input gate i and the output gate o tend to let all information through, the gate g tends to block all information, and the forget gate f cannot decide to let which information through.", "p and values centered around 1 for the input gate i.", "In fact, the binarization process changes the probability density of the gates and hidden states during the training phase." ]

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[ "We propose high-performance LSTMs with binary/ternary weights, that can greatly reduce implementation complexity" ]

[ "This paper addresses unsupervised few-shot object recognition, where all training images are unlabeled and do not share classes with labeled support images for few-shot recognition in testing.", "We use a new GAN-like deep architecture aimed at unsupervised learning of an image representation which will encode latent object parts and thus generalize well to unseen classes in our few-shot recognition task.", "Our unsupervised training integrates adversarial, self-supervision, and deep metric learning.", "We make two contributions.", "First, we extend the vanilla GAN with reconstruction loss to enforce the discriminator capture the most relevant characteristics of \"fake\" images generated from randomly sampled codes.", "Second, we compile a training set of triplet image examples for estimating the triplet loss in metric learning by using an image masking procedure suitably designed to identify latent object parts.", "Hence, metric learning ensures that the deep representation of images showing similar object classes which share some parts are closer than the representations of images which do not have common parts.", "Our results show that we significantly outperform the state of the art, as well as get similar performance to the common episodic training for fully-supervised few-shot learning on the Mini-Imagenet and Tiered-Imagenet datasets.", "This paper presents a new deep architecture for unsupervised few-shot object recognition.", "In training, we are given a set of unlabeled images.", "In testing, we are given a small number K of support images with labels sampled from N object classes that do not appear in the training set (also referred to as unseen classes).", "Our goal in testing is to predict the label of a query image as one of these N previously unseen classes.", "A common approach to this N -way K-shot recognition problem is to take the label of the closest support to the query.", "Thus, our key challenge is to learn a deep image representation on unlabeled data such that it would in testing generalize well to unseen classes, so as to enable accurate distance estimation between the query and support images.", "Our unsupervised few-shot recognition problem is different from the standard few-shot learning (Snell et al., 2017; Finn et al., 2017) , as the latter requires labeled training images (e.g., for episodic training (Vinyals et al., 2016) ).", "Also, our problem is different from the standard semi-supervised learning (Chapelle et al., 2009) , where both unlabeled and labeled data are typically allowed to share either all or a subset of classes.", "When classes of unlabeled and labeled data are different in semi-supervised learning (Chapelle et al., 2009) , the labeled dataset is typically large enough to allow transfer learning of knowledge from unlabeled to labeled data, which is not the case in our few-shot setting.", "There is scant work on unsupervised few-shot recognition.", "The state of the art (Hsu et al., 2018) first applies unsupervised clustering (Caron et al., 2018) for learning pseudo labels of unlabeled training images, and then uses the standard few-shot learning on these pseudo labels for episodic traininge.g.", ", Prototypical Network (Snell et al., 2017) or MAML (Finn et al., 2017) .", "However, performance of this method is significantly below that of counterpart approaches to supervised few-shot learning.", "Our approach is aimed at learning an image representation from unlabeled data that captures presence or absence of latent object parts.", "We expect that such a representation would generalize well We use a GAN-like deep architecture to learn an image encoding z on unlabeled training data that will be suitable for few-shot recognition in testing.", "Our unsupervised training integrates adversarial, self-supervision, and metric learning.", "The figure illustrates our first contribution that extends the vanilla GAN (the red dashed line) with regularization so the encodingẑ of a \"fake\" image is similar to the randomly sampled code z which has been used for generating the \"fake\" image.", "The self-supervision task is to predict the rotation angle of rotated real training images.", "Deep metric learning is illustrated in greater detail in Fig. 3 .", "to unseen classes in our few-shot recognition task.", "This is because of the common assumption in computer vision that various distinct object classes share certain parts.", "Thus, while our labeled and unlabeled images do not show the same object classes, there may be some parts