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Question: Deep neural networks (DNNs) are inspired from the human brain and the interconnection between the two has been widely studied in the literature. However, it is still an open question whether DNNs are able to make decisions like the brain. Previous work has demonstrated that DNNs, trained by matching the neural responses from inferior temporal (IT) cortex in monkey's brain, is able to achieve human-level performance on the image object recognition tasks. This indicates that neural dynamics can provide informative knowledge to help DNNs accomplish specific tasks. In this paper, we introduce the concept of a neuro-AI interface, which aims to use human's neural responses as supervised information for helping AI systems solve a task that is difficult when using traditional machine learning strategies. In order to deliver the idea of neuro-AI interfaces, we focus on deploying it to one of the fundamental problems in generative adversarial networks (GANs): designing a proper evaluation metric to evaluate the quality of images produced by GANs. Deep neural networks (DNNs) have successfully been applied to a number of different areas such as computer vision and natural language processing where they have demonstrated state-of-the-art , often matching and even sometimes surpassing a human's ability. Moreover, DNNs have been studied with respect to how similar processing is carried out in the human brain, where identifying these overlaps and interconnections has been a focus of study and investigation in the literature BID5 BID4 BID11 BID18 BID30 BID1 BID35 BID17 BID15. In this research area, convolutional neural networks (CNNs) are widely studied to be compared with the visual system in human's brain because of following reasons: CNNs and human's visual system are both hierarchical system; Steps of processing input between CNNs and human's visual system are similar to each other e.g., in a object recognition task, both CNNs and human recognize a object based on their its shape, edge, color etc.. Work BID35 outlines the use of CNNs approach for delving even more deeply into understanding the development and organization of sensory cortical processing. It has been demonstrated that CNNs are able to reflect the spatio-temporal neural dynamics in human's brain visual area BID5 BID30 BID18. Despite lots of work is carried out to reveal the similarity between CNNs and brain system, research on interacting between CNNs and neural dynamics is less discussed in the literature as understanding of neural dynamics in the neuroscience area is still limited. There is a growing interest in studying generative adversarial networks (GANs) in the deep learning community BID10. Specifically, GANs have been widely applied to various domains such as computer vision BID14, natural language processing BID7 and speech synthesis BID6. Compared with other deep generative models (e.g. variational autoencoders (VAEs)), GANs are favored for effectively handling sharp estimated density functions, efficiently generating desired samples and eliminating deterministic bias. Due to these properties GANs have successfully contributed to plausible image generation BID14, image to image translation BID38, image super-resolution BID19, image completion BID37 etc.. However, three main challenges still exist currently in the research of GANs: Mode collapse -the model cannot learn the distribution of the full dataset well, which leads to poor generalization ability; Difficult to trainit is non-trivial for discriminator and generator to achieve Nash equilibrium during the training; Hard to evaluate -the evaluation of GANs can be considered as an effort to measure the dissimilarity between real distribution p r and generated distribution p g. Unfortunately, the accurate estimation of p r is intractable. Thus, it is challenging to have a good estimation of the correspondence between p r and p g. Aspects and are more concerned with computational aspects where much research has been carried out to mitigate these issues BID20; BID0. Aspect is similarly fundamental, however, limited literature is available and most of the current metrics only focus on measuring the dissimilarity between training and generated images. A more meaning-ful GANs evaluation metric that is consistent with human perceptions is paramount in helping researchers to further refine and design better GANs. Although some evaluation metrics, e.g., Inception Score (IS), Kernel Maximum Mean Discrepancy (MMD) and Fréchet Inception Distance (FID), have already been proposed (; BID13 BID2, their limitations are obvious: These metrics do not agree with human perceptual judgments and human rankings of GAN models. A small artefact on images can have a large effect on the decision made by a machine learning system BID16, whilst the intrinsic image content does not change. In this aspect, we consider human perception to be more robust to adversarial images samples when compared to a machine learning system; These metrics require large sample sizes for evaluation ). Large-scale samples for evaluation sometimes are not realistic in real-world applications since it is time-consuming; and They are not able to rank individual GAN-generated images by their quality i.e., the metrics are generated on a collection of images rather than on a single image basis. The within GAN variances are crucial because it can provide the insight on the variability of that GAN.Work BID36 demonstrates that CNN matched with neural data recorded from inferior temporal cortex BID3 has high performance in object recognition tasks. Given the evidence above that a CNN is able to predict the neural response in the brain, we describe a neuro-AI interface system, where human being's neural response is used as supervised information to help the AI system (CNNs used in this work) solve more difficult problems in real-world. As a starting point for exploiting the idea of neuro-AI interface, we focus on utilizing it to solve one of the fundamental problems in GANs: designing a proper evaluation metric. Neural response Stimulus Figure 1. Schematic of neuro-AI interface. Stimuli (image stimuli used in this work) are simultaneously presented to an AI system and participants. Participants' neural responses are transferred to the AI system as supervised information for assisting the AI system make decision. In this paper, we first demonstrate the ability of a brainproduced score (we call it Neuroscore), generated from human being's electroencephalography (EEG) signals, in terms of the quality evaluation on GANs. Secondly, we demonstrate and validate a neural-AI interface (as seen in Fig. 1), which uses neural responses as supervised information to train a CNN. The trained CNN model is able to predict Neuroscore for images without corresponding neural responses. We test this framework via three models: Shallow convolutional neural network, Mobilenet V2 BID26 and Inception V3 BID29.In detail, Neuroscore is calculated via measurement of the P300, an event-related potential (ERP) BID23 present in EEG, via a rapid serial visual presentation (RSVP) paradigm BID32. P300 and RSVP paradigm are mature techniques in the brain-computer interface (BCI) community and have been applied in a wider variety of tasks such as image search BID9, information retrieval BID22, and etc. The unique benefit of Neuroscore is that it more directly reflects the human perceptual judgment of images, which is intuitively more reliable compared to the conventional metrics in the literature BID2. Current literature has demonstrated that CNNs are able to predict neural responses in inferior temporal cortex in image recognition task BID36 BID35 via invasive BCI techniques BID31. Evidence shows that neural responses in inferior temporal cortex directly link the information processing during the image recognition task. Therefore, a CNN trained by predicting neural responses in inferior temporal cortex also achieves the good performance during the image recognition BID36. Comparing the traditional end-toend machine learning system, use of DNNs for predicting neural responses in the brain favors following benefits: It enables the information processing of DNNs closer to human being's brain system; For some difficult tasks in real-world e.g, evaluation of image quality demonstrated in this paper, it is still challenging to design the machine learning algorithms, which teach DNNs to process the information like humans; and Neural signals directly reflect the human perception and interfacing between neural responses and DNNs can be more efficient than the traditional methods regarding the area of human and AI.The investigation of using CNNs to predict neural response from non-invasive BCI aspect is still blank in the literature. Comparing to invasively measured neural dynamics, EEG favors pros such as simple measurement, unpainful experience during recording, free to ethic argument and more easily generalized to real-world applications. However, EEG suffers challenges such as low signal quality (i.e TAB1 Neuro-AI Interface low SNR), low spatial resolution (interested neural activities span all scalp and difficult to be localized), which makes the prediction for EEG response still challenging. With advanced machine leaching technologies applied to non-invasive BCI area, source localization and reconstruction are feasible for EEG signals today. Previously work BID33 a) have demonstrated the efficacy of using spatial filtering approaches for reconstructing P300 source ERP signals. The low SNR issue can be remedied by averaging the EEG trials. Based on this evidence, we explore the use of DNNs to predict Neuroscore when neural information is available. We propose a neuro-AI interface in order to generalize the use of Neuroscore. This kind of framework interfaces between neural responses and AI systems (CNN used in this study), which uses neural responses as supervised information to train a CNN. The trained CNN is then used for predicting Neuroscore given images generated by one of the popular GAN models. Figure 2 demonstrates the schematic of neuro-AI interface used in this work 1. Flow 1 shows that the image processed by human being's brain and produces single trial P300 source signal