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Data-Driven Conditional Robust Optimization
| null |
In this paper, we study a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Specifically, we solve this problem from a Conditional Robust Optimization (CRO) point of view. We propose an integrated framework that designs the conditional uncertainty set by jointly learning the partitions in the covariate data space and simultaneously constructing partition specific deep uncertainty sets for the random vector that perturbs the CRO problem. We also provide theoretical guarantees for the coverage of the uncertainty sets and value at risk performances obtained using the proposed CRO approach. Finally, we use the simulated and real world data to show the implementation of our approach and compare it against two non-contextual benchmark approaches to demonstrate the value of exploiting contextual information in robust optimization.
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Abhilash Reddy Chenreddy, Nymisha Bandi, Erick Delage
| null | null | 2,022 |
neurips
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Learning Mixed Multinomial Logits with Provable Guarantees
| null |
A mixture of multinomial logits (MMNL) generalizes the single logit model, which is commonly used in predicting the probabilities of different outcomes. While extensive algorithms have been developed in the literature to learn MMNL models, theoretical results are limited. Built on the Frank-Wolfe (FW) method, we propose a new algorithm that learns both mixture weights and component-specific logit parameters with provable convergence guarantees for an arbitrary number of mixtures. Our algorithm utilizes historical choice data to generate a set of candidate choice probability vectors, each being close to the ground truth with a high probability. We further provide a sample complexity analysis to show that only a polynomial number of samples is required to secure the performance guarantee of our algorithm. Finally, we conduct simulation studies to evaluate the performance and demonstrate how to apply our algorithm to real-world applications.
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Yiqun Hu, David Simchi-Levi, Zhenzhen Yan
| null | null | 2,022 |
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Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Bandits
| null |
We study the Bayesian regret of the renowned Thompson Sampling algorithm in contextual bandits with binary losses and adversarially-selected contexts. We adapt the information-theoretic perspective of Russo and Van Roy [2016] to the contextual setting by considering a lifted version of the information ratio defined in terms of the unknown model parameter instead of the optimal action or optimal policy as done in previous works on the same setting. This allows us to bound the regret in terms of the entropy of the prior distribution through a remarkably simple proof, and with no structural assumptions on the likelihood or the prior. The extension to priors with infinite entropy only requires a Lipschitz assumption on the log-likelihood. An interesting special case is that of logistic bandits with $d$-dimensional parameters, $K$ actions, and Lipschitz logits, for which we provide a $\tilde{O}(\sqrt{dKT})$ regret upper-bound that does not depend on the smallest slope of the sigmoid link function.
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Gergely Neu, Iuliia Olkhovskaia, Matteo Papini, Ludovic Schwartz
| null | null | 2,022 |
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Characterizing the Ventral Visual Stream with Response-Optimized Neural Encoding Models
| null |
Decades of experimental research based on simple, abstract stimuli has revealed the coding principles of the ventral visual processing hierarchy, from the presence of edge detectors in the primary visual cortex to the selectivity for complex visual categories in the anterior ventral stream. However, these studies are, by construction, constrained by their $\textit{a priori}$ hypotheses. Furthermore, beyond the early stages, precise neuronal tuning properties and representational transformations along the ventral visual pathway remain poorly understood. In this work, we propose to employ response-optimized encoding models trained solely to predict the functional MRI activation, in order to gain insights into the tuning properties and representational transformations in the series of areas along the ventral visual pathway. We demonstrate the strong generalization abilities of these models on artificial stimuli and novel datasets. Intriguingly, we find that response-optimized models trained towards the ventral-occipital and lateral-occipital areas, but not early visual areas, can recapitulate complex visual behaviors like object categorization and perceived image-similarity in humans. We further probe the trained networks to reveal representational biases in different visual areas and generate experimentally testable hypotheses. Our analyses suggest a shape-based processing along the ventral visual stream and provide a unified picture of multiple neural phenomena characterized over the last decades with controlled fMRI studies.
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Meenakshi Khosla, Keith Jamison, Amy Kuceyeski, Mert Sabuncu
| null | null | 2,022 |
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Statistical Learning and Inverse Problems: A Stochastic Gradient Approach
| null |
Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used to solve linear SIP. We provide consistency and finite sample bounds for the excess risk. We also propose a modification for the SGD algorithm where we leverage machine learning methods to smooth the stochastic gradients and improve empirical performance. We exemplify the algorithm in a setting of great interest nowadays: the Functional Linear Regression model. In this case we consider a synthetic data example and a classification problem for predicting the main activity of bitcoin addresses based on their balances.
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Yuri Fonseca, Yuri Saporito
| null | null | 2,022 |
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Few-shot Learning for Feature Selection with Hilbert-Schmidt Independence Criterion
| null |
We propose a few-shot learning method for feature selection that can select relevant features given a small number of labeled instances. Existing methods require many labeled instances for accurate feature selection. However, sufficient instances are often unavailable. We use labeled instances in multiple related tasks to alleviate the lack of labeled instances in a target task. To measure the dependency between each feature and label, we use the Hilbert-Schmidt Independence Criterion, which is a kernel-based independence measure. By modeling the kernel functions with neural networks that take a few labeled instances in a task as input, we can encode the task-specific information to the kernels such that the kernels are appropriate for the task. Feature selection with such kernels is performed by using iterative optimization methods, in which each update step is obtained as a closed-form. This formulation enables us to directly and efficiently minimize the expected test error on features selected by a small number of labeled instances. We experimentally demonstrate that the proposed method outperforms existing feature selection methods.
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Atsutoshi Kumagai, Tomoharu Iwata, Yasutoshi Ida, Yasuhiro Fujiwara
| null | null | 2,022 |
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Object Scene Representation Transformer
| null |
A compositional understanding of the world in terms of objects and their geometry in 3D space is considered a cornerstone of human cognition. Facilitating the learning of such a representation in neural networks holds promise for substantially improving labeled data efficiency. As a key step in this direction, we make progress on the problem of learning 3D-consistent decompositions of complex scenes into individual objects in an unsupervised fashion. We introduce Object Scene Representation Transformer (OSRT), a 3D-centric model in which individual object representations naturally emerge through novel view synthesis. OSRT scales to significantly more complex scenes with larger diversity of objects and backgrounds than existing methods. At the same time, it is multiple orders of magnitude faster at compositional rendering thanks to its light field parametrization and the novel Slot Mixer decoder. We believe this work will not only accelerate future architecture exploration and scaling efforts, but it will also serve as a useful tool for both object-centric as well as neural scene representation learning communities.
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Mehdi S. M. Sajjadi, Daniel Duckworth, Aravindh Mahendran, Sjoerd van Steenkiste, Filip Pavetic, Mario Lucic, Leonidas J. Guibas, Klaus Greff, Thomas Kipf
| null | null | 2,022 |
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Matching in Multi-arm Bandit with Collision
| null |
In this paper, we consider the matching of multi-agent multi-armed bandit problem, i.e., while agents prefer arms with higher expected reward, arms also have preferences on agents. In such case, agents pulling the same arm may encounter collisions, which leads to a reward of zero.For this problem, we design a specific communication protocol which uses deliberate collision to transmit information among agents, and propose a layer-based algorithm that helps establish optimal stable matching between agents and arms. With this subtle communication protocol, our algorithm achieves a state-of-the-art $O(\log T)$ regret in the decentralized matching market, and outperforms existing baselines in experimental results.
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YiRui Zhang, Siwei Wang, Zhixuan Fang
| null | null | 2,022 |
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Learning to Drop Out: An Adversarial Approach to Training Sequence VAEs
| null |
In principle, applying variational autoencoders (VAEs) to sequential data offers a method for controlled sequence generation, manipulation, and structured representation learning. However, training sequence VAEs is challenging: autoregressive decoders can often explain the data without utilizing the latent space, known as posterior collapse. To mitigate this, state-of-the-art models weaken' thepowerful decoder' by applying uniformly random dropout to the decoder input.We show theoretically that this removes pointwise mutual information provided by the decoder input, which is compensated for by utilizing the latent space. We then propose an adversarial training strategy to achieve information-based stochastic dropout. Compared to uniform dropout on standard text benchmark datasets, our targeted approach increases both sequence modeling performance and the information captured in the latent space.
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Djordje Miladinovic, Kumar Shridhar, Kushal Jain, Max Paulus, Joachim M Buhmann, Carl Allen
| null | null | 2,022 |
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TVLT: Textless Vision-Language Transformer
| null |
In this work, we present the Textless Vision-Language Transformer (TVLT), where homogeneous transformer blocks take raw visual and audio inputs for vision-and-language representation learning with minimal modality-specific design, and do not use text-specific modules such as tokenization or automatic speech recognition (ASR). TVLT is trained by reconstructing masked patches of continuous video frames and audio spectrograms (masked autoencoding) and contrastive modeling to align video and audio. TVLT attains performance comparable to its text-based counterpart on various multimodal tasks, such as visual question answering, image retrieval, video retrieval, and multimodal sentiment analysis, with 28x faster inference speed and only 1/3 of the parameters. Our findings suggest the possibility of learning compact and efficient visual-linguistic representations from low-level visual and audio signals without assuming the prior existence of text. Our code and checkpoints are available at: https://github.com/zinengtang/TVLT
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Zineng Tang, Jaemin Cho, Yixin Nie, Mohit Bansal
| null | null | 2,022 |
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Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions
| null |
Neural Networks (NNs) have been successfully employed to represent the state evolution of complex dynamical systems. Such models, referred to as NN dynamic models (NNDMs), use iterative noisy predictions of NN to estimate a distribution of system trajectories over time. Despite their accuracy, safety analysis of NNDMs is known to be a challenging problem and remains largely unexplored. To address this issue, in this paper, we introduce a method of providing safety guarantees for NNDMs. Our approach is based on stochastic barrier functions, whose relation with safety are analogous to that of Lyapunov functions with stability. We first show a method of synthesizing stochastic barrier functions for NNDMs via a convex optimization problem, which in turn provides a lower bound on the system's safety probability. A key step in our method is the employment of the recent convex approximation results for NNs to find piece-wise linear bounds, which allow the formulation of the barrier function synthesis problem as a sum-of-squares optimization program. If the obtained safety probability is above the desired threshold, the system is certified. Otherwise, we introduce a method of generating controls for the system that robustly minimize the unsafety probability in a minimally-invasive manner. We exploit the convexity property of the barrier function to formulate the optimal control synthesis problem as a linear program. Experimental results illustrate the efficacy of the method. Namely, they show that the method can scale to multi-dimensional NNDMs with multiple layers and hundreds of neurons per layer, and that the controller can significantly improve the safety probability.