that appear in both training and test image sets.", "Therefore, an image representation that would capture presence of these common parts in unlabeled images is expected to also be suitable for representing unseen classes, and thus facilitate our N -way K-shot recognition.", "Toward learning such an image representation, in our unsupervised training, we integrate adversarial, self-supervision, and deep metric learning.", "As shown in Fig. 1 , we use a GAN-like architecture for training a discriminator network D to encode real images", "d , which will be later used for few-shot recognition in testing.", "We also consider a discrete encoding z = D z (x) ∈ {−1, 1} d , and empirically discover that it gives better performance than the continuous counterpart.", "Hence our interpretation that binary values in the discrete z indicate presence or absence of d latent parts in images.", "In addition to D z , the discriminator has two other outputs (i.e., heads), D r/f and D rot , for adversarial and self-supervised learning, respectively as illustrated in Fig. 2 .", "D is adversarially trained to distinguish between real and \"fake\" images, where the latter x are produced by a generator network G, x = G(z ), from image encodings z which are randomly sampled from the uniform distribution", "Sampling from the uniform distribution is justified, because latent parts shared among a variety of object classes appearing in the unlabeled training set are likely to be uniformly distributed across the training set.", "We extend the vanilla GAN with regularization aimed at minimizing a reconstruction loss between the sampled z and the corresponding embeddingẑ = D(G(z )).", "As our experiments demonstrate, this reconstruction loss plays an important role in training both D and G in combination with the adversarial loss, as both losses enforce G generate as realistic images as possible and D capture the most relevant image characteristics for reconstruction and real/fake recognition.", "Furthermore, following recent advances in self-supervised learning (Doersch et al., 2015; Zhang et al., 2016; Noroozi & Favaro, 2016; Noroozi et al., 2017; Zhang et al., 2017) , we also augment our training set with rotated versions of the real images around their center, and train D to predict their rotation angles,α = D rot (Rotate(x, α)) ∈ {0, 1, 2, 3} * 90", "• .", "As in other approaches that use self-supervised learning, our results demonstrate that this data augmentation strengthens our unsupervised training and improves few-shot recognition.", "Finally, we use deep metric learning toward making the image encoding z = D z (x) represent latent parts and in this way better capture similarity of object classes for our few-shot recognition.", "We expect that various object classes share parts, and that more similar classes have more common parts.", "Therefore, the encodings of images showing similar (or different) object classes should have a small (or large) distance.", "To ensure this property, we use metric learning and compile a new training set of triplet images for estimating the standard triple loss, as illustrated in Fig. 3 .", "Since classes in our training set are not annotated, we form the triplet training examples by using an image masking procedure which is particularly suitable for identifying latent object parts.", "In the triplet, the anchor is the original (unmasked) image, the positive is an image obtained from the original by masking rectangular patches at the image periphery (e.g., top corner), and the negative is an image obtained from the original by masking centrally located image patches.", "By design, the negative image masks an important object part, and thus the deep representations of the anchor and the negative should have a large distance.", "Conversely, masking peripheral corners in the positive image does not cover any important parts of the object, and thus the deep representation of the positive should be very close to that of the anchor.", "In this way, our metric learning on the triplet training examples ensures that the learned image representation z accounts for similarity of object classes in terms of their shared latent parts.", "As our results show, this component of our unsupervised training further improves few-shot recognition in testing, to the extent that not only do we significantly outperform the state of the art but also get a performance that is on par with the common episodic training for fullysupervised few-shot learning on the Mini-Imagenet (Vinyals et al., 2016; Ravi & Larochelle, 2016) and Tiered-Imagenet (Ren et al., 2018) datasets.", "Our contributions are twofold:", "• Extending the vanilla GAN with a reconstruction loss between uniformly sampled codes,", ", and embeddings of the corresponding \"fake\" images,ẑ = D(G(z )).", "• The masking procedure for compiling triplet image examples and deep metric learning of z so it accounts for image similarity in terms of shared latent parts.", "The rest of this paper is organized as follows.", "Sec. 2 reviews previous work, Sec. 3 specifies