for each input image. Flow 2 in Fig. 2 demonstrates a CNN with including EEG signals during training stage. The convolutional and pooling layers process the image similarly as retina done BID21. Fully connected layers (FC) 1-3 aim to emulate the brain's functionality that produces EEG signal. Yellow dense layer in the architecture aims to predict the single trial P300 source signal in 400-600 ms response from each image input. In order to help model make a more accurate prediction for the single trial P300 amplitude for the output, the single trial P300 source signal in 400-600 ms is fed to the yellow dense layer to learn parameters for the previous layers in the training step. The model was then trained to predict the single trial P300 source amplitude (red point shown in signal trail P300 source signal of Fig. 2). Mobilenet V2, Inception V3 and Shallow network were explored in this work, where in flow 2 we use these three network bones: such as Conv1-pooling layers. For Mobilenet V2 and Inception V3. We used pretrained parameters from up to the FC 1 shown in Fig. 2. We trained parameters from FC 1 to FC 4 for Mobilenet V2 and Inception V3. θ 1 is 1 We understand that human being's brain system is much more complex than what we demonstrated in this work and the flow in the brain is not one-directional BID27 BID2. Our framework can be further extended to be more biologically plausible. Add windowed single trial P300 source signal Figure 2. A neuro-AI interface and training details with adding EEG information. Our training strategy includes two stages: Learning from image to P300 source signal; and Learning from P300 source signal to P300 amplitude. loss1 is the L2 distance between the yellow layer and the single trial P300 source signal in the 400 -600 ms corresponding to the single input image. loss2 is the mean square error between model prediction and the single trial P300 amplitude. loss1 and loss2 will be introduced in section 3.2.used to denote the parameters from FC 1 to FC 3 and θ 2 indicates the parameters in FC 4. For the Shallow model, we trained all parameters from scratch. We added EEG to the model because we first want to find a function f (χ) → s that maps the images space χ to the corresponding single trial P300 source signal s. This prior knowledge can help us to predict the single trial P300 amplitude in the second learning stage. We compared the performance of the models with and without EEG for training. We defined two stage loss function (loss 1 for single trial P300 source signal in the 400 -600 ms time window and loss 2 for single trial P300 amplitude) as DISPLAYFORM0 where S true i ∈ R 1×T is the single trial P300 signal in the 400 -600 ms time window to the presented image, and y i refers to the single trial P300 amplitude to each image. The training of the models without using EEG is straightforward, models were trained directly to minimize loss 2 (θ 1, θ 2) by feeding images and the corresponding single trial P300 amplitude. Training with EEG information is explained in Algorithm 1 and visualized in the "Flow 2" of Fig. 2 with two stages. Stage 1 learns parameters θ 1 to predict P300 source signal while stage 2 learns parameters θ 2 to predict single trial P300 amplitude with θ 1 fixed. Update θ 2 by descending its stochastic gradient: and without EEG. All models with EEG perform better than models without EEG, with much smaller errors and variances. Statistic tests between model with EEG and without EEG are also carried out to verify the significance of including EEG information during the training phase. One-way ANOVA tests (P-value) for each model with EEG and without EEG are stated as: P Shallow = 0.003, P M obilenet = 0.012 and P Inception = 5.980e − 05. Results here demonstrate that including EEG during the training stage helps all three CNNs improve the performance on predicting the Neuroscore. The performance of models with EEG is ranked as follows: Inception-EEG, Mobilenet-EEG, and Shallow-EEG, which indicates that deeper neural networks may achieve better performance in this task. We used the randomized EEG signal here as a baseline to see the efficacy of adding EEG to produce better Neuroscore output. When randomizing the EEG, it shows that the error for each three model increases significantly. For Mobilenet and Inception, the error of the randomized EEG is even higher than those without EEG in the training stage, demonstrating that the EEG information in the training stage is crucial to each model. Figure 3 shows that the models with EEG information have a stronger correlation between predicted Neuroscore and real Neuroscore. The cluster (blue, orange, and green circles) for each category of the model trained with EEG (left column) is more separable than the cluster produced by model without EEG (right column). This conveys with EEG for training models: Neuroscore is more accurate; and Neuroscore is able to rank the performances of different GANs, which cannot be achieved by other metrics BID2. Figure 3. Scatter plot of predicted and real Neuroscore of 6 models (Shallow, Mobilenet, Inception with and without EEG for training) cross participants by 20 times repeated shuffling training and testing set. Each circle represents the cluster for a specific category. Small triangle markers inside each cluster correspond to each shuffling process. The dot at the center of each cluster is the mean. In this paper, we introduce a neuro-AI interface that interacts CNNs with neural signals. We demonstrate the use of neuro-AI interface by introducing a challenge in the area of GANs i.e., evaluate the quality of images produced by GANs. Three deep network architectures are explored and the demonstrate that including neural responses during the training phase of the neuro-AI interface improves its accuracy even when neural measurements are absent when evaluating on the test set. More details of the performance of Neuroscore can be referred in Appendix. FIG1 shows the averaged reconstructed P300 signal across all participants (using LDA beamformer) in the RSVP experiment. It should be noted here that the averaged reconstructed P300 signal is calculated as the difference between averaged target trials and averaged standard trials after applying the LDA beamformer method. The solid lines in FIG1 are the means of the averaged reconstructed P300 signals for each image category (across 12 participants) while the shaded areas represent the standard deviations (across participants). It can be seen that the averaged reconstructed P300 (across participants) clearly distinguishes between different image categories. In order to statistically measure this correlative relationship, we calculated the Pearson correlation coefficient and p-value (two-tailed) between Neuroscore and BE accuracy and found (r = −0.767, p = 2.089e − 10). We also did the Pearson statistical test and bootstrap on the correlation between Neuroscore and BE accuracy (human judgment performance) only for GANs i.e., DCGAN, BEGAN and PROGAN. Pearson statistic is (r=-0.827, p=4.766e-10) and the bootstrapped p ≤ 0.0001. Three traditional methods are also employed to evaluate the GANs used in this study. score indicates better GAN performance), we use 1/Neuroscore for comparison. It can be seen that all three methods are consistent with each other and they rank the GANs in the same order of PROGAN, DCGAN and BEGAN from high to low performance. By comparing the three traditional evaluation metrics to the human, it can be seen that they are not consistent with human judgment of GAN performance. It should be remembered that Inception Score is able to measure the quality of the generated images while the other two methods cannot do so. However, Inception Score still rates DCGAN as outperforming BE-GAN. Our proposed Neuroscore is consistent with human judgment. Another property of using Neuroscore is the ability to track the quality of an individual image. Traditional evaluation metrics are unable to score each individual image for two reasons: They need large-scale samples for evaluation; Most methods (e.g. MMD and FID) evaluate GANs based on the dissimilarity between real images and generated images so they are not able to score the generated image one by one. For our proposed method, the score of each single image can also be evaluated as a single trial P300 amplitude. We demonstrate that using the predicted single trial P300 amplitude to observe the single image quality in Fig. 6. This property provides Neuroscore with a novel capability that can observe the variations within a typical GAN. Although Neuroscore and IS are generated from deep neural networks. Neuroscore is more suitable than IS for evaluating GANs in that: It is more explainable than IS as it is a direct reflection of human perception; Much smaller sample size is required for evaluation; Higher Neuroscore exactly indicates better image quality while IS Figure 6. P300 for each single image predicted by the proposed neuro-AI interface in our paper. Higher predicted P300 indicates the better image quality.does not. We also included the RFACE images in our generalization test. FIG3 (c) demonstrates that the predicted Neuroscore is still correlated with the real Neuroscore when adding the RFACE images and the model ranks the types of images as: PROGAN>RFACE>BEGAN>DCGAN, which is consistent with the Neuroscore that has been measured directly from participants shown in FIG3.Compared to traditional evaluation metrics, Neuroscore is able to score the GAN based on very few image samples, relatively. Recording EEG in the training stage could be the limitation of generalizing Neuroscore to evaluate a new GAN. However, the use of dry electrode EEG recording system BID8 can accelerate and simplify the data acquisition significantly. Moreover, GANs enable the possibility of synthesizing the EEG BID12, which has wide applications in brain-machine interface research.

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Describe a neuro-AI interface technique to evaluate generative adversarial networks

Inspired by trial-to-trial variability in the brain that can result from multiple noise sources, we introduce variability through noise in the knowledge distillation framework and studied their effect on generalization and robustness.