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Rayan Mazouz, Karan Muvvala, Akash Ratheesh Babu, Luca Laurenti, Morteza Lahijanian
| null | null | 2,022 |
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A Deep Reinforcement Learning Framework for Column Generation
| null |
Column Generation (CG) is an iterative algorithm for solving linear programs (LPs) with an extremely large number of variables (columns). CG is the workhorse for tackling large-scale integer linear programs, which rely on CG to solve LP relaxations within a branch and bound algorithm. Two canonical applications are the Cutting Stock Problem (CSP) and Vehicle Routing Problem with Time Windows (VRPTW). In VRPTW, for example, each binary variable represents the decision to include or exclude a route, of which there are exponentially many; CG incrementally grows the subset of columns being used, ultimately converging to an optimal solution. We propose RLCG, the first Reinforcement Learning (RL) approach for CG. Unlike typical column selection rules which myopically select a column based on local information at each iteration, we treat CG as a sequential decision-making problem, as the column selected in an iteration affects subsequent iterations of the algorithm. This perspective lends itself to a Deep Reinforcement Learning approach that uses Graph Neural Networks (GNNs) to represent the variable-constraint structure in the LP of interest. We perform an extensive set of experiments using the publicly available BPPLIB benchmark for CSP and Solomon benchmark for VRPTW. RLCG converges faster and reduces the number of CG iterations by 22.4% for CSP and 40.9% for VRPTW on average compared to a commonly used greedy policy.
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Cheng Chi, Amine Aboussalah, Elias Khalil, Juyoung Wang, Zoha Sherkat-Masoumi
| null | null | 2,022 |
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Composition Theorems for Interactive Differential Privacy
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An interactive mechanism is an algorithm that stores a data set and answers adaptively chosen queries to it. The mechanism is called differentially private, if any adversary cannot distinguish whether a specific individual is in the data set by interacting with the mechanism. We study composition properties of differential privacy in concurrent compositions. In this setting, an adversary interacts with $k$ interactive mechanisms in parallel and can interleave its queries to the mechanisms arbitrarily. Previously, Vadhan and Wang [2021] proved an optimal concurrent composition theorem for pure-differential privacy. We significantly generalize and extend their results. Namely, we prove optimal parallel composition properties for several major notions of differential privacy in the literature, including approximate DP, Renyi DP, and zero-concentrated DP. Our results demonstrate that the adversary gains no advantage by interleaving its queries to independently running mechanisms. Hence, interactivity is a feature that differential privacy grants us for free.Concurrently and independently of our work, Vadhan and Zhang [2022] proved an optimal concurrent composition theorem for f-DP [Dong et al., 2022], which implies our result for the approximate DP case.
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Xin Lyu
| null | null | 2,022 |
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Information bottleneck theory of high-dimensional regression: relevancy, efficiency and optimality
| null |
Avoiding overfitting is a central challenge in machine learning, yet many large neural networks readily achieve zero training loss. This puzzling contradiction necessitates new approaches to the study of overfitting. Here we quantify overfitting via residual information, defined as the bits in fitted models that encode noise in training data. Information efficient learning algorithms minimize residual information while maximizing the relevant bits, which are predictive of the unknown generative models. We solve this optimization to obtain the information content of optimal algorithms for a linear regression problem and compare it to that of randomized ridge regression. Our results demonstrate the fundamental trade-off between residual and relevant information and characterize the relative information efficiency of randomized regression with respect to optimal algorithms. Finally, using results from random matrix theory, we reveal the information complexity of learning a linear map in high dimensions and unveil information-theoretic analogs of double and multiple descent phenomena.
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Vudtiwat Ngampruetikorn, David J. Schwab
| null | null | 2,022 |
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Multimodal Contrastive Learning with LIMoE: the Language-Image Mixture of Experts
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Large sparsely-activated models have obtained excellent performance in multiple domains.However, such models are typically trained on a single modality at a time.We present the Language-Image MoE, LIMoE, a sparse mixture of experts model capable of multimodal learning.LIMoE accepts both images and text simultaneously, while being trained using a contrastive loss.MoEs are a natural fit for a multimodal backbone, since expert layers can learn an appropriate partitioning of modalities.However, new challenges arise; in particular, training stability and balanced expert utilization, for which we propose an entropy-based regularization scheme.Across multiple scales, we demonstrate performance improvement over dense models of equivalent computational cost.LIMoE-L/16 trained comparably to CLIP-L/14 achieves 77.9% zero-shot ImageNet accuracy (vs. 76.2%), and when further scaled to H/14 (with additional data) it achieves 83.8%, approaching state-of-the-art methods which use custom per-modality backbones and pre-training schemes.We analyse the quantitative and qualitative behavior of LIMoE, and demonstrate phenomena such as differing treatment of the modalities and the emergence of modality-specific experts.
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Basil Mustafa, Carlos Riquelme, Joan Puigcerver, Rodolphe Jenatton, Neil Houlsby
| null | null | 2,022 |
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Learning single-index models with shallow neural networks
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Single-index models are a class of functions given by an unknown univariate ``link'' function applied to an unknown one-dimensional projection of the input. These models are particularly relevant in high dimension, when the data might present low-dimensional structure that learning algorithms should adapt to. While several statistical aspects of this model, such as the sample complexity of recovering the relevant (one-dimensional) subspace, are well-understood, they rely on tailored algorithms that exploit the specific structure of the target function. In this work, we introduce a natural class of shallow neural networks and study its ability to learn single-index models via gradient flow. More precisely, we consider shallow networks in which biases of the neurons are frozen at random initialization. We show that the corresponding optimization landscape is benign, which in turn leads to generalization guarantees that match the near-optimal sample complexity of dedicated semi-parametric methods.
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Alberto Bietti, Joan Bruna, Clayton Sanford, Min Jae Song
| null | null | 2,022 |
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COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics
| null |
Many applications of text generation require incorporating different constraints to control the semantics or style of generated text. These constraints can be hard (e.g., ensuring certain keywords are included in the output) and soft (e.g., contextualizing the output with the left- or right-hand context). In this paper, we present Energy-based Constrained Decoding with Langevin Dynamics (COLD), a decoding framework which unifies constrained generation as specifying constraints through an energy function, then performing efficient differentiable reasoning over the constraints through gradient-based sampling. COLD decoding is a flexible framework that can be applied directly to off-the-shelf left-to-right language models without the need for any task-specific fine-tuning, as demonstrated through three challenging text generation applications: lexically-constrained generation, abductive reasoning, and counterfactual reasoning. Our experiments on these constrained generation tasks point to the effectiveness of our approach, both in terms of automatic and human evaluation.
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Lianhui Qin, Sean Welleck, Daniel Khashabi, Yejin Choi
| null | null | 2,022 |
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Effective Backdoor Defense by Exploiting Sensitivity of Poisoned Samples
| null |
Poisoning-based backdoor attacks are serious threat for training deep models on data from untrustworthy sources. Given a backdoored model, we observe that the feature representations of poisoned samples with trigger are more sensitive to transformations than those of clean samples. It inspires us to design a simple sensitivity metric, called feature consistency towards transformations (FCT), to distinguish poisoned samples from clean samples in the untrustworthy training set. Moreover, we propose two effective backdoor defense methods. Built upon a sample-distinguishment module utilizing the FCT metric, the first method trains a secure model from scratch using a two-stage secure training module. And the second method removes backdoor from a backdoored model with a backdoor removal module which alternatively unlearns the distinguished poisoned samples and relearns the distinguished clean samples. Extensive results on three benchmark datasets demonstrate the superior defense performance against eight types of backdoor attacks, to state-of-the-art backdoor defenses. Codes are available at: https://github.com/SCLBD/Effectivebackdoordefense.
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Weixin Chen, Baoyuan Wu, Haoqian Wang
| null | null | 2,022 |
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On the Adversarial Robustness of Mixture of Experts
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Adversarial robustness is a key desirable property of neural networks. It has been empirically shown to be affected by their sizes, with larger networks being typically more robust. Recently, \citet{bubeck2021universal} proved a lower bound on the Lipschitz constant of functions that fit the training data in terms of their number of parameters. This raises an interesting open question, do---and can---functions with more parameters, but not necessarily more computational cost, have better robustness? We study this question for sparse Mixture of Expert models (MoEs), that make it possible to scale up the model size for a roughly constant computational cost. We theoretically show that under certain conditions on the routing and the structure of the data, MoEs can have significantly smaller Lipschitz constants than their dense counterparts. The robustness of MoEs can suffer when the highest weighted experts for an input implement sufficiently different functions. We next empirically evaluate the robustness of MoEs on ImageNet using adversarial attacks and show they are indeed more robust than dense models with the same computational cost. We make key observations showing the robustness of MoEs to the choice of experts, highlighting the redundancy of experts in models trained in practice.