our proposed approach, Sec. 4 presents our implementation details and our experimental results, and finally, Sec. 5 gives our concluding remarks.", "We have addressed unsupervised few-shot object recognition, where all training images are unlabeled and do not share classes with test images.", "A new GAN-like deep architecture has been (Donahue et al., 2016) 25.56 ± 1.08 31.10 ± 0.63 --AAL-ProtoNets (Antoniou & Storkey, 2019) 37.67 ± 0.39 40.29 ± 0.68 --UMTRA + AutoAugment (Khodadadeh et al., 2018) 39.93 50.73 --DeepCluster CACTUs -ProtoNets (Hsu et al., 2018) 39.", "(Snell et al., 2017) 46.56 ± 0.76 62.29 ± 0.71 46.52 ± 0.72 66.15 ± 0.74", "Figure 4: Our image masking with rectangular patches for Mini-Imagenet.", "In every row, the images are organized from left to right in the descending order by their estimated distance to the original (unmasked) image.", "proposed for unsupervised learning of an image representation which respects image similarity in terms of shared latent object parts.", "We have made two contributions by extending the vanilla GAN with reconstruction loss and by integrating deep metric learning with the standard adversarial and self-supervision learning.", "Our results demonstrate that our approach generalizes will to unseen classes, outperforming the sate of the art by more than 8% in both 1-shot and 5-shot recognition tasks on the benchmark Mini-Imagenet dataset.", "We have reported the first results of unsupervised few-shot recognition on the Tiered-Imagenet dataset.", "Our ablations have evaluated that solely our first contribution leads to superior performance relative to that of closely related approaches, and that the addition of the second contribution further improves our 1-shot and 5-shot recognition by 3%.", "We also outperform a recent fully-supervised approach to few-shot learning that uses the common episodic training on the same datasets." ]

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[ "We address the problem of unsupervised few-shot object recognition, where all training images are unlabeled and do not share classes with test images." ]

[ "Existing black-box attacks on deep neural networks (DNNs) so far have largely focused on transferability, where an adversarial instance generated for a locally trained model can “transfer” to attack other learning models.", "In this paper, we propose novel Gradient Estimation black-box attacks for adversaries with query access to the target model’s class probabilities, which do not rely on transferability.", "We also propose strategies to decouple the number of queries required to generate each adversarial sample from the dimensionality of the input.", "An iterative variant of our attack achieves close to 100% adversarial success rates for both targeted and untargeted attacks on DNNs.", "We carry out extensive experiments for a thorough comparative evaluation of black-box attacks and show that the proposed Gradient Estimation attacks outperform all transferability based black-box attacks we tested on both MNIST and CIFAR-10 datasets, achieving adversarial success rates similar to well known, state-of-the-art white-box attacks.", "We also apply the Gradient Estimation attacks successfully against a real-world content moderation classifier hosted by Clarifai.", "Furthermore, we evaluate black-box attacks against state-of-the-art defenses.", "We show that the Gradient Estimation attacks are very effective even against these defenses.", "The ubiquity of machine learning provides adversaries with both opportunities and incentives to develop strategic approaches to fool learning systems and achieve their malicious goals.", "Many attack strategies devised so far to generate adversarial examples to fool learning systems have been in the white-box setting, where adversaries are assumed to have access to the learning model BID18 ; BID0 ; BID1 ; BID6 ).", "However, in many realistic settings, adversaries may only have black-box access to the model, i.e. they have no knowledge about the details of the learning system such as its parameters, but they may have query access to the model's predictions on input samples, including class probabilities.", "For example, we find this to be the case in some popular commercial AI offerings, such as those from IBM, Google and Clarifai.", "With access to query outputs such as class probabilities, the training loss of the target model can be found, but without access to the entire model, the adversary cannot access the gradients required to carry out white-box attacks.Most existing black-box attacks on DNNs have focused on transferability based attacks BID12 ; BID7 ; BID13 ), where adversarial examples crafted for a local surrogate model can be used to attack the target model to which the adversary has no direct access.", "The exploration of other black-box attack strategies is thus somewhat lacking so far in the literature.", "In this paper, we design powerful new black-box attacks using limited query access to learning systems which achieve adversarial success rates close to that of white-box