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Question: While recent developments in autonomous vehicle (AV) technology highlight substantial progress, we lack tools for rigorous and scalable testing. Real-world testing, the de facto evaluation environment, places the public in danger, and, due to the rare nature of accidents, will require billions of miles in order to statistically validate performance claims. We implement a simulation framework that can test an entire modern autonomous driving system, including, in particular, systems that employ deep-learning perception and control algorithms. Using adaptive sampling methods to accelerate rare-event probability evaluation, we estimate the probability of an accident under a base distribution governing standard traffic behavior. We demonstrate our framework on a highway scenario. Several fatal accidents involving autonomous vehicles (AVs) underscore the importance of testing whether AV perception and control pipelines-when considered as a whole systemcan safely interact with other human traffic participants. Unfortunately, testing AVs in real environments, the most straightforward validation framework for system-level inputoutput behavior, requires prohibitive amounts of time due to the rare nature of serious accidents BID22. Concretely, a recent study BID8 argues that AVs need to drive "hundreds of millions of miles, and, under some scenarios, hundreds of billions of miles to create enough data to clearly demonstrate their safety." On the other hand, formally verifying an AV algorithm's "correctness" BID11 BID0 BID21 BID13 is inherently difficult because all driving policies are subject to crashes caused by other drivers BID22. Ruling out scenarios where the AV should not be blamed for such accidents is a task subject to logical inconsistency and subjective assignment of fault. Motivated by the challenges underlying real-world testing and formal verification, we consider a probabilistic paradigmwhich we describe as a risk-based framework BID14 -where the goal is to evaluate the probability of an accident under a base distribution representing standard traffic behavior. By assigning learned probabilities to environmental states and agent behaviors, our risk-based framework considers performance of the AV policy under a data-driven model of the world. Formally, we let P 0 denote the base distribution that models standard traffic behavior and X ∼ P 0 be a realization of the simulation (e.g. weather conditions and driving policies of other agents). For an objective function f: X → R that measures "safety"-so that low values of f (x) correspond to dangerous scenarios-our goal is to evaluate the probability of a dangerous event p γ:= P 0 (f (X) ≤ γ) for some threshold γ. Our riskbased framework is agnostic to the complexity of the ego-policy and views it as a black-box module. Importantly, this approach allows deep-learning based perception systems that make formal verification methods intractable. For control algorithms which approach or exceed humanlevel performance, an adverse event will be rare, and the probability p γ close to 0. Thus, estimating p γ is a rare event simulation problem (see BID1 for an overview of this topic). For rare probabilities p γ, the naive Monte Carlo method can be prohibitively inefficient. For a sample X i DISPLAYFORM0 DISPLAYFORM1 In order to achieve -relative accuracy, we need N 1−pγ pγ 2 rollouts from our simulator. For light-tailed f (X), then p γ ∝ exp(−γ) so that the required sample size for naive Monte Carlo grows exponentially in γ. In the next section, we use adaptive sampling techniques that sample unsafe events more frequently to make the evaluation of p γ tractable. To address the shortcomings of naive Monte Carlo for estimating rare event probabilities, we use a multilevel splitting method BID7 BID3 BID5 BID24 ] that decomposes the rare-event probability p γ into conditional probabilities with interim threshold levels DISPLAYFORM0 This decomposition introduces a product of non-rare probabilities that are easy to estimate individually. Markov chain Monte Carlo (MCMC) is used to estimate each term, which can be accurately estimated as long as consecutive levels are close and the conditional probability is therefore large. Intuitively, the splitting method iteratively steers samples X i to the rare set {X|f (X) < γ} through a series of supersets {X|f (X) DISPLAYFORM1 Since it is a priori unclear how to choose the levels ∞ =: The discarding fraction δ trades off two dueling objectives; for small values, each term in the product is large and hence easy to estimate by MCMC; for large values, the number of total iterations K until convergence is reduced and more samples (δN) at each iteration can be simulated in parallel. DISPLAYFORM2 The AMS approach complements other procedures such as adaptive importance sampling (AIS) methods. AIS methods require computation of likelihood ratios between different distributions and become numerically unstable in high dimensions. AMS does not require computation of likelihood ratios, nor does it need to postulate models for the form of the optimal importance sampling distribution P 0 (·|f (·) < γ). On the other hand, the "modes" of failure AMS discovers are limited by the number of samples and the mixing properties of the MCMC sampler employed. Contrary to model-based AIS methods such as the cross-entropy method BID19, AMS has several convergence guarantees including those for bias, variance, and runtime (see BID4 for details). Notably, AMS is unbiased and has relative variance which scales as log(1/p γ) as opposed to 1/p γ for naive Monte Carlo (cf. Section II). Intuitively, AMS computes O(log(1/p γ)) independent probabilities, each of which has variance independent of p γ. To implement our risk-based framework, we first learn a base distribution P 0 of nominal traffic behavior. Using videos of highway traffic in the NGSim BID12 dataset, we train policies of human drivers via imitation learning BID20 BID17 BID18 BID6 BID2. It has recently been observed that supervised approaches to imitationlearning-where expert data is used to predict actions given vehicle states-suffer from poor performance in regions of the state space not encountered in data BID17 BID18. Reinforcementlearning techniques such as generative adversarial imitation learning (GAIL) BID6 improve generalization performance, as the imitation agent explores novel regions of the state space during training. We use the model-based variant of GAIL (MGAIL) BID2 that allows end-to-end differentiation. GAIL has been validated by Kuefler et al. BID10 to realistically mimic human-like driving behavior from the NGSim dataset across multiple metrics. These include the similarity of low-level actions (speeds, accelerations, turn-rates, jerks, and time-to-collision), as well as higher-level behaviors (lane change rate, collision rate, hard-brake rate, etc).We consider a scenario consisting of six agents, five of which are considered part of the environment. The environment vehicles' policies follow the distribution learned via GAIL. All vehicles are constrained to start within a set of possible initial configurations consisting of pose and velocity, and each vehicle has a goal of reaching the end of the approximately 2 km stretch of road. We created a photorealistic simulator of the portion of I-80 in Emeryville, CA where the traffic data was collected BID12 (see Appendix B for details). FIG1 details the performance of the AMS algorithm on the scenario, where the risk metric f (X) is the minimum time-to-collision (TTC) over a rollout (cf. Appendix C). For events with probability 10 −5 or less, AMS outperforms naive Monte Carlo, and the variance of the failure probability is reduced by up to 56×. We can also combine AMS with importance sampling. Since AMS outputs particles sampled from the desired failure region(s), we simply fit a model to this empirical distribution. FIG2 shows the output from 10 5 samples from a normalizing-flow-based importance sampler (cf. Appendix D) built upon the output of AMS. It is significantly more efficient than naive sampling. A fundamental tradeoff emerges when comparing the requirements of our risk-based framework to other testing paradigms. Real-world testing endangers the public but is still in some sense a gold standard. Verified subsystems provide evidence that the AV should drive safely in all specified scenarios; they are limited by computational intractability and require both white-box models and a complete specifications for assigning blame (e.g. BID22). In turn, our risk-based framework is most useful when the base distribution P 0 is accurate. Although an estimate of p γ is not informative when P 0 is misspecified, our adaptive sampling techniques still efficiently identify dangerous scenarios in this case; such dangerous scenarios are independent of potentially subjective assignments of blame. Principled techniques for building and validating the model of the environment P 0 represent an open research question. Rigorous safety evaluation of AVs necessitates benchmarks based on adaptive adversarial conditions rather than standard nominal conditions. Importantly, our framework only requires black-box access to the driving policy and simulation environment. Our approach offers significant speedups over realworld testing and allows efficient evaluation of black-box AV input/output behavior, providing a powerful tool to aid in the design of safe AVs. DISPLAYFORM0 Evaluate and sort f (X i) in decreasing order BID5: DISPLAYFORM1 Discard X,..., X (δN) and reinitialize by resampling with replacement from X (δN +1),..., X (N) Apply T MCMC transitions separately to each of X,..., X (δN) 11: end while Our simulator is a distributed, modular framework, which is necessary to support the inclusion of new AV systems and updates to the environment-vehicle policies. A benefit of this design is that simulation rollouts are simple to parallelize. In particular, we allow instantiation of multiple simulations simultaneously, without requiring that each include the entire set of components. For example, a desktop may support only one instance of Unreal Engine (for perception pipelines) but could be capable of simulating 10 physics simulations in parallel; it would be impossible to fully utilize the compute resource with a monolithic executable wrapping all engines together. Our architecture enables instances of components to be distributed on heterogeneous GPU clusters while maintaining the ability to perform meaningful analysis locally on commodity desktops. Using the asynchronous messaging