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Joan Puigcerver, Rodolphe Jenatton, Carlos Riquelme, Pranjal Awasthi, Srinadh Bhojanapalli
| null | null | 2,022 |
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Simple and Optimal Greedy Online Contention Resolution Schemes
| null |
Matching based markets, like ad auctions, ride-sharing, and eBay, are inherently online and combinatorial, and therefore have been extensively studied under the lens of online stochastic combinatorial optimization models. The general framework that has emerged uses Contention Resolution Schemes (CRSs) introduced by Chekuri, Vondrák, and Zenklusen for combinatorial problems, where one first obtains a fractional solution to a (continuous) relaxation of the objective, and then proceeds to round it. When the order of rounding is controlled by an adversary, it is called an Online Contention Resolution Scheme (OCRSs), which has been successfully applied in online settings such as posted-price mechanisms, prophet inequalities and stochastic probing.The study of greedy OCRSs against an almighty adversary has emerged as one of the most interesting problems since it gives a simple-to-implement scheme against the worst possible scenario. Intuitively, a greedy OCRS has to make all its decisions before the online process starts. We present simple $1/e$ - selectable greedy OCRSs for the single-item setting, partition matroids, and transversal matroids. This improves upon the previous state-of-the-art greedy OCRSs of [FSZ16] that achieves $1/4$ for these constraints. Finally, we show that no better competitive ratio than $1/e$ is possible, making our greedy OCRSs the best possible.
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Vasilis Livanos
| null | null | 2,022 |
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On Margins and Generalisation for Voting Classifiers
| null |
We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. (2021) for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the ``margins theory'' proposed by Schapire et al. (1998) for the generalisation of ensemble classifiers.
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Felix Biggs, Valentina Zantedeschi, Benjamin Guedj
| null | null | 2,022 |
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Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures
| null |
Antibodies are immune system proteins that protect the host by binding to specific antigens such as viruses and bacteria. The binding between antibodies and antigens is mainly determined by the complementarity-determining regions (CDR) of the antibodies. In this work, we develop a deep generative model that jointly models sequences and structures of CDRs based on diffusion probabilistic models and equivariant neural networks. Our method is the first deep learning-based method that generates antibodies explicitly targeting specific antigen structures and is one of the earliest diffusion probabilistic models for protein structures. The model is a "Swiss Army Knife" capable of sequence-structure co-design, sequence design for given backbone structures, and antibody optimization. We conduct extensive experiments to evaluate the quality of both sequences and structures of designed antibodies. We find that our model could yield competitive results in binding affinity measured by biophysical energy functions and other protein design metrics.
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Shitong Luo, Yufeng Su, Xingang Peng, Sheng Wang, Jian Peng, Jianzhu Ma
| null | null | 2,022 |
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On the Safety of Interpretable Machine Learning: A Maximum Deviation Approach
| null |
Interpretable and explainable machine learning has seen a recent surge of interest. We focus on safety as a key motivation behind the surge and make the relationship between interpretability and safety more quantitative. Toward assessing safety, we introduce the concept of maximum deviation via an optimization problem to find the largest deviation of a supervised learning model from a reference model regarded as safe. We then show how interpretability facilitates this safety assessment. For models including decision trees, generalized linear and additive models, the maximum deviation can be computed exactly and efficiently. For tree ensembles, which are not regarded as interpretable, discrete optimization techniques can still provide informative bounds. For a broader class of piecewise Lipschitz functions, we leverage the multi-armed bandit literature to show that interpretability produces tighter (regret) bounds on the maximum deviation. We present case studies, including one on mortgage approval, to illustrate our methods and the insights about models that may be obtained from deviation maximization.
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Dennis Wei, Rahul Nair, Amit Dhurandhar, Kush R. Varshney, Elizabeth Daly, Moninder Singh
| null | null | 2,022 |
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Hyperparameter Sensitivity in Deep Outlier Detection: Analysis and a Scalable Hyper-Ensemble Solution
| null |
Outlier detection (OD) literature exhibits numerous algorithms as it applies to diverse domains. However, given a new detection task, it is unclear how to choose an algorithm to use, nor how to set its hyperparameter(s) (HPs) in unsupervised settings. HP tuning is an ever-growing problem with the arrival of many new detectors based on deep learning, which usually come with a long list of HPs. Surprisingly, the issue of model selection in the outlier mining literature has been “the elephant in the room”; a significant factor in unlocking the utmost potential of deep methods, yet little said or done to systematically tackle the issue. In the first part of this paper, we conduct the first large-scale analysis on the HP sensitivity of deep OD methods, and through more than 35,000 trained models, quantitatively demonstrate that model selection is inevitable. Next, we design a HP-robust and scalable deep hyper-ensemble model called ROBOD that assembles models with varying HP configurations, bypassing the choice paralysis. Importantly, we introduce novel strategies to speed up ensemble training, such as parameter sharing, batch/simultaneous training, and data subsampling, that allow us to train fewer models with fewer parameters. Extensive experiments on both image and tabular datasets show that ROBOD achieves and retains robust, state-of-the-art detection performance as compared to its modern counterparts, while taking only 2-10% of the time by the naïve hyper-ensemble with independent training.
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Xueying Ding, Lingxiao Zhao, Leman Akoglu
| null | null | 2,022 |
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Theoretically Better and Numerically Faster Distributed Optimization with Smoothness-Aware Quantization Techniques
| null |
To address the high communication costs of distributed machine learning, a large body of work has been devoted in recent years to designing various compression strategies, such as sparsification and quantization, and optimization algorithms capable of using them. Recently, Safaryan et al. (2021) pioneered a dramatically different compression design approach: they first use the local training data to form local smoothness matrices and then propose to design a compressor capable of exploiting the smoothness information contained therein. While this novel approach leads to substantial savings in communication, it is limited to sparsification as it crucially depends on the linearity of the compression operator. In this work, we generalize their smoothness-aware compression strategy to arbitrary unbiased compression operators, which also include sparsification. Specializing our results to stochastic quantization, we guarantee significant savings in communication complexity compared to standard quantization. In particular, we prove that block quantization with $n$ blocks theoretically outperforms single block quantization, leading to a reduction in communication complexity by an $\mathcal{O}(n)$ factor, where $n$ is the number of nodes in the distributed system. Finally, we provide extensive numerical evidence with convex optimization problems that our smoothness-aware quantization strategies outperform existing quantization schemes as well as the aforementioned smoothness-aware sparsification strategies with respect to three evaluation metrics: the number of iterations, the total amount of bits communicated, and wall-clock time.
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Bokun Wang, Mher Safaryan, Peter Richtarik
| null | null | 2,022 |
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Rethinking the Reverse-engineering of Trojan Triggers
| null |
Deep Neural Networks are vulnerable to Trojan (or backdoor) attacks. Reverse-engineering methods can reconstruct the trigger and thus identify affected models. Existing reverse-engineering methods only consider input space constraints, e.g., trigger size in the input space.Expressly, they assume the triggers are static patterns in the input space and fail to detect models with feature space triggers such as image style transformations. We observe that both input-space and feature-space Trojans are associated with feature space hyperplanes.Based on this observation, we design a novel reverse-engineering method that exploits the feature space constraint to reverse-engineer Trojan triggers. Results on four datasets and seven different attacks demonstrate that our solution effectively defends both input-space and feature-space Trojans. It outperforms state-of-the-art reverse-engineering methods and other types of defenses in both Trojaned model detection and mitigation tasks. On average, the detection accuracy of our method is 93%. For Trojan mitigation, our method can reduce the ASR (attack success rate) to only 0.26% with the BA (benign accuracy) remaining nearly unchanged. Our code can be found at https://github.com/RU-System-Software-and-Security/FeatureRE.
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Zhenting Wang, Kai Mei, Hailun Ding, Juan Zhai, Shiqing Ma
| null | null | 2,022 |
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RainNet: A Large-Scale Imagery Dataset and Benchmark for Spatial Precipitation Downscaling
| null |
AI-for-science approaches have been applied to solve scientific problems (e.g., nuclear fusion, ecology, genomics, meteorology) and have achieved highly promising results. Spatial precipitation downscaling is one of the most important meteorological problem and urgently requires the participation of AI. However, the lack of a well-organized and annotated large-scale dataset hinders the training and verification of more effective and advancing deep-learning models for precipitation downscaling. To alleviate these obstacles, we present the first large-scale spatial precipitation downscaling dataset named RainNet, which contains more than 62,400 pairs of high-quality low/high-resolution precipitation maps for over 17 years, ready to help the evolution of deep learning models in precipitation downscaling. Specifically, the precipitation maps carefully collected in RainNet cover various meteorological phenomena (e.g., hurricane, squall), which is of great help to improve the model generalization ability. In addition, the map pairs in RainNet are organized in the form of image sequences (720 maps per month or 1 map/hour), showing complex physical properties, e.g., temporal misalignment, temporal sparse, and fluid properties. Furthermore, two deep-learning-oriented metrics are specifically introduced to evaluate or verify the comprehensive performance of the trained model (e.g., prediction maps reconstruction accuracy). To illustrate the applications of RainNet, 14 state-of-the-art models, including deep models and traditional approaches, are evaluated. To fully explore potential downscaling solutions, we propose an implicit physical estimation benchmark framework to learn the above characteristics. Extensive experiments demonstrate the value of RainNet in training and evaluating downscaling models. Our dataset is available at https://neuralchen.github.io/RainNet/.