attacks.", "These black-box attacks help us understand the extent of the threat posed to deployed systems by adversarial samples.", "The code to reproduce our results can be found at https://github.com/ anonymous 1 .New", "black-box attacks. We", "propose novel Gradient Estimation attacks on DNNs, where the adversary is only assumed to have query access to the target model. These", "attacks do not need any access to a representative dataset or any knowledge of the target model architecture. In the", "Gradient Estimation attacks, the adversary adds perturbations proportional to the estimated gradient, instead of the true gradient as in white-box attacks BID0 ; Kurakin et al. (2016) ). Since", "the direct Gradient Estimation attack requires a number of queries on the order of the dimension of the input, we explore strategies for reducing the number of queries to the target model. We also", "experimented with Simultaneous Perturbation Stochastic Approximation (SPSA) and Particle Swarm Optimization (PSO) as alternative methods to carry out query-based black-box attacks but found Gradient Estimation to work the best.Query-reduction strategies We propose two strategies: random feature grouping and principal component analysis (PCA) based query reduction. In our", "experiments with the Gradient Estimation attacks on state-of-the-art models on MNIST (784 dimensions) and CIFAR-10 (3072 dimensions) datasets, we find that they match white-box attack performance, achieving attack success rates up to 90% for single-step attacks in the untargeted case and up to 100% for iterative attacks in both targeted and untargeted cases. We achieve", "this performance with just 200 to 800 queries per sample for single-step attacks and around 8,000 queries for iterative attacks. This is much", "fewer than the closest related attack by . While they achieve", "similar success rates as our attack, the running time of their attack is up to 160× longer for each adversarial sample (see Appendix I.6).A further advantage", "of the Gradient Estimation attack is that it does not require the adversary to train a local model, which could be an expensive and complex process for real-world datasets, in addition to the fact that training such a local model may require even more queries based on the training data.Attacking real-world systems. To demonstrate the", "effectiveness of our Gradient Estimation attacks in the real world, we also carry out a practical black-box attack using these methods against the Not Safe For Work (NSFW) classification and Content Moderation models developed by Clarifai, which we choose due to their socially relevant application. These models have", "begun to be deployed for real-world moderation BID4 , which makes such black-box attacks especially pernicious. We carry out these", "attacks with no knowledge of the training set. We have demonstrated", "successful attacks ( FIG0 ) with just around 200 queries per image, taking around a minute per image. In FIG0 , the target", "model classifies the adversarial image as 'safe' with high confidence, in spite of the content that had to be moderated still being clearly visible. We note here that due", "to the nature of the images we experiment with, we only show one example here, as the others may be offensive to readers. The full set of images", "is hosted anonymously at https://www.dropbox.com/s/ xsu31tjr0yq7rj7/clarifai-examples.zip?dl=0.Comparative evaluation", "of black-box attacks. We carry out a thorough empirical", "comparison of various black-box attacks (given in TAB8 ) on both MNIST and CIFAR-10 datasets. We study attacks that require zero", "queries to the learning model, including the addition of perturbations that are either random or proportional to the difference of means of the original and targeted classes, as well as various transferability based black-box attacks. We show that the proposed Gradient", "Estimation attacks outperform other black-box attacks in terms of attack success rate and achieve results comparable with white-box attacks.In addition, we also evaluate the effectiveness of these attacks on DNNs made more robust using adversarial training BID0 BID18 and its recent variants including ensemble adversarial training BID21 and iterative adversarial training BID9 . We find that although standard and", "ensemble adversarial training confer some robustness against single-step attacks, they are vulnerable to iterative Gradient Estimation attacks, with adversar-ial success rates in excess of 70% for both targeted and untargeted attacks. We find that our methods outperform", "other black-box attacks and achieve performance comparable to white-box attacks.Related Work. Existing black-box attacks that do", "not use a local model were first proposed for convex inducing two-class classifiers by BID11 . For malware data, Xu et al. (2016)", "use genetic algorithms to craft adversarial samples, while Dang et al. (2017) use hill climbing algorithms. These methods are prohibitively expensive", "for non-categorical and high-dimensional data such as