library ZeroMQ, our implementation is fully-distributed among available CPUs and GPUs; our rollouts are up to 30P times faster than real time, where P is the number of processors. A video of a rollout from the simulator is available at https://youtu.be/CLXJ0CitDck and a snapshot from this rollout is shown in FIG4. In our implementation the safety measure is minimum timeto-collision (TTC). TTC is defined as the time it would take for two vehicles to intercept one another given that they each maintain their current heading and velocity BID23. The TTC between the ego-vehicle and vehicle i is given by DISPLAYFORM0 where r i is the distance between the ego vehicle and vehicle i, andṙ i the time derivative of this distance (which is simply computed by projecting the relative velocity of vehicle i onto the vector between the vehicles' poses). The operator [·] + is defined as [x] +:= max(x, 0). We define T T C i (t) = ∞ foṙ r i (t) ≥ 0. In this paper, vehicles are described as oriented rectangles in the 2D plane. Since we are interested in the time it would take for the ego-vehicle to intersect the polygonal boundary of another vehicle on the road, we utilize a finite set of range and range measurements in order to approximate the TTC metric. For a given configuration of vehicles, we compute N uniformly spaced angles θ 1,..., θ N in the range [0, 2π] with respect to the ego vehicle's orientation and cast rays outward from the center of the ego vehicle. For each direction we compute the distance which a ray could travel before intersecting one of the M other vehicles in the environment. These form N range measurements s 1,..., s N. Further, for each ray s i, we determine which vehicle (if any) that ray hit; projecting the relative velocity of this vehicle with respect to ego vehicle gives the range-rate measurementṡ i. Finally, we approximate the minimum TTC for a given simulation rollout X of length T discrete time steps by: DISPLAYFORM1 where we again define the approximate instantaneous TTC as ∞ forṡ i (t) ≥ 0. Note that this measure can approximate the true TTC arbitrarily well via choice of N and the discretization of time used by the simulator. Furthermore, note that our definition of TTC is with respect to the center of the ego vehicle touching the boundary of another vehicle. Crashing, on the other hand, is defined in our simulation as the intersection of boundaries of two vehicles. Thus, TTC values we evaluate in our simulation are nonzero even during crashes, since the center of the ego vehiclehas not yet collided with the boundary of another vehicle. Normalizing flows are used to describe classes of distributions using multi-layer neural networks, which are more expressive than typical analytical parameterizations such as exponential families. First a base distribution (usually something easy to sample from e.g. a standard normal distribution) is chosen. Then a series of transformations are applied to the samples from this distribution. Note that if the transformations are invertible, it is possible to work backwards from new samples to determine their likelihood using standard methods. Suppose a non-linear function y = f (x) is applied to x ∈ X then we can determine the density p(y) as follows: DISPLAYFORM0 where J(·) denotes the Jacobian. Composing a sequence of such transforms f 1 (x), f 2 (f 1 (x))... allows expressive transformations to the base density. Rezende and Mohamed BID16 describe a modern version of the approach which ensures that the Jacobian is upper triangular, rendering the determinant computation efficient. Given that each transform is parameterized by trainable weights, the architecture can be used to learn a density by maximizing the log-probability of the observed data in the transformed distribution p(y). Further enhancements to this architecture for fitting distributions can be found in BID9 BID15.

Using adaptive sampling methods to accelerate rare-event probability evaluation, we estimate the probability of an accident under a base distribution governing standard traffic behavior.

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For instance, <<We characterize problematic global optima of the VAE objective and present a novel inference method to avoid such optima.>>  to "Variational Auto-encoders (VAEs) are deep generative latent variable models consisting of two components: a generative model that captures a data distribution p(x) by transforming a distribution p(z) over latent space, and an inference model that infers likely latent codes for each data point . Recent work shows that traditional training methods tend to yield solutions that violate modeling desiderata: the learned generative model captures the observed data distribution but does so while ignoring the latent codes, ing in codes that do not represent the data (e.g. van den ;); the aggregate of the learned latent codes does not match the prior p(z). This mismatch means that the learned generative model will be unable to generate realistic data with samples from p(z)(e.g. ;). In this paper, we demonstrate that both issues stem from the fact that the global optima of the VAE training objective often correspond to undesirable solutions. Our analysis builds on two observations: the generative model is unidentifiable – there exist many generative models that explain the data equally well, each with different (and potentially unwanted) properties and bias in the VAE objective – the VAE objective may prefer generative models that explain the data poorly but have posteriors that are easy to approximate. We present a novel inference method, LiBI, mitigating the problems identified in our analysis. On synthetic datasets, we show that LiBI can learn generative models that capture the data distribution and inference models that better satisfy modeling assumptions when traditional methods struggle to do so. Introduction Variational Auto-encoders (VAEs) are deep generative latent variable models consisting of two components: a generative model that captures a data distribution p(x) by transforming a distribution p(z) over latent space, and an inference model that infers likely latent codes for each data point . Recent work shows that traditional training methods tend to yield solutions that violate modeling desiderata: the learned generative model captures the observed data distribution but does so while ignoring the latent codes, ing in codes that do not represent the data (e.g. van den ;); the aggregate of the learned latent codes does not match the prior p(z). This mismatch means that the learned generative model will be unable to generate realistic data with samples from p(z)(e.g. ;). In this paper, we demonstrate that both issues stem from the fact that the global optima of the VAE training objective often correspond to undesirable solutions. Our analysis builds on two observations: the generative model is unidentifiable -there exist many generative models that explain the data equally well, each with different (and potentially unwanted) properties and bias in the VAE objective -the VAE objective may prefer generative models that explain the data poorly but have posteriors that are easy to approximate. We present a novel inference method, LiBI, mitigating the problems identified in our analysis. On synthetic datasets, we show that LiBI can learn generative models that capture the data distribution and inference models that better satisfy modeling assumptions when traditional methods struggle to do so. Background A VAE is comprised of a generative model and an inference model. Under the generative model, we posit that the observed data and the latent codes are jointly distributed as p θ (x, z) = p θ (x|z)p(z). The likelihood p θ (x|z) is defined by a neural network f with parameters θ and an output noise model ∼ p such that x|z = f θ (z) +. Direct maximization of the expected observed data log-likelihood E p(x) log Z p θ (x, z)dz over θ is intractable. Instead, we maximize the variational lower bound (ELBO), where q η(x) ∈ Q is a variational distribution with parameters η(x). Since the bound is tight when q η(x) (z) = p θ (z|x), we aim to infer p θ (z|x). To speed up finding the variational parameters η for some new input x, we train a neural inference model g with parameters We demonstrate two general ways wherein global optima of the ELBO correspond to undesirable models. In the following, we fix our variational family to be mean-field Gaussian. Case 1: Learning the Inference Model Compromises the Quality of the Generative Model. Suppose that the variational family does not contain the posteriors of the data-generating-model. Then, often, inference must trade-off between learning a generative model that explains the data well and one that has posteriors that are easy for the inference network to approximate. Thus, the global minima of the VAE objective can specify models that both fail to capture the data distribution and whose aggregated posterior fails to match the prior. As demonstration, consider the following model (described fully in Appendix C.2): with σ 2 = 0.01, B = [0.006 0 0 0.006] and A = 0.75 0.25 1.5 −1.0 as the data generating model. Here, we fix B (which also fixes the covariance of the observation noise) and learn the parameter θ = A. In this example, the ground-truth posteriors are non-diagonal Gaussians. Here, the VAE objective can achieve a lower loss by compromising the MLE objective in order to better satisfy the PM objective -i.e. the VAE objective will prefer a model that fails to capture the data distribution but has a diagonal Gaussian posterior over the ground-truth model. Figure 1C shows the data distribution of the ground truth model θ GT, φ GT (with L(θ GT, φ GT) = 0.532) differs from the distribution of the learned model θ *, φ * in Figure 1D (with L(θ *, φ *) = 0.196). Moreover, since the learned model fails to capture the data distribution, its aggregated posterior fails to match the prior (see Figures 1E vs. 1F): Even when we restrict the class of generative models to ones that fit the data well, the posterior matching objective will still select a model with a simple posterior. Unfortunately, the selected generative model may have undesirable properties like uninformative latent codes. As demonstration, consider the model from Equation 3 with the data generating model specified by: σ 2 = 0.01, A = 0.75 0.25 1.5 −1.0, and B is some diagonal matrix with values in [0, σ 2]. In this case, we fix A and and learn the parameter θ = B. Since the observation noise covariance I ·σ 2 −B changes with B, the data marginal is fixed at p θ (x) = N 0, AA + I · σ 2 for every B. Thus, for