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Xuanhong Chen, Kairui Feng, Naiyuan Liu, Bingbing Ni, Yifan Lu, Zhengyan Tong, Ziang Liu
| null | null | 2,022 |
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Risk-Driven Design of Perception Systems
| null |
Modern autonomous systems rely on perception modules to process complex sensor measurements into state estimates. These estimates are then passed to a controller, which uses them to make safety-critical decisions. It is therefore important that we design perception systems to minimize errors that reduce the overall safety of the system. We develop a risk-driven approach to designing perception systems that accounts for the effect of perceptual errors on the performance of the fully-integrated, closed-loop system. We formulate a risk function to quantify the effect of a given perceptual error on overall safety, and show how we can use it to design safer perception systems by including a risk-dependent term in the loss function and generating training data in risk-sensitive regions. We evaluate our techniques on a realistic vision-based aircraft detect and avoid application and show that risk-driven design reduces collision risk by 37% over a baseline system.
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Anthony Corso, Sydney Katz, Craig Innes, Xin Du, Subramanian Ramamoorthy, Mykel J Kochenderfer
| null | null | 2,022 |
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ZeroC: A Neuro-Symbolic Model for Zero-shot Concept Recognition and Acquisition at Inference Time
| null |
Humans have the remarkable ability to recognize and acquire novel visual concepts in a zero-shot manner. Given a high-level, symbolic description of a novel concept in terms of previously learned visual concepts and their relations, humans can recognize novel concepts without seeing any examples. Moreover, they can acquire new concepts by parsing and communicating symbolic structures using learned visual concepts and relations. Endowing these capabilities in machines is pivotal in improving their generalization capability at inference time. In this work, we introduce Zero-shot Concept Recognition and Acquisition (ZeroC), a neuro-symbolic architecture that can recognize and acquire novel concepts in a zero-shot way. ZeroC represents concepts as graphs of constituent concept models (as nodes) and their relations (as edges). To allow inference time composition, we employ energy-based models (EBMs) to model concepts and relations. We design ZeroC architecture so that it allows a one-to-one mapping between a symbolic graph structure of a concept and its corresponding EBM, which for the first time, allows acquiring new concepts, communicating its graph structure, and applying it to classification and detection tasks (even across domains) at inference time. We introduce algorithms for learning and inference with ZeroC. We evaluate ZeroC on a challenging grid-world dataset which is designed to probe zero-shot concept recognition and acquisition, and demonstrate its capability.
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Tailin Wu, Megan Tjandrasuwita, Zhengxuan Wu, Xuelin Yang, Kevin Liu, Rok Sosic, Jure Leskovec
| null | null | 2,022 |
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Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting
| null |
Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over time. Previous studies primarily adopt stationarization to attenuate the non-stationarity of original series for better predictability. But the stationarized series deprived of inherent non-stationarity can be less instructive for real-world bursty events forecasting. This problem, termed over-stationarization in this paper, leads Transformers to generate indistinguishable temporal attentions for different series and impedes the predictive capability of deep models. To tackle the dilemma between series predictability and model capability, we propose Non-stationary Transformers as a generic framework with two interdependent modules: Series Stationarization and De-stationary Attention. Concretely, Series Stationarization unifies the statistics of each input and converts the output with restored statistics for better predictability. To address the over-stationarization problem, De-stationary Attention is devised to recover the intrinsic non-stationary information into temporal dependencies by approximating distinguishable attentions learned from raw series. Our Non-stationary Transformers framework consistently boosts mainstream Transformers by a large margin, which reduces MSE by 49.43% on Transformer, 47.34% on Informer, and 46.89% on Reformer, making them the state-of-the-art in time series forecasting. Code is available at this repository: https://github.com/thuml/Nonstationary_Transformers.
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Yong Liu, Haixu Wu, Jianmin Wang, Mingsheng Long
| null | null | 2,022 |
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Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation
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Researchers have proposed many methods for fair and robust machine learning, but comprehensive empirical evaluation of their subgroup robustness is lacking. In this work, we address this gap in the context of tabular data, where sensitive subgroups are clearly-defined, real-world fairness problems abound, and prior works often do not compare to state-of-the-art tree-based models as baselines. We conduct an empirical comparison of several previously-proposed methods for fair and robust learning alongside state-of-the-art tree-based methods and other baselines. Via experiments with more than $340{,}000$ model configurations on eight datasets, we show that tree-based methods have strong subgroup robustness, even when compared to robustness- and fairness-enhancing methods. Moreover, the best tree-based models tend to show good performance over a range of metrics, while robust or group-fair models can show brittleness, with significant performance differences across different metrics for a fixed model. We also demonstrate that tree-based models show less sensitivity to hyperparameter configurations, and are less costly to train. Our work suggests that tree-based ensemble models make an effective baseline for tabular data, and are a sensible default when subgroup robustness is desired. See https://github.com/jpgard/subgroup-robustness-grows-on-trees for code to reproduce our experiments and detailed experimental results.
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Josh Gardner, Zoran Popovic, Ludwig Schmidt
| null | null | 2,022 |
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Dataset Distillation using Neural Feature Regression
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Dataset distillation aims to learn a small synthetic dataset that preserves most of the information from the original dataset. Dataset distillation can be formulated as a bi-level meta-learning problem where the outer loop optimizes the meta-dataset and the inner loop trains a model on the distilled data. Meta-gradient computation is one of the key challenges in this formulation, as differentiating through the inner loop learning procedure introduces significant computation and memory costs. In this paper, we address these challenges using neural Feature Regression with Pooling (FRePo), achieving the state-of-the-art performance with an order of magnitude less memory requirement and two orders of magnitude faster training than previous methods. The proposed algorithm is analogous to truncated backpropagation through time with a pool of models to alleviate various types of overfitting in dataset distillation. FRePo significantly outperforms the previous methods on CIFAR100, Tiny ImageNet, and ImageNet-1K. Furthermore, we show that high-quality distilled data can greatly improve various downstream applications, such as continual learning and membership inference defense. Please check out our webpage at https://sites.google.com/view/frepo.
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Yongchao Zhou, Ehsan Nezhadarya, Jimmy Ba
| null | null | 2,022 |
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GhostNetV2: Enhance Cheap Operation with Long-Range Attention
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Light-weight convolutional neural networks (CNNs) are specially designed for applications on mobile devices with faster inference speed. The convolutional operation can only capture local information in a window region, which prevents performance from being further improved. Introducing self-attention into convolution can capture global information well, but it will largely encumber the actual speed. In this paper, we propose a hardware-friendly attention mechanism (dubbed DFC attention) and then present a new GhostNetV2 architecture for mobile applications. The proposed DFC attention is constructed based on fully-connected layers, which can not only execute fast on common hardware but also capture the dependence between long-range pixels. We further revisit the expressiveness bottleneck in previous GhostNet and propose to enhance expanded features produced by cheap operations with DFC attention, so that a GhostNetV2 block can aggregate local and long-range information simultaneously. Extensive experiments demonstrate the superiority of GhostNetV2 over existing architectures. For example, it achieves 75.3% top-1 accuracy on ImageNet with 167M FLOPs, significantly suppressing GhostNetV1 (74.5%) with a similar computational cost. The source code will be available at https://github.com/huawei-noah/Efficient-AI-Backbones/tree/master/ghostnetv2_pytorch and https://gitee.com/mindspore/models/tree/master/research/cv/ghostnetv2.
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Yehui Tang, Kai Han, Jianyuan Guo, Chang Xu, Chao Xu, Yunhe Wang
| null | null | 2,022 |
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Sparse Structure Search for Delta Tuning
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Adapting large pre-trained models (PTMs) through fine-tuning imposes prohibitive computational and storage burdens. Recent studies of delta tuning (DT), i.e., parameter-efficient tuning, find that only optimizing a small portion of parameters conditioned on PTMs could yield on-par performance compared to conventional fine-tuning. Generally, DT methods exquisitely design delta modules (DT modules) which could be applied to arbitrary fine-grained positions inside PTMs. However, the effectiveness of these fine-grained positions largely relies on sophisticated manual designation, thereby usually producing sub-optimal results. In contrast to the manual designation, we explore constructing DT modules in an automatic manner. We automatically \textbf{S}earch for the \textbf{S}parse \textbf{S}tructure of \textbf{Delta} Tuning (S$^3$Delta). Based on a unified framework of various DT methods, S$^3$Delta conducts the differentiable DT structure search through bi-level optimization and proposes shifted global sigmoid method to explicitly control the number of trainable parameters. Extensive experiments show that S$^3$Delta surpasses manual and random structures with less trainable parameters. The searched structures preserve more than 99\% fine-tuning performance with 0.01\% trainable parameters. Moreover, the advantage of S$^3$Delta is amplified with extremely low trainable parameters budgets (0.0009\%$\sim$0.01\%). The searched structures are transferable and explainable, providing suggestions and guidance for the future design of DT methods. Our codes are publicly available at \url{https://github.com/thunlp/S3Delta}.