images. BID13 proposed using queries to a target", "model to train a local surrogate model, which was then used to to generate adversarial samples. This attack relies on transferability.To", "the best of our knowledge, the only previous literature on query-based black-box attacks in the deep learning setting is independent work by BID10 and . BID10 propose a greedy local search to generate", "adversarial samples by perturbing randomly chosen pixels and using those which have a large impact on the output probabilities. Their method uses 500 queries per iteration, and", "the greedy local search is run for around 150 iterations for each image, resulting in a total of 75,000 queries per image, which is much higher than any of our attacks. Further, we find that our methods achieve higher", "targeted and untargeted attack success rates on both MNIST and CIFAR-10 as compared to their method. propose a black-box attack method named ZOO, which", "also uses the method of finite differences to estimate the derivative of a function. However, while we propose attacks that compute an", "adversarial perturbation, approximating FGSM and iterative FGS; ZOO approximates the Adam optimizer, while trying to perform coordinate descent on the loss function proposed by BID1 . Neither of these works demonstrates the effectiveness", "of their attacks on real-world systems or on state-of-the-art defenses.", "Overall, in this paper, we conduct a systematic analysis of new and existing black-box attacks on state-of-the-art classifiers and defenses.", "We propose Gradient Estimation attacks which achieve high attack success rates comparable with even white-box attacks and outperform other state-of-the-art black-box attacks.", "We apply random grouping and PCA based methods to reduce the number of queries required to a small constant and demonstrate the effectiveness of the Gradient Estimation attack even in this setting.", "We also apply our black-box attack against a real-world classifier and state-of-the-art defenses.", "All of our results show that Gradient Estimation attacks are extremely effective in a variety of settings, making the development of better defenses against black-box attacks an urgent task.Stephen" ]

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[ "Query-based black-box attacks on deep neural networks with adversarial success rates matching white-box attacks" ]

[ "We propose a novel subgraph image representation for classification of network fragments with the target being their parent networks.", "The graph image representation is based on 2D image embeddings of adjacency matrices.", "We use this image representation in two modes.", "First, as the input to a machine learning algorithm.", "Second, as the input to a pure transfer learner.", "Our conclusions from multiple datasets are that\n", "1. deep learning using structured image features performs the best compared to graph kernel and classical features based methods; and,\n", "2. pure transfer learning works effectively with minimum interference from the user and is robust against small data.\n", "Our experiments overwhelmingly show that the structured image representation of graphs achieves successful graph classification with ease.", "The image representation is lossless, that is the image embeddings contain all the information in the corresponding adjacency matrix.", "Our results also show that even with very little information about the parent network, Deep network models are able to extract network signatures.", "Specifically, with just 64-node samples from networks with up to 1 million nodes, we were able to predict the parent network with > 90% accuracy while being significantly better than random with only 8-node samples.", "Further, we demonstrated that the image embedding approach provides many advantages over graph kernel and feature-based methods.We also presented an approach to graph classification using transfer learning from a completely different domain.", "Our approach converts graphs into 2D image embeddings and uses a pre-trained image classifier (Caffe) to obtain label-vectors.", "In a range of experiments with real-world data sets, we have obtained accuracies from 70% to 94% for 2-way classification and 61% for multi-way classification.", "Further, our approach is highly resilient to training-to-test ratio, that is, can work with sparse training samples.", "Our results show that such an approach is very promising, especially for applications where training data is not readily available (e.g. terrorist networks).Future", "work includes improvements to the transfer learning by improving the distance function between label-vectors, as well as using the probabilities from Caffe. Further", ", we would also look to generalize this approach to other domains, for example classifying radio frequency map samples using transfer learning." ]

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[ "We convert subgraphs into structured images and classify them using 1. deep learning and 2. transfer learning (Caffe) and achieve stunning results." ]