every θ, the MLE objective is 0. However, although every choice of θ explain the data equally well, the posterior matching objective (and hence the VAE objective) is minimized by θ's whose posteriors have the least amount of correlation. Figure 1A shows that L(θ, φ) prefers high value in the upper diagonal of B and low value in the lower diagonal. Figure 1B shows the informativeness of the latent codes for the corresponding θ. We see that the data to latent code mutual information I(X; Z) corresponding to the θ selected by L(θ, φ) is not optimal. That is, even if the true data generating model produces highly informative latent codes, the VAE objective may select a model that produces uninformative latent codes. Discussion The principles of our analysis extend to non-linear VAEs and complex variational families. In the VAE objective, the posterior matching objective acts like a regularizing term, biasing the learned generative models towards simple models with posteriors that are easy to approximate (with respect to the choice of variational family). Thus, joint training of the inference and generative models introduces unintended and undesirable optima, which would not appear when these models are learned separately. Case 2: Learning the Inference Model Selects an Undesirable Generative Model. Even if the variational family is rich, the inference for the posterior can nonetheless bias the learning for the generative model. It is well known that the generative model is nonidentifiable under the MLE objective -there are many models that minimize the MLE objective. To focus on the effects of non-identifiability, let us assume that the variational family is expressive enough that it contains the posteriors of multiple models that could have generated the data. Then the posterior matching objective is 0 since we can find parameters φ such that q φ (z|x) = p θ (z|x) for any such θ. Consequently, L(θ, φ) has multiple global minima corresponding to the multiple generative models that maximizes the date likelihood. Some of these models may not satisfy our desiderata; e.g., the latent codes have low mutual information with the data. As demonstration, consider the following model (fully described in Appendix C.1): In this case, the mean-field variational family includes the posterior p θ (z|x) for all θ, i.e. the posterior matching objective can be fully minimized. Furthermore, every θ ∈ [0, σ 2] yields the same data marginal, p θ (x) = N 0, σ 2, and thus minimizes the MLE objective. However, not all choice of θ are equivalent. Given θ, the mutual information between the learned latent codes and the data is I θ (X; Z) = Const − 1 2 log(σ 2 − θ 2). Thus, the set of global minima of L(θ, φ) contain many models that produce uninformative latent codes. Discussion We've shown that posterior collapse can happen at global optima of the VAE objective and that, in these cases, collapse cannot always be mitigated by improving the inference model (as in) or by limiting the capacity of the generative model (as in ; ;). In Section 1, we showed that common problems with traditional VAE training stem from the non-identifiability of the likelihood and the bias of the VAE objective towards models with simple posteriors, even if such models cannot capture the data distribution. We propose a novel inference method to specifically target these problems. To avoid the biasing effect of the PM objective on learning the generative model, we decouple the training of the generative and inference models -first we learn a generative model, then we learn an inference model while fixing the learned generative model (note that amortization allows for efficient posterior inference). To avoid undesirable global optima of the likelihood, we learn a generative model constrained by task-specific modeling desiderata. For instance, if informative latent codes are necessary for the task, the likelihood can be constrained so that the mutual information between the data and latent codes under θ is at least δ. While there are a number of works in literature that incorporate task-specific constraints to VAE training (e.g. ; Zhao et al. (2017 Zhao et al. (, 2018 ;), adding these constraints to the VAE objective directly affects both the generative and the inference models, and, consequently, may introduce additional undesirable global optima. In our approach, added constraints only directly affects the generative model -i.e. the quality of inference cannot be compromised by the added constraints. We call our training framework Likelihood Before Inference (LiBI), and propose one possible instantiation of this framework here. Step 1: Learning the Generative Model We compute a tractable approximation to the MLE objective, constrained so that the likelihood satisfies task-specific modeling desiderata (such as high I(X; Z)) as needed.: where each c i is a constraint applied to the likelihood. We do this by computing joint maximum likelihood estimates for θ and z n while additionally constraining the z n's to have come from our assumed model (see Appendix D for a formal derivation of this approximation): where HZ(·) is the Henze-Zirkler test statistic for Gaussianity, µ(·), Σ(·) represent the empirical mean and covariance, and the z n's are amortized using a neural network z n = h(x n ; ϕ) parametrized by ϕ. These constraints encourage the generative model to capture p(x) given p(z), i.e. the aggregated posterior under this model will match the prior p(z). Step 2: Learning the Inference Model Given the θ learned in Step 1, we learn φ to compute approximate posteriors q φ (z|x):. We note that φ, too, will satisfy our modeling assumptions, since with a fixed θ, the model nonidentifiability we describe in Section 1 is no longer present. Step 3: Reinitialize Inference for the Generative Model We repeat the process, initializing h(x n ; ϕ) = µ(x n ; φ), where µ(x n ; φ) is the mean of q φ (z n |x n). This steps provides an intelligent random initialization allowing step 1 to learn a better quality model. In theory, if the generative model and the inference models are learned perfectly in Steps 1 and 2, then Step 3 is obviated. In practice, we find that Step 3 improves the quality of the generative model and only a very small number of iterations is actually needed. Discussion Using LiBI, we can now evaluate the quality of the generative model and the inference models independently. This is in contrast to traditional VAE inference, in which the ELBO entangles issues of modeling and issues of inference. On 4 synthetic data sets for which we know the data generating model, we compare LiBI with existing inference methods: VAE , β-VAE , β-VAE with annealing, Lagging inference networks . Across all datasets, LiBI learns generative models that better capture p(x) (as quantified by loglikelihood and the Smooth k-NN test statistic ) and for which the aggregated posterior better matches the prior (see Appendix B). Conclusion In this paper, we show that commonly noted issues with VAE training are attributable to the fact that global optima of the VAE training objective often includes undesirable solutions. Based on our analysis, we propose a novel training procedure, LiBI, that avoid these undesirable optima while retaining the tractability of traditional VAE inference. On synthetic datasets, we show that LiBI able to learn generative models that capture the data distribution and inference models whose aggregated posterior matches the prior while traditional methods struggle to do so. Two common issues noted in VAE literature are posterior collapse and the mismatch between aggregated posterior and prior. Posterior collapse occurs when the posterior under both the generative model and approximate posterior learned by the inference model are equal the prior p(z) . Surprisingly, under posterior collapse, the model is still able to generate samples from p data (x)(e.g. ;). This is often attributed to the fact the generative model is very powerful and is therefore able to maximize the log data marginal likelihood without the help of the auxiliary latent codes (van den). Existing literature focuses on mitigating model collapse in one of the three ways: 1. modifying the optimization procedure to bias training way from collapse ; 2. choosing variational families that make collapse less likely to occur ; 3. modifying the generative and inference model architecture to encourage more information sharing between the x's and the z's . Although much of existing literature describes issue of posterior collapse and proposes methods to avoid it, less attention has been given to explaining why it occurs. conjecture that it occurs as a of the joint training: since the likelihood changes over the course of training, it is incentivized to ignore the output of the inference network whose output in the early stages of training is not yet meaningful. Mismatch between aggregated posterior and prior refers to the case when q φ (z) = p(z), where One might expect the two distributions to match because for any given likelihood θ, one should be able to recover the prior from the true posterior p(z|x) as follows: An x produced by the generated model from a z that is likely under the prior but unlikely under the aggregate posterior may have "poor sample quality", since the the generative model is unlikely to have encountered such a z during training . Existing literature mitigate this issue by either increasing the flexibility of the prior to better fit the aggregate posterior or developing a method to sample more robustly from the latent space . Examples of the latter include training a second VAE to be able to generate z from u and then sampling from p θ (x, z) using a Gibbs sampler . In this work, we provide a unifying analysis of both posterior collapse and mismatch, showing that both can occur as global optima of the VAE objective. Through our analysis, we also show that at these optima, neither issue can be reliably resolved by existing methods. In Figures 2 and 3, we compare the posteriors learned by traditional VAE inference and by LiBI, respectively, on the synthetic dataset LinearJTEx. Here we demonstrate that traditional inference learns a generative model θ under which it is easy to approximate the corresponding posteriors. However, this comes at the cost of θ being unable to capture the data distribution. Assume the following generative process for the data: For this generative process, p θ (x) = N 0, σ 2 for any value of θ such that 0 ≤ θ ≤ σ 2. Additionally, θ directly controls I(X; Z) -when θ = 0, we have that I(X; Z); when θ = σ 2, we have that I(X; Z) = ∞. To see this, we