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Shengding Hu, Zhen Zhang, Ning Ding, Yadao Wang, Yasheng Wang, Zhiyuan Liu, Maosong Sun
| null | null | 2,022 |
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Joint Entropy Search for Multi-Objective Bayesian Optimization
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Many real-world problems can be phrased as a multi-objective optimization problem, where the goal is to identify the best set of compromises between the competing objectives. Multi-objective Bayesian optimization (BO) is a sample efficient strategy that can be deployed to solve these vector-valued optimization problems where access is limited to a number of noisy objective function evaluations. In this paper, we propose a novel information-theoretic acquisition function for BO called Joint Entropy Search (JES), which considers the joint information gain for the optimal set of inputs and outputs. We present several analytical approximations to the JES acquisition function and also introduce an extension to the batch setting. We showcase the effectiveness of this new approach on a range of synthetic and real-world problems in terms of the hypervolume and its weighted variants.
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Ben Tu, Axel Gandy, Nikolas Kantas, Behrang Shafei
| null | null | 2,022 |
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Hard ImageNet: Segmentations for Objects with Strong Spurious Cues
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Deep classifiers are known to rely on spurious features, leading to reduced generalization. The severity of this problem varies significantly by class. We identify $15$ classes in ImageNet with very strong spurious cues, and collect segmentation masks for these challenging objects to form \emph{Hard ImageNet}. Leveraging noise, saliency, and ablation based metrics, we demonstrate that models rely on spurious features in Hard ImageNet far more than in RIVAL10, an ImageNet analog to CIFAR10. We observe Hard ImageNet objects are less centered and occupy much less space in their images than RIVAL10 objects, leading to greater spurious feature reliance. Further, we use robust neural features to automatically rank our images based on the degree of spurious cues present. Comparing images with high and low rankings within a class reveals the exact spurious features models rely upon, and shows reduced performance when spurious features are absent. With Hard ImageNet's image rankings, object segmentations, and our extensive evaluation suite, the community can begin to address the problem of learning to detect challenging objects \emph{for the right reasons}, despite the presence of strong spurious cues.
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Mazda Moayeri, Sahil Singla, Soheil Feizi
| null | null | 2,022 |
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Distribution-Informed Neural Networks for Domain Adaptation Regression
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In this paper, we study the problem of domain adaptation regression, which learns a regressor for a target domain by leveraging the knowledge from a relevant source domain. We start by proposing a distribution-informed neural network, which aims to build distribution-aware relationship of inputs and outputs from different domains. This allows us to develop a simple domain adaptation regression framework, which subsumes popular domain adaptation approaches based on domain invariant representation learning, reweighting, and adaptive Gaussian process. The resulting findings not only explain the connections of existing domain adaptation approaches, but also motivate the efficient training of domain adaptation approaches with overparameterized neural networks. We also analyze the convergence and generalization error bound of our framework based on the distribution-informed neural network. Specifically, our generalization bound focuses explicitly on the maximum mean discrepancy in the RKHS induced by the neural tangent kernel of distribution-informed neural network. This is in sharp contrast to the existing work which relies on domain discrepancy in the latent feature space heuristically formed by one or several hidden neural layers. The efficacy of our framework is also empirically verified on a variety of domain adaptation regression benchmarks.
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Jun Wu, Jingrui He, Sheng Wang, Kaiyu Guan, Elizabeth Ainsworth
| null | null | 2,022 |
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You Never Stop Dancing: Non-freezing Dance Generation via Bank-constrained Manifold Projection
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One of the most overlooked challenges in dance generation is that the auto-regressive frameworks are prone to freezing motions due to noise accumulation. In this paper, we present two modules that can be plugged into the existing models to enable them to generate non-freezing and high fidelity dances. Since the high-dimensional motion data are easily swamped by noise, we propose to learn a low-dimensional manifold representation by an auto-encoder with a bank of latent codes, which can be used to reduce the noise in the predicted motions, thus preventing from freezing. We further extend the bank to provide explicit priors about the future motions to disambiguate motion prediction, which helps the predictors to generate motions with larger magnitude and higher fidelity than possible before. Extensive experiments on AIST++, a public large-scale 3D dance motion benchmark, demonstrate that our method notably outperforms the baselines in terms of quality, diversity and time length.
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Jiangxin Sun, Chunyu Wang, Huang Hu, Hanjiang Lai, Zhi Jin, Jian-Fang Hu
| null | null | 2,022 |
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Momentum Adversarial Distillation: Handling Large Distribution Shifts in Data-Free Knowledge Distillation
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Data-free Knowledge Distillation (DFKD) has attracted attention recently thanks to its appealing capability of transferring knowledge from a teacher network to a student network without using training data. The main idea is to use a generator to synthesize data for training the student. As the generator gets updated, the distribution of synthetic data will change. Such distribution shift could be large if the generator and the student are trained adversarially, causing the student to forget the knowledge it acquired at the previous steps. To alleviate this problem, we propose a simple yet effective method called Momentum Adversarial Distillation (MAD) which maintains an exponential moving average (EMA) copy of the generator and uses synthetic samples from both the generator and the EMA generator to train the student. Since the EMA generator can be considered as an ensemble of the generator's old versions and often undergoes a smaller change in updates compared to the generator, training on its synthetic samples can help the student recall the past knowledge and prevent the student from adapting too quickly to the new updates of the generator. Our experiments on six benchmark datasets including big datasets like ImageNet and Places365 demonstrate the superior performance of MAD over competing methods for handling the large distribution shift problem. Our method also compares favorably to existing DFKD methods and even achieves state-of-the-art results in some cases.
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Kien Do, Thai Hung Le, Dung Nguyen, Dang Nguyen, HARIPRIYA HARIKUMAR, Truyen Tran, Santu Rana, Svetha Venkatesh
| null | null | 2,022 |
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LION: Latent Point Diffusion Models for 3D Shape Generation
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Denoising diffusion models (DDMs) have shown promising results in 3D point cloud synthesis. To advance 3D DDMs and make them useful for digital artists, we require (i) high generation quality, (ii) flexibility for manipulation and applications such as conditional synthesis and shape interpolation, and (iii) the ability to output smooth surfaces or meshes. To this end, we introduce the hierarchical Latent Point Diffusion Model (LION) for 3D shape generation. LION is set up as a variational autoencoder (VAE) with a hierarchical latent space that combines a global shape latent representation with a point-structured latent space. For generation, we train two hierarchical DDMs in these latent spaces. The hierarchical VAE approach boosts performance compared to DDMs that operate on point clouds directly, while the point-structured latents are still ideally suited for DDM-based modeling. Experimentally, LION achieves state-of-the-art generation performance on multiple ShapeNet benchmarks. Furthermore, our VAE framework allows us to easily use LION for different relevant tasks: LION excels at multimodal shape denoising and voxel-conditioned synthesis, and it can be adapted for text- and image-driven 3D generation. We also demonstrate shape autoencoding and latent shape interpolation, and we augment LION with modern surface reconstruction techniques to generate smooth 3D meshes. We hope that LION provides a powerful tool for artists working with 3D shapes due to its high-quality generation, flexibility, and surface reconstruction. Project page and code: https://nv-tlabs.github.io/LION.
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xiaohui zeng, Arash Vahdat, Francis Williams, Zan Gojcic, Or Litany, Sanja Fidler, Karsten Kreis
| null | null | 2,022 |
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MExMI: Pool-based Active Model Extraction Crossover Membership Inference
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With increasing popularity of Machine Learning as a Service (MLaaS), ML models trained from public and proprietary data are deployed in the cloud and deliver prediction services to users. However, as the prediction API becomes a new attack surface, growing concerns have arisen on the confidentiality of ML models. Existing literatures show their vulnerability under model extraction (ME) attacks, while their private training data is vulnerable to another type of attacks, namely, membership inference (MI). In this paper, we show that ME and MI can reinforce each other through a chained and iterative reaction, which can significantly boost ME attack accuracy and improve MI by saving the query cost. As such, we build a framework MExMI for pool-based active model extraction (PAME) to exploit MI through three modules: “MI Pre-Filter”, “MI Post-Filter”, and “semi-supervised boosting”. Experimental results show that MExMI can improve up to 11.14% from the best known PAME attack and reach 94.07% fidelity with only 16k queries. Furthermore, the precision and recall of the MI attack in MExMI are on par with state-of-the-art MI attack which needs 150k queries.
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Yaxin Xiao, Qingqing Ye, Haibo Hu, Huadi Zheng, Chengfang Fang, Jie Shi
| null | null | 2,022 |
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Robustness to Unbounded Smoothness of Generalized SignSGD
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Traditional analyses in non-convex optimization typically rely on the smoothness assumption, namely requiring the gradients to be Lipschitz. However, recent evidence shows that this smoothness condition does not capture the properties of some deep learning objective functions, including the ones involving Recurrent Neural Networks and LSTMs. Instead, they satisfy a much more relaxed condition, with potentially unbounded smoothness. Under this relaxed assumption, it has been theoretically and empirically shown that the gradient-clipped SGD has an advantage over the vanilla one. In this paper, we show that clipping is not indispensable for Adam-type algorithms in tackling such scenarios: we theoretically prove that a generalized SignSGD algorithm can obtain similar convergence rates as SGD with clipping but does not need explicit clipping at all. This family of algorithms on one end recovers SignSGD and on the other end closely resembles the popular Adam algorithm. Our analysis underlines the critical role that momentum plays in analyzing SignSGD-type and Adam-type algorithms: it not only reduces the effects of noise, thus removing the need for large mini-batch in previous analyses of SignSGD-type algorithms, but it also substantially reduces the effects of unbounded smoothness and gradient norms. To the best of our knowledge, this work is the first one showing the benefit of Adam-type algorithms compared with non-adaptive gradient algorithms such as gradient descent in the unbounded smoothness setting. We also compare these algorithms with popular optimizers on a set of deep learning tasks, observing that we can match the performance of Adam while beating others.