will compute I θ (X; Z) directly (by computing p θ (x, z) and p(x)p(z)): As such, we can compute the mutual information between x and z as follows: For this model, the posterior p θ (z|x), is: Since this example is univariate, the mean-field Gaussian variational family will include the true posterior for any θ. Assume the following generative process for the data: where B is a diagonal matrix with diagonal elements between 0 and σ 2. For this generative process, p B (x) = N 0, AA + I · σ 2 for all valid values of B. For this model, the complete data likelihood and marginals are, Therefore, I B (X; Z) can be computed as follows: Lastly, the posterior for this model, p B (z|x), is a Gaussian with mean and covariance, For our choice of A, the mean-field Gaussian will not include the true posterior for this model. The best-fitting mean-field approximation to the true posterior can be computed as in Appendix C.3. Let B be a diagonal matrix and let Σ be a full-covariance matrix. where each element in the above sum is independent and is minimized when B ii = 1 Σ, and where Σ −1 ii is the ith diagonal entry of Σ −1. The LiBI Framework The LiBI framework is composed of two steps: learning a high-quality likelihood capable of generating the observed data distribution, and fixing the likelihood learned in Step 1, performing inference to learn the latent codes given the data. We emphasize that our framework is general, so one can use various existing methods for either step. For example, one can use a GAN for Step 1, and MCMC sampling for Step 2. In this section, we derive a tractable approximation to Step 1 that can be easily enhanced to include constraints for task-specific desiderata, and that is amenable to gradient-based optimization methods. wherein Equation 31, we approximate E p(z) [p θ (x n |z)] with a single sample, z n, that makes its corresponding x n most likely (this is analogous to the Empirical Bayes EB MAP Type II estimates often used to tune prior hyper-parameters). This step, however, has a problem: it is biased towards learning z n's close to 0. We will now demonstrate that this issue exists and is a of non-identifiability in the MLE estimate with respect to θ, {z n} N n=1. We then provide a solution to this problem. Characterization of Non-Identifiability in Tractable Approximation Consider the following: let Z = {z n} N n=1 be the true z's and θ used to generate the observed data, X = {x n} N n=1 in the following generative process: Now, consider, an alternative Z = {ẑ n} N n=1 andθ such that, yielding the following alternative generative process: Under these generative processes, both the data marginals and the likelihoods are equal: However, since in our model we assumed the prior is fixed p(z) = N (0, I), the alternate parameters Z,θ are preferred by the joint log-likelihood when c > 1, since log pθ(x n |ẑ n) = log p θ (x n |z n) by construction and log N (ẑ n |0, I) > log N (z n |0, I) since theẑ n's are closer to 0 when c > 1. This will cause our approximation from Equation 31 to prefer the modelθ, which generates a different data distribution that the true data distribution: Identifying the Tractable Approximation using the Henze-Zirkler Test Statistic Returning to our approximation of the MLE objective in Equation 31, we can avoid this issue by constraining the z n's to have come from the prior: We do this by constraining the z n's to be Gaussian using the Henze-Zirkler test for Gaussianity and by constraining the empirical mean and covariance of the z n's to be that of the standard normal: We hypothesize that if the likelihood function, f θ, is "smooth" and well-behaved (that is, that it maps nearby z's to nearby x's), that our approximation of the likelihood will come close to the true one. Using this framework, we first recover a high-quality likelihood (a likelihood that, unlike in the traditional VAE objective, is not compromised to match the approximate posterior). Our framework therefore naturally encourages this likelihood to satisfy modeling assumptions; that is, if we find a θ for which the x's are reconstructed accurately given Gaussian z's, the aggregated posterior under θ, p θ (z), will match the prior p(z). Given this likelihood, we can then learn a posterior that accurately approximates p θ (z|x). We note that φ, too, will satisfy our modeling assumptions, since with a fixed θ, the model non-identifiability we describe is no longer present. The LiBI Inference Method We incorporate the constraints in Equation 43 as smooth penalties into the Lagrangian in Equation 44. We additionally define h(x n ; ϕ) to be a neural network parameterized by ϕ that, given x n, returns the specific z n that generated it. ϕ allows us to amortize Equation 44. We repeat the following steps R times: 1. Step 1: θ t, ϕ t = argmin θ,ϕ − 1 N n log p θ (x n |h(x n ; ϕ)) + HZ exp HZ {h(x n ; ϕ)} N n=1 + exp Σ {h(x n ; ϕ)} N n=1 − I 2. Step 2: = argmin φ 1 N n −ELBO(θ t, φ)"

The paper designs two algorithms for the stochastic AUC maximization problem with state-of-the-art complexities when using deep neural network as predictive model, which are also verified by empirical studies.


Question: represent the article for finding a single-sentence tldr

Question: Many tasks in natural language understanding require learning relationships between two sequences for various tasks such as natural language inference, paraphrasing and entailment. These aforementioned tasks are similar in nature, yet they are often modeled individually. Knowledge transfer can be effective for closely related tasks, which is usually carried out using parameter transfer in neural networks. However, transferring all parameters, some of which irrelevant for a target task, can lead to sub-optimal and can have a negative effect on performance, referred to as \textit{negative} transfer. Hence, this paper focuses on the transferability of both instances and parameters across natural language understanding tasks by proposing an ensemble-based transfer learning method in the context of few-shot learning. Our main contribution is a method for mitigating negative transfer across tasks when using neural networks, which involves dynamically bagging small recurrent neural networks trained on different subsets of the source task/s. We present a straightforward yet novel approach for incorporating these networks to a target task for few-shot learning by using a decaying parameter chosen according to the slope changes of a smoothed spline error curve at sub-intervals during training. Our proposed method show improvements over hard and soft parameter sharing transfer methods in the few-shot learning case and shows competitive performance against models that are trained given full supervision on the target task, from only few examples. Learning relationships between sentences is a fundamental task in natural language understanding (NLU). Given that there is gradience between words alone, the task of scoring or categorizing sentence pairs is made even more challenging, particularly when either sentence is less grounded and more conceptually abstract e.g sentence-level semantic textual similarity and textual inference. The area of pairwise-based sentence classification/regression has been active since research on distributional compositional semantics that use distributed word representations (word or sub-word vectors) coupled with neural networks for supervised learning e.g pairwise neural networks for textual entailment, paraphrasing and relatedness scoring BID15.Many of these tasks are closely related and can benefit from transferred knowledge. However, for tasks that are less similar in nature, the likelihood of negative transfer is increased and therefore hinders the predictive capability of a model on the target task. However, challenges associated with transfer learning, such as negative transfer, are relatively less explored explored with few exceptions BID23; BID5 and even fewer in the context of natural language tasks BID18. More specifically, there is only few methods for addressing negative transfer in deep neural networks BID9.Therefore, we propose a transfer learning method to address negative transfer and describe a simple way to transfer models learned from subsets of data from a source task (or set of source tasks) to a target task. The relevance of each subset per task is weighted based on the respective models validation performance on the target task. Hence, models within the ensemble trained on subsets of a source task which are irrelevant to the target task are assigned a lower weight in the overall ensemble prediction on the target task. We gradually transition from using the source task ensemble models for prediction on the target task to making predictions solely using the single model trained on few examples from the target task. The transition is made using a decaying parameter chosen according to the slope changes of a smoothed spline error curve at sub-intervals during training. The idea is that early in training the target task benefits more from knowledge learned from other tasks than later in training and hence the influence of past knowledge is annealed. We refer to our method as Dropping Networks as the approach involves using a combination of Dropout and Bagging in neural networks for effective regularization in neural networks, combined with a way to weight the models within the ensembles. For our experiments we focus on two Natural Language Inference (NLI) tasks and one Question Matching (QM) dataset. NLI deals with inferring whether a hypothesis is true given a premise. Such examples are seen in entailment and contradiction. QM is a relatively new pairwise learning task in NLU for semantic relatedness that aims to identify pairs of questions that have the same intent. We purposefully restrict the analysis to no more than three datasets as the number of combinations of transfer grows combinatorially. Moreover, this allows us to analyze how the method performs when transferring between two closely related tasks (two NLI tasks where negative transfer is less apparent) to less related tasks (between NLI and QM). We show the model averaging properties of our negative transfer method show significant benefits over Bagging neural networks or a single neural network with Dropout, particularly when dropout is high (p=0.5). Additionally, we find that distant tasks that have some knowledge transfer can be overlooked if possible effects of negative transfer are not addressed. The proposed weighting scheme takes this issue into account, improving over alternative approaches as we will discuss. In transfer