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Michael Crawshaw, Mingrui Liu, Francesco Orabona, Wei Zhang, Zhenxun Zhuang
| null | null | 2,022 |
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Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability
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Recent findings demonstrate that modern neural networks trained by full-batch gradient descent typically enter a regime called Edge of Stability (EOS). In this regime, the sharpness, i.e., the maximum Hessian eigenvalue, first increases to the value 2/(step size) (the progressive sharpening phase) and then oscillates around this value (the EOS phase). This paper aims to analyze the GD dynamics and the sharpness along the optimization trajectory.Our analysis naturally divides the GD trajectory into four phases depending on the change in the sharpness value. We empirically identify the norm of output layer weight as an interesting indicator of the sharpness dynamics. Based on this empirical observation, we attempt to theoretically and empirically explain the dynamics of various key quantities that lead to the change of the sharpness in each phase of EOS. Moreover, based on certain assumptions, we provide a theoretical proof of the sharpness behavior in the EOS regime in two-layer fully-connected linear neural networks. We also discuss some other empirical findings and the limitation of our theoretical results.
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Zixuan Wang, Zhouzi Li, Jian Li
| null | null | 2,022 |
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MultiGuard: Provably Robust Multi-label Classification against Adversarial Examples
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Multi-label classification, which predicts a set of labels for an input, has many applications. However, multiple recent studies showed that multi-label classification is vulnerable to adversarial examples. In particular, an attacker can manipulate the labels predicted by a multi-label classifier for an input via adding carefully crafted, human-imperceptible perturbation to it. Existing provable defenses for multi-class classification achieve sub-optimal provable robustness guarantees when generalized to multi-label classification. In this work, we propose MultiGuard, the first provably robust defense against adversarial examples to multi-label classification. Our MultiGuard leverages randomized smoothing, which is the state-of-the-art technique to build provably robust classifiers. Specifically, given an arbitrary multi-label classifier, our MultiGuard builds a smoothed multi-label classifier via adding random noise to the input. We consider isotropic Gaussian noise in this work. Our major theoretical contribution is that we show a certain number of ground truth labels of an input are provably in the set of labels predicted by our MultiGuard when the $\ell_2$-norm of the adversarial perturbation added to the input is bounded. Moreover, we design an algorithm to compute our provable robustness guarantees. Empirically, we evaluate our MultiGuard on VOC 2007, MS-COCO, and NUS-WIDE benchmark datasets. Our code is available at: https://github.com/quwenjie/MultiGuard
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Jinyuan Jia, Wenjie Qu, Neil Gong
| null | null | 2,022 |
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Near-Isometric Properties of Kronecker-Structured Random Tensor Embeddings
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We give uniform concentration inequality for random tensors acting on rank-1 Kronecker structured signals, which parallels a Gordon-type inequality for this class of tensor structured data. Two variants of the random embedding are considered, where the embedding dimension depends on explicit quantities characterizing the complexity of the signal. As applications of the tools developed herein, we illustrate with examples from signal recovery and optimization.
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Qijia Jiang
| null | null | 2,022 |
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Lost in Latent Space: Examining failures of disentangled models at combinatorial generalisation
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Recent research has shown that generative models with highly disentangled representations fail to generalise to unseen combination of generative factor values. These findings contradict earlier research which showed improved performance in out-of-training distribution settings when compared to entangled representations. Additionally, it is not clear if the reported failures are due to (a) encoders failing to map novel combinations to the proper regions of the latent space, or (b) novel combinations being mapped correctly but the decoder is unable to render the correct output for the unseen combinations. We investigate these alternatives by testing several models on a range of datasets and training settings. We find that (i) when models fail, their encoders also fail to map unseen combinations to correct regions of the latent space and (ii) when models succeed, it is either because the test conditions do not exclude enough examples, or because excluded cases involve combinations of object properties with it's shape. We argue that to generalise properly, models not only need to capture factors of variation, but also understand how to invert the process that causes the visual stimulus.
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Milton Montero, Jeffrey Bowers, Rui Ponte Costa, Casimir Ludwig, Gaurav Malhotra
| null | null | 2,022 |
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A New Family of Generalization Bounds Using Samplewise Evaluated CMI
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We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated, samplewise, evaluated conditional mutual information (CMI), an information measure that depends on the losses incurred by the selected hypothesis, rather than on the hypothesis itself, as is common in probably approximately correct (PAC)-Bayesian results. We demonstrate the generality of this framework by recovering and extending previously known information-theoretic bounds. Furthermore, using the evaluated CMI, we derive a samplewise, average version of Seeger's PAC-Bayesian bound, where the convex function is the binary KL divergence. In some scenarios, this novel bound results in a tighter characterization of the population loss of deep neural networks than previous bounds. Finally, we derive high-probability versions of some of these average bounds. We demonstrate the unifying nature of the evaluated CMI bounds by using them to recover average and high-probability generalization bounds for multiclass classification with finite Natarajan dimension.
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Fredrik Hellström, Giuseppe Durisi
| null | null | 2,022 |
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On Measuring Excess Capacity in Neural Networks
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We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a priori) constrain this class while retaining an empirical error on a par with the unconstrained regime? To assess excess capacity in modern architectures (such as residual networks), we extend and unify prior Rademacher complexity bounds to accommodate function composition and addition, as well as the structure of convolutions. The capacity-driving terms in our bounds are the Lipschitz constants of the layers and a (2,1) group norm distance to the initializations of the convolution weights. Experiments on benchmark datasets of varying task difficulty indicate that (1) there is a substantial amount of excess capacity per task, and (2) capacity can be kept at a surprisingly similar level across tasks. Overall, this suggests a notion of compressibility with respect to weight norms, complementary to classic compression via weight pruning. Source code is available at https://github.com/rkwitt/excess_capacity.
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Florian Graf, Sebastian Zeng, Bastian Rieck, Marc Niethammer, Roland Kwitt
| null | null | 2,022 |
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Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees
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Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherent nested structure: the inner loop finds the optimal policy given parametrized rewards while the outer loop updates the estimates towards optimizing a measure of fit. For high dimensional environments such nested-loop structure entails a significant computational burden. To reduce the computational burden of a nested loop, novel methods such as SQIL \cite{reddy2019sqil} and IQ-Learn \cite{garg2021iq} emphasize policy estimation at the expense of reward estimation accuracy. However, without accurate estimated rewards, it is not possible to do counterfactual analysis such as predicting the optimal policy under different environment dynamics and/or learning new tasks. In this paper we develop a novel {\em single-loop} algorithm for IRL that does not compromise reward estimation accuracy. In the proposed algorithm, each policy improvement step is followed by a stochastic gradient step for likelihood maximization. We show that the proposed algorithm provably converges to a stationary solution with a finite-time guarantee. If the reward is parameterized linearly we show the identified solution corresponds to the solution of the maximum entropy IRL problem. Finally, by using robotics control problems in Mujoco and their transfer settings, we show that the proposed algorithm achieves superior performance compared with other IRL and imitation learning benchmarks.
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Siliang Zeng, Chenliang Li, Alfredo Garcia, Mingyi Hong
| null | null | 2,022 |
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Scalable design of Error-Correcting Output Codes using Discrete Optimization with Graph Coloring
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We study the problem of scalable design of Error-Correcting Output Codes (ECOC) for multi-class classification. Prior works on ECOC-based classifiers are limited to codebooks with small number of rows (classes) or columns, and do not provide optimality guarantees for the codebook design problem. We address these limitations by developing a codebook design approach based on a Mixed-Integer Quadratically Constrained Program (MIQCP). This discrete formulation is naturally suited for maximizing the error-correction capability of ECOC-based classifiers and incorporates various design criteria in a flexible manner. Our solution approach is tractable in that it incrementally increases the codebook size by adding columns to maximize the gain in error-correcting capability. In particular, we show that the maximal gain in error-correction can be upper bounded by solving a graph-coloring problem. As a result, we can efficiently generate near-optimal codebooks for very large problem instances. These codebooks provide competitive multi-class classification performance on small class datasets such as MNIST and CIFAR10. Moreover, by leveraging transfer-learned binary classifiers, we achieve better classification performance over transfer-learned multi-class CNNs on large class datasets such as CIFAR100, Caltech-101/256. Our results highlight the advantages of simple and modular ECOC-based classifiers in improving classification accuracy without the risk of overfitting.