learning we aim to transfer knowledge from a one or more source task T s in the form of instances, parameters and/or external resources to improve performance on a target task T t. This work is concerned about improving in this manner, but also not to degrade the original performance of T s, referred to as Sequential Learning. In the past few decades, research on transfer learning in neural networks has predominantly been parameter based transfer. BID29 have found lower-level representations to be more transferable than upper-layer representations since they are more general and less specific to the task, hence negative transfer is less severe. We will later describe a method for overcoming this using an ensembling-based method, but before we note the most relevant work on transferability in neural networks. BID21 introduced the notion of parameter transfer in neural networks, also showing the benefits of transfer in structured tasks, where transfer is applied on an upstream task from its sub-tasks. Further to this , a hyperplane utility measure as defined by θ s from T t which then rescales the weight magnitudes was shown to perform well, showing faster convergence when transferred to T t. BID22 focused on constructing a covariance matrix for informative Gaussian priors transferred from related tasks on binary text classification. The purpose was to overcome poor generalization from weakly informative priors due to sparse text data for training. The off-diagonals of represent the parameter dependencies, therefore being able to infer word relationships to outputs even if a word is unseen on the test data since the relationship to observed words is known. More recently, transfer learning (TL) in neural networks has been predominantly studied in Computer Vision (CV). Models such as AlexNet allow features to append to existing networks for further fine tuning on new tasks. They quantify the degree of generalization each layer provides in transfer and also evaluate how multiple CNN weights are used to be of benefit in TL. This also reinforces to the motivation behind using ensembles in this paper. BID14 describe the transferability of parameters in neural networks for NLP tasks. Questions posed included the transferability between varying degrees of "similar" tasks, the transferability of different hidden layers, the effectiveness of hard parameter transfer and the use of multi-task learning as opposed to sequential based TL. They focus on transfer using hard parameter transfer, most relevantly, between and. They too find that lower level features are more general, therefore more useful to transfer to other similar task, whereas the output layer is more task specific. Another important point raised in their paper was that a large learning rate can in the transferred parameters being changed far from their original transferred state. As we will discuss, the method proposed here will inadvertently address this issue since the learning rates are kept intact within the ensembled models, a parameter adjustment is only made to their respective weight in a vote. BID7 have recently popularized transfer learning by transferring domain agnostic neural language models (AWD-LSTM Merity et al. FORMULA2). Similarly, lexical word definitions have also been recently used for transfer learning O' Neill & Buitelaar FORMULA2, which too provide a model that is learned independent of a domain. This mean the sample complexity for a specific task greatly reduces and we only require enough labels to do label fitting which requires fine-tuning of layers nearer to the output BID25. Before discussing the methodology we describe the current SoTA for pairwise learning in NLU. BID24 use a Word Embedding Correlation (WEC) model to score co-occurrence probabilities for Question-Answer sentence pairs on Yahoo! Answers dataset and Baidu Zhidao Q&A pairs using both a translation model and word embedding correlations. The objective of the paper was to find a correlation scoring function where a word vector is given while modelling word co-occurrence given as C(FORMULA2 have described a character-based intra attention network for NLI on the SNLI corpus, showing an improvement over the 5-hidden layer Bi-LSTM network introduced by used on the MultiNLI corpus. Here, the architecture also looks to solve to use attention to produce interactions to influence the sentence encoding pairs. Originally, this idea was introduced for pairwise learning by using three Attention-based Convolutional Neural Networks BID28 that use attention at different hidden layers and not only on the word level. Although, this approach shows good , word ordering is partially lost in the sentence encoded interdependent representations in CNNs, particularly when max or average pooling is applied on layers upstream. DISPLAYFORM0 In this section we start by describing a co-attention GRU network that is used as one of the baselines when comparing ensembled GRU networks for the pairwise learning-based tasks. We then describe the proposed transfer learning method. Co-Attention GRU Encoded representations for paired sentences are obtained from h DISPLAYFORM0 where h (l) represents the last hidden layer representation in a recurrent neural network. Since longer dependencies are difficult to encode, only using the last hidden state as the context vector c t can lead to words at the beginning of a sentence have diminishing effect on the overall representation. Furthermore, it ignores interdependencies between pairs of sentences which is the case for pairwise learning. Hence, in the single task learning case we consider using a cross-attention network as a baseline which accounts for interdependencies by placing more weight on words that are more salient to the opposite sentence when forming the hidden representation, using the attention mechanism BID0. The softmax function produces the attention weights α by passing all outputs of the source RNN, h S to the softmax conditioned on the target word of the opposite sentence h t. A context vector c t is computed as the sum of the attention weighted outputs byh s. This in a matrix A ∈ R |S|×|T | where |S| and |T | are the respective sentence lengths (the max length of a given batch). The final attention vector α t is used as a weighted input of the context vector c t and the hidden state output h t parameterized by a xavier uniform initialized weight vector W c to a hyperbolic tangent unit. Here we describe the two approaches that are considered for accelerating learning and avoiding negative transfer on T t given the voting parameters of a learned model from T s. We first start by describing a method that learns to guide weights on T t by measuring similarity between θŝ and θt during training by using moving averages on the slope of the error curve. This is then followed by a description on the use of smoothing splines to avoid large changes due to volatility in the error curve during training. Dropping Transfer Both dropout and bagging are common approaches for regularizing models, the former is commonly used in neural networks. Dropout trains a number of subnetworks by dropping parameters and/or input features during training while also have less parameter updates per epoch. Bagging trains multiple models by sampling instances x k ∈ R d from a distribution p(x) (e.g uniform distribution) prior to training. Herein, we refer to using both in conjunction as Dropping. The proposed methods is similar to Adaptive Boosting (AdaBoost) in that there is a weight assigned based on performance during training. However, in our proposed method, the weights are assigned based on the performance of each batch after Bagging, instead of each data sample. Furthermore, the use of Dropout promotes sparsity, combining both arithmetic mean and geometric mean model averaging. Avoiding negative transfer with standard AdaBoost is too costly in practice too use on large datasets and is prone to overfitting in the presence of noise BID12. A fundamental concern in TL is that we do not want to transfer irrelevant knowledge which leads to slower convergence and/or suboptimal performance. Therefore, dropping places soft attention based on the performance of each model from T s → T t using a softmax as a weighted vote. Once a target model f t is learned from only few examples on T t (referred to as few-shot learning), the weighted ensembled models from T s can be transferred and merged with the T t model. Equation DISPLAYFORM0 Equation 2 then shows a straightforward update rule that decays the importance of T s Dropping networks as the T t neural network begins to learn from only few examples. The prediction from few samples a l t is the single output from T l t and γ is the slope of the error curve that is updated at regular intervals during training. We expect this approach to lead to faster convergence and more general features as the regularization is in the form of a decaying constraint from a related task. The rate of the shift towards the T t model is proportional to the gradient of the error ∇ xs for a set of mini-batches xs. In our experiments, we have set the update of the slope to occur every 100 iterations. DISPLAYFORM1 The assumption is that in the initial stages of learning, incorporating past knowledge is more important. As the model specializes on the target task we then rely less on incorporating prior knowledge over time. In its simplest form, this can be represented as a moving average over the development set error curve so to choose δ t = E[∇ [t,t+k] ], where k is the size of the sliding window. In some cases an average over time is not suitable when the training error is volatile between slope estimations. Hence, alternative smoothing approaches would include kernel and spline models for fitting noisy, or volatile error curves. A kernel ψ can be used to smooth over the error curve, which takes the form of a Gaussian kernel ψ(x, DISPLAYFORM2 Another approach is to use Local Weighted Scatterplot Smoothing (LOWESS); which is a non-parametric regression technique that is more robust against outliers in comparison to standard least square regression by adding a penalty term. Equation 3 shows the regularized least squares function for a set of cubic smoothing splines ψ which are piecewise polynomials that are connected by knots, distributed uniformly across the given interval [0, T]. Splines are solved using least squares with a regularization term λθ 2 j ∀ j and ψ j a single piecewise polynomial at the subinterval [t, t + k] ∈ [0, T], as shown in Equation 3. Each subinterval represents the space that γ is adapted for over time i.e change the influence of the T s Dropping Network as T t model learns from few examples over time. This type of cubic spline is used for the subsequent section for Dropping Network transfer. DISPLAYFORM3 The standard cross-entropy (CE) loss is used as the objective as shown in Equation 4. DISPLAYFORM4 This approach is relatively straightforward and on average across all three datasets, 58% more computational time for training 10 smaller ensembles for each single-task was needed, in comparison to a larger global model on a single NVIDIA Quadro M2000 Graphic Processing Unit. Some benefits of the proposed method can be noted at this point. Firstly, the distance measure to related tasks is directly proportional to the online error of the target task. In contrast, hard parameter sharing does not address such issues, nor does recent approaches that use Gaussian Kernel Density estimates as parameter contraints on the target task O BID17. Secondly, although not the focus of this work, the T t model can be trained on a new task with more or less classes by adding or discarding connections on the last softmax layer. Lastly, by weighting the models within the ensemble that perform better on T t we mitigate negative transfer problems. We now discuss some of the main of the proposed Dropping Network transfer. FORMULA2 provides the first large scale corpus with a total of 570K annotated sentence pairs (much larger than previous semantic matching datasets such as the dataset that consisted of 9927 sentence pairs). As described in the opening statement of McCartney's thesis MacCartney FORMULA3, "the emphasis is on informal reasoning, lexical semantic knowledge, and variability of linguistic expression." The SNLI corpus addresses issues with previous manual and semi-automatically annotated datasets of its kind which suffer in quality, scale and entity co-referencing that leads to ambiguous and ill-defined labeling. They do this by grounding the instances with a given scenario which leaves a precedent for comparing the contradiction, entailment and neutrality between premise and hypothesis sentences. Since the introduction of this large annotated corpus, further resources for Multi-Genre NLI (MultiNLI) have recently been made available as apart of a Shared RepEval task Nangia et al. FORMULA2;. MultiNLI extends a 433k instance dataset to provide a wider coverage containing 10 distinct genres of both written and spoken English, leading to a more detailed analysis of where machine learning models perform well or not, unlike the original SNLI corpus that only relies only on image captions. As authors describe, "temporal reasoning, belief, and modality become irrelevant to task performance" are not addressed by the original SNLI corpus. Another motivation for curating the dataset is particularly relevant to this problem, that is the evaluation of transfer learning across domains, hence the inclusion of these datasets in the analysis. These two NLI datasets allow us to analyze the transferability for two closely related datasets. Question Matching (QM) is a relatively new pairwise learning task in NLU for semantic relatedness, first introduced by the Quora team in the form of a Kaggle competition 1. The task has implications for Question-Answering (QA) systems and more generally, machine comprehension. A known difficulty in QA is the problem of responding to a question with the most relevant answers. In order to respond appropriately, grouping and relating similar questions can greatly reduce the possible set of correct answers. For single-task learning, the baseline proposed for evaluating the co-attention model and the ensemblebased model consists of a standard GRU network with varying architecture settings for all three datasets. During experiments we tested different combinations of hyperparameter settings. All models are trained for 30,000 epochs, using a dropout rate p = 0.5 with Adaptive Momentum (ADAM) gradient based optimization in a 2-hidden layer network with an initial learning rate η = 0.001 and a batch size b T = 128. As a baseline for TL we use hard parameter transfer with fine tuning on 50% of X ∈ T s of upper layers. For comparison to other transfer approaches we note previous findings by BID29 which show that lower level features are more generalizable. Hence, it is common that lower level features are transferred and fixed for T t while the upper layers are fine tuned for the task, as described in Section 2.2. Therefore, the baseline comparison simply transfers all weights from θ s → θ t The evaluation is carried out on both the rate of convergence and optimal performance. Hence, we particularly analyze the speedup obtained in the early stages of learning. Table 1 shows the on all three datasets for single-task learning, the purpose of which is to clarify the potential performance if learned from most of the available training data (between 70%-80% of the overall dataset for the three datasets).The ensemble model slightly outperforms other networks proposed, while the co-attention network produces similar performance with a similar architecture to the ensemble models except for the use of local attention over hidden layers shared across both sentences. The improvements are most notable on MNLI, reaching competitive performance in comparison to state of the art (SoTA) on the RepEval task 2, held by BID2 which similarly uses a Gated Attention Network. These SoTA are considered as an upper bound to the potential performance when evaluating the Dropping based TL strategy for few shot learning. FIG4 demonstrates the performance of the zero-shot learning of the ensemble network which averages the probability estimates from each models prediction on the T t test set (few-shot T t training set or development set not included). As the ensembles learn on T s it is evident that most of the learning has already been carried out by 5,000-10,000 epochs. Producing entailment and contradiction predictions for multi-genre sources is significantly more difficult, demonstrated by lower test accuracy when transferring SNLI → MNLI, in comparison to MNLI → SNLI that performs better relative to recent SoTA on SNLI. TAB2 shows best performance of this hard parameter transfer from T s → T t. The QM dataset is not as "similar" in nature and in the zero-shot learning setting the model's weights a S and a Q are normalized to 1 (however, this could have been weighted based on a prior belief of how "similar" the tasks are). Hence, it is unsurprising that the QM dataset has reduced the test accuracy given that it is further to T t than S is. The second approach is shown on the LHS of TAB4 which is the baseline few-shot learning performance with fixed parameter transferred from T t on the lower layer with fine-tuning of the 2 nd layer. Here, we ensure that instances from each genre within MNLI are sampled at least 100 times and that the batch of 3% the original size of the corpus is used (14,000 instances). Since SNLI and QM are created from a single source, we did not to impose such a constraint, also using a 3% random sample for testing. Therefore, these and all subsequent denoted as Train Acc. % refers to the training accuracy on the small batches for each respective dataset. We see improvements that are made from further tuning on the small T t batch that are made, particularly on MNLI with a 2.815 percentage point increase in test accuracy. For both SNLI + QM → MNLI and MNLI + QM → SNLI cases final predictions are made by averaging over the class probability estimates before using CE loss. Dropping-GRU CSES On the RHS, we present the of the proposed method which transfers parameters from the Dropping network trained with the output shown in Equation 2 using a spline smoother with piecewise polynomials (as described in FIG4). As aforementioned, this approach finds the slope of the online error curve between sub-intervals so to choose γ i.e the balance between the source ensemble and target model trained on few examples. In the case with SNLI + QM (ie. SNLI + Question Matching) and MNLI + QM, 20 ensembles are transferred, 10 from each model with a dropout rate p d = 0.5. We note that unlike the previous two baselines methods shown in TAB2 and 3, the performance does not decrease by transferring the QM models to both SNLI and MultiNLI. This is explained by the use of the weighting scheme proposed with spline smoothing of the error curve i.e γ decreases at a faster rate for T t due to the ineffectiveness of the ensembles created on the QM dataset. In summary, we find transfer of MNLI + QM → SNLI and SNLI+QM → MNLI showing most improvement using the proposed transfer method, in comparison to standard hard and soft parameter transfer. This is reflected in the fact that the proposed method is the only one which improved on SNLI while still transferring the more distant QM dataset. The method for transfer only relies on one additional parameter γ. We find that in practice using a higher decay rate γ (0.9-0.95) is more suitable for closely related tasks. Decreasing γ in proportion to the slope of a smooth spline fitted to the online error curve performs better than arbitrary step changes or a fixed rate for γ (equivalent to static hard parameter ensemble transfer). Lastly, If a distant tasks has some knowledge transfer they can be overlooked if possible effects of negative transfer are not addressed. The proposed weighting scheme takes this into account, which is reflected on the RHS of TAB4, showing M + Q → S and S + Q → M show most improvement, in comparison to alternative approaches posed in TAB2 where transferring M + Q → S performed worse than M → S. Our proposed method combines neural network-based bagging with dynamic cubic spline error curve fitting to transition between source models and a single target model trained on only few target samples. We find our proposed method overcomes limitations in transfer learning such as avoiding negative transfer when attempting to transfer from more distant task, which arises during few-shot learning setting. This paper has empirically demonstrated this for learning complex semantic relationships between sentence pairs for pairwise learning tasks. Additionally, we find the co-attention network and the ensemble GRU network to perform comparably for single-task learning.

A dynamic bagging methods approach to avoiding negatve transfer in neural network few-shot transfer learning

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We provide insightful understanding of sequence-labeling NER and propose to use two types of cross structures, both of which bring theoretical and empirical improvements.