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Samarth Gupta, Saurabh Amin
| null | null | 2,022 |
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Parameter-Efficient Masking Networks
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A deeper network structure generally handles more complicated non-linearity and performs more competitively. Nowadays, advanced network designs often contain a large number of repetitive structures (e.g., Transformer). They empower the network capacity to a new level but also increase the model size inevitably, which is unfriendly to either model restoring or transferring. In this study, we are the first to investigate the representative potential of fixed random weights with limited unique values by learning diverse masks and introduce the Parameter-Efficient Masking Networks (PEMN). It also naturally leads to a new paradigm for model compression to diminish the model size. Concretely, motivated by the repetitive structures in modern neural networks, we utilize one random initialized layer, accompanied with different masks, to convey different feature mappings and represent repetitive network modules. Therefore, the model can be expressed as \textit{one-layer} with a bunch of masks, which significantly reduce the model storage cost. Furthermore, we enhance our strategy by learning masks for a model filled by padding a given random weights vector. In this way, our method can further lower the space complexity, especially for models without many repetitive architectures. We validate the potential of PEMN learning masks on random weights with limited unique values and test its effectiveness for a new compression paradigm based on different network architectures.Code is available at \href{https://github.com/yueb17/PEMN}{\textcolor{magenta}{https://github.com/yueb17/PEMN}}.
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Yue Bai, Huan Wang, Xu Ma, Yitian Zhang, Zhiqiang Tao, Yun Fu
| null | null | 2,022 |
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On Leave-One-Out Conditional Mutual Information For Generalization
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We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). In contrast to other CMI bounds, which may be hard to evaluate in practice, our loo-CMI bounds are easier to compute and can be interpreted in connection to other notions such as classical leave-one-out cross-validation, stability of the optimization algorithm, and the geometry of the loss-landscape. It applies both to the output of training algorithms as well as their predictions. We empirically validate the quality of the bound by evaluating its predicted generalization gap in scenarios for deep learning. In particular, our bounds are non-vacuous on image-classification tasks.
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Mohamad Rida Rammal, Alessandro Achille, Aditya Golatkar, Suhas Diggavi, Stefano Soatto
| null | null | 2,022 |
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VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Training
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Pre-training video transformers on extra large-scale datasets is generally required to achieve premier performance on relatively small datasets. In this paper, we show that video masked autoencoders (VideoMAE) are data-efficient learners for self-supervised video pre-training (SSVP). We are inspired by the recent ImageMAE and propose customized video tube masking with an extremely high ratio. This simple design makes video reconstruction a more challenging and meaningful self-supervision task, thus encouraging extracting more effective video representations during the pre-training process. We obtain three important findings with VideoMAE: (1) An extremely high proportion of masking ratio (i.e., 90% to 95%) still yields favorable performance for VideoMAE. The temporally redundant video content enables higher masking ratio than that of images. (2) VideoMAE achieves impressive results on very small datasets (i.e., around 3k-4k videos) without using any extra data. This is partially ascribed to the challenging task of video reconstruction to enforce high-level structure learning. (3) VideoMAE shows that data quality is more important than data quantity for SSVP. Domain shift between pre-training and target datasets is an important factor. Notably, our VideoMAE with the vanilla ViT backbone can achieve 87.4% on Kinects-400, 75.4% on Something-Something V2, 91.3% on UCF101, and 62.6% on HMDB51, without using any extra data. Code is available at https://github.com/MCG-NJU/VideoMAE.
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Zhan Tong, Yibing Song, Jue Wang, Limin Wang
| null | null | 2,022 |
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A Closer Look at the Adversarial Robustness of Deep Equilibrium Models
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Deep equilibrium models (DEQs) refrain from the traditional layer-stacking paradigm and turn to find the fixed point of a single layer. DEQs have achieved promising performance on different applications with featured memory efficiency. At the same time, the adversarial vulnerability of DEQs raises concerns. Several works propose to certify robustness for monotone DEQs. However, limited efforts are devoted to studying empirical robustness for general DEQs. To this end, we observe that an adversarially trained DEQ requires more forward steps to arrive at the equilibrium state, or even violates its fixed-point structure. Besides, the forward and backward tracks of DEQs are misaligned due to the black-box solvers. These facts cause gradient obfuscation when applying the ready-made attacks to evaluate or adversarially train DEQs. Given this, we develop approaches to estimate the intermediate gradients of DEQs and integrate them into the attacking pipelines. Our approaches facilitate fully white-box evaluations and lead to effective adversarial defense for DEQs. Extensive experiments on CIFAR-10 validate the adversarial robustness of DEQs competitive with deep networks of similar sizes.
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Zonghan Yang, Tianyu Pang, Yang Liu
| null | null | 2,022 |
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Automatic Differentiation of Programs with Discrete Randomness
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Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability $p$ of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters ($p$) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code package is available at https://github.com/gaurav-arya/StochasticAD.jl.
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Gaurav Arya, Moritz Schauer, Frank Schäfer, Christopher Rackauckas
| null | null | 2,022 |
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HorNet: Efficient High-Order Spatial Interactions with Recursive Gated Convolutions
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Recent progress in vision Transformers exhibits great success in various tasks driven by the new spatial modeling mechanism based on dot-product self-attention. In this paper, we show that the key ingredients behind the vision Transformers, namely input-adaptive, long-range and high-order spatial interactions, can also be efficiently implemented with a convolution-based framework. We present the Recursive Gated Convolution ($\textit{g}^\textit{n}$Conv) that performs high-order spatial interactions with gated convolutions and recursive designs. The new operation is highly flexible and customizable, which is compatible with various variants of convolution and extends the two-order interactions in self-attention to arbitrary orders without introducing significant extra computation. $\textit{g}^\textit{n}$Conv can serve as a plug-and-play module to improve various vision Transformers and convolution-based models. Based on the operation, we construct a new family of generic vision backbones named HorNet. Extensive experiments on ImageNet classification, COCO object detection and ADE20K semantic segmentation show HorNet outperform Swin Transformers and ConvNeXt by a significant margin with similar overall architecture and training configurations. HorNet also shows favorable scalability to more training data and larger model sizes. Apart from the effectiveness in visual encoders, we also show $\textit{g}^\textit{n}$Conv can be applied to task-specific decoders and consistently improve dense prediction performance with less computation. Our results demonstrate that $\textit{g}^\textit{n}$Conv can be a new basic module for visual modeling that effectively combines the merits of both vision Transformers and CNNs. Code is available at https://github.com/raoyongming/HorNet.
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Yongming Rao, Wenliang Zhao, Yansong Tang, Jie Zhou, Ser Nam Lim, Jiwen Lu
| null | null | 2,022 |
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A Unified Diversity Measure for Multiagent Reinforcement Learning
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Promoting behavioural diversity is of critical importance in multi-agent reinforcement learning, since it helps the agent population maintain robust performance when encountering unfamiliar opponents at test time, or, when the game is highly non-transitive in the strategy space (e.g., Rock-Paper-Scissor). While a myriad of diversity metrics have been proposed, there are no widely accepted or unified definitions in the literature, making the consequent diversity-aware learning algorithms difficult to evaluate and the insights elusive. In this work, we propose a novel metric called the Unified Diversity Measure (UDM) that offers a unified view for existing diversity metrics. Based on UDM, we design the UDM-Fictitious Play (UDM-FP) and UDM-Policy Space Response Oracle (UDM-PSRO) algorithms as efficient solvers for normal-form games and open-ended games. In theory, we prove that UDM-based methods can enlarge the gamescape by increasing the response capacity of the strategy pool, and have convergence guarantee to two-player Nash equilibrium. We validate our algorithms on games that show strong non-transitivity, and empirical results show that our algorithms achieve better performances than strong PSRO baselines in terms of the exploitability and population effectivity.
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Zongkai Liu, Chao Yu, Yaodong Yang, peng sun, Zifan Wu, Yuan Li
| null | null | 2,022 |
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EcoFormer: Energy-Saving Attention with Linear Complexity
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Transformer is a transformative framework for deep learning which models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention mechanism. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way. Based on the equivalence between the inner product of binary codes and the Hamming distance as well as the associative property of matrix multiplication, we can approximate the attention in linear complexity by expressing it as a dot-product of binary codes. Moreover, the compact binary representations of queries and keys in EcoFormer enable us to replace most of the expensive multiply-accumulate operations in attention with simple accumulations to save considerable on-chip energy footprint on edge devices. Extensive experiments on both vision and language tasks show that EcoFormer consistently achieves comparable performance with standard attentions while consuming much fewer resources. For example, based on PVTv2-B0 and ImageNet-1K, EcoFormer achieves a 73% reduction in on-chip energy footprint with only a slight performance drop of 0.33% compared to the standard attention. Code is available at https://github.com/ziplab/EcoFormer.
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Jing Liu, Zizheng Pan, Haoyu He, Jianfei Cai, Bohan Zhuang
| null | null | 2,022 |
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BEVFusion: A Simple and Robust LiDAR-Camera Fusion Framework
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Fusing the camera and LiDAR information has become a de-facto standard for 3D object detection tasks. Current methods rely on point clouds from the LiDAR sensor as queries to leverage the feature from the image space. However, people discovered that this underlying assumption makes the current fusion framework infeasible to produce any prediction when there is a LiDAR malfunction, regardless of minor or major. This fundamentally limits the deployment capability to realistic autonomous driving scenarios. In contrast, we propose a surprisingly simple yet novel fusion framework, dubbed BEVFusion, whose camera stream does not depend on the input of LiDAR data, thus addressing the downside of previous methods. We empirically show that our framework surpasses the state-of-the-art methods under the normal training settings. Under the robustness training settings that simulate various LiDAR malfunctions, our framework significantly surpasses the state-of-the-art methods by 15.7% to 28.9% mAP. To the best of our knowledge, we are the first to handle realistic LiDAR malfunction and can be deployed to realistic scenarios without any post-processing procedure.
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Tingting Liang, Hongwei Xie, Kaicheng Yu, Zhongyu Xia, Zhiwei Lin, Yongtao Wang, Tao Tang, Bing Wang, Zhi Tang
| null | null | 2,022 |
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Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need?
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Finding accurate solutions to the Schrödinger equation is the key unsolved challenge of computational chemistry. Given its importance for the development of new chemical compounds, decades of research have been dedicated to this problem, but due to the large dimensionality even the best available methods do not yet reach the desired accuracy.Recently the combination of deep learning with Monte Carlo methods has emerged as a promising way to obtain highly accurate energies and moderate scaling of computational cost. In this paper we significantly contribute towards this goal by introducing a novel deep-learning architecture that achieves 40-70% lower energy error at 6x lower computational cost compared to previous approaches. Using our method we establish a new benchmark by calculating the most accurate variational ground state energies ever published for a number of different atoms and molecules.We systematically break down and measure our improvements, focusing in particular on the effect of increasing physical prior knowledge.We surprisingly find that increasing the prior knowledge given to the architecture can actually decrease accuracy.
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Leon Gerard, Michael Scherbela, Philipp Marquetand, Philipp Grohs
| null | null | 2,022 |
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NS3: Neuro-symbolic Semantic Code Search
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Semantic code search is the task of retrieving a code snippet given a textual description of its functionality. Recent work has been focused on using similarity metrics between neural embeddings of text and code. However, current language models are known to struggle with longer, compositional sentences, and multi-step reasoning. To overcome this limitation, we propose supplementing the query sentence with a layout of its semantic structure. The semantic layout is used to break down the final reasoning decision into a series of lower-level decisions. We use a Neural Module Network architecture to implement this idea. We compare our model - $NS^3$ (Neuro-Symbolic Semantic Search) - to a number of baselines, including state-of-the-art semantic code retrieval methods, such as CodeBERT, CuBERT and GraphCodeBERT, and evaluate on two datasets - Code Search Net (CSN) and Code Search and Question Answering (CoSQA). On these datasets, we demonstrate that our approach results in higher performance. We also perform additional studies to show the effectiveness of our modular design when handling compositional queries.
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Shushan Arakelyan, Anna Hakhverdyan, Miltiadis Allamanis, Luis Garcia, Christophe Hauser, Xiang Ren
| null | null | 2,022 |
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Toward Robust Spiking Neural Network Against Adversarial Perturbation
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As spiking neural networks (SNNs) are deployed increasingly in real-world efficiency critical applications, the security concerns in SNNs attract more attention.Currently, researchers have already demonstrated an SNN can be attacked with adversarial examples. How to build a robust SNN becomes an urgent issue.Recently, many studies apply certified training in artificial neural networks (ANNs), which can improve the robustness of an NN model promisely. However, existing certifications cannot transfer to SNNs directly because of the distinct neuron behavior and input formats for SNNs. In this work, we first design S-IBP and S-CROWN that tackle the non-linear functions in SNNs' neuron modeling. Then, we formalize the boundaries for both digital and spike inputs. Finally, we demonstrate the efficiency of our proposed robust training method in different datasets and model architectures. Based on our experiment, we can achieve a maximum $37.7\%$ attack error reduction with $3.7\%$ original accuracy loss. To the best of our knowledge, this is the first analysis on robust training of SNNs.
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LING LIANG, Kaidi Xu, Xing Hu, Lei Deng, Yuan Xie
| null | null | 2,022 |
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Decomposed Knowledge Distillation for Class-Incremental Semantic Segmentation
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Class-incremental semantic segmentation (CISS) labels each pixel of an image with a corresponding object/stuff class continually. To this end, it is crucial to learn novel classes incrementally without forgetting previously learned knowledge. Current CISS methods typically use a knowledge distillation (KD) technique for preserving classifier logits, or freeze a feature extractor, to avoid the forgetting problem. The strong constraints, however, prevent learning discriminative features for novel classes. We introduce a CISS framework that alleviates the forgetting problem and facilitates learning novel classes effectively. We have found that a logit can be decomposed into two terms. They quantify how likely an input belongs to a particular class or not, providing a clue for a reasoning process of a model. The KD technique, in this context, preserves the sum of two terms ($\textit{i.e.}$, a class logit), suggesting that each could be changed and thus the KD does not imitate the reasoning process. To impose constraints on each term explicitly, we propose a new decomposed knowledge distillation (DKD) technique, improving the rigidity of a model and addressing the forgetting problem more effectively. We also introduce a novel initialization method to train new classifiers for novel classes. In CISS, the number of negative training samples for novel classes is not sufficient to discriminate old classes. To mitigate this, we propose to transfer knowledge of negatives to the classifiers successively using an auxiliary classifier, boosting the performance significantly. Experimental results on standard CISS benchmarks demonstrate the effectiveness of our framework.
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Donghyeon Baek, Youngmin Oh, Sanghoon Lee, Junghyup Lee, Bumsub Ham
| null | null | 2,022 |
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How Sampling Impacts the Robustness of Stochastic Neural Networks
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Stochastic neural networks (SNNs) are random functions whose predictions are gained by averaging over multiple realizations. Consequently, a gradient-based adversarial example is calculated based on one set of samples and its classification on another set. In this paper, we derive a sufficient condition for such a stochastic prediction to be robust against a given sample-based attack. This allows us to identify the factors that lead to an increased robustness of SNNs and gives theoretical explanations for: (i) the well known observation, that increasing the amount of samples drawn for the estimation of adversarial examples increases the attack's strength,(ii) why increasing the number of samples during an attack can not fully reduce the effect of stochasticity, (iii) why the sample size during inference does not influence the robustness, and(iv) why a higher gradient variance and a shorter expected value of the gradient relates to a higher robustness. Our theoretical findings give a unified view on the mechanisms underlying previously proposed approaches for increasing attack strengths or model robustness and are verified by an extensive empirical analysis.
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Sina Däubener, Asja Fischer
| null | null | 2,022 |
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Sound and Complete Causal Identification with Latent Variables Given Local Background Knowledge
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Great efforts have been devoted to causal discovery from observational data, and it is well known that introducing some background knowledge attained from experiments or human expertise can be very helpful. However, it remains unknown that \emph{what causal relations are identifiable given background knowledge in the presence of latent confounders}. In this paper, we solve the problem with sound and complete orientation rules when the background knowledge is given in a \emph{local} form. Furthermore, based on the solution to the problem, this paper proposes a general active learning framework for causal discovery in the presence of latent confounders, with its effectiveness and efficiency validated by experiments.
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Tian-Zuo Wang, Tian Qin, Zhi-Hua Zhou
| null | null | 2,022 |
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Wild-Time: A Benchmark of in-the-Wild Distribution Shift over Time
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Distribution shifts occur when the test distribution differs from the training distribution, and can considerably degrade performance of machine learning models deployed in the real world. While recent works have studied robustness to distribution shifts, distribution shifts arising from the passage of time have the additional structure of timestamp metadata. Real-world examples of such shifts are underexplored, and it is unclear whether existing models can leverage trends in past distribution shifts to reliably extrapolate into the future. To address this gap, we curate Wild-Time, a benchmark of 5 datasets that reflect temporal distribution shifts arising in a variety of real-world applications, including drug discovery, patient prognosis, and news classification. On these datasets, we systematically benchmark 13 approaches with various inductive biases. We evaluate methods in domain-generalization, continual learning, self-supervised learning, and ensemble learning, which leverage timestamps to extract the common structure of the distribution shifts. We extend several domain-generalization methods to the temporal distribution shift setting by treating windows of time as different domains. Finally, we propose two evaluation strategies to evaluate model performance under temporal distribution shifts---evaluation with a fixed time split (Eval-Fix) and evaluation with a data stream (Eval-Stream). Eval-Fix, our primary evaluation strategy, aims to provide a simple evaluation protocol for the broader machine learning community, while Eval-Stream serves as a complementary benchmark for continual learning approaches. Our experiments demonstrate that existing methods are limited in tackling temporal distribution shift: across all settings, we observe an average performance drop of 20% from in-distribution to out-of-distribution data.
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Huaxiu Yao, Caroline Choi, Bochuan Cao, Yoonho Lee, Pang Wei W. Koh, Chelsea Finn
| null | null | 2,022 |
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End-to-end Symbolic Regression with Transformers
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Symbolic regression, the task of predicting the mathematical expression of a function from the observation of its values, is a difficult task which usually involves a two-step procedure: predicting the "skeleton" of the expression up to the choice of numerical constants, then fitting the constants by optimizing a non-convex loss function. The dominant approach is genetic programming, which evolves candidates by iterating this subroutine a large number of times. Neural networks have recently been tasked to predict the correct skeleton in a single try, but remain much less powerful.In this paper, we challenge this two-step procedure, and task a Transformer to directly predict the full mathematical expression, constants included. One can subsequently refine the predicted constants by feeding them to the non-convex optimizer as an informed initialization. We present ablations to show that this end-to-end approach yields better results, sometimes even without the refinement step. We evaluate our model on problems from the SRBench benchmark and show that our model approaches the performance of state-of-the-art genetic programming with several orders of magnitude faster inference.
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Pierre-alexandre Kamienny, Stéphane d'Ascoli, Guillaume Lample, Francois Charton
| null | null | 2,022 |
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GRASP: Navigating Retrosynthetic Planning with Goal-driven Policy
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Retrosynthetic planning occupies a crucial position in synthetic chemistry and, accordingly, drug discovery, which aims to find synthetic pathways of a target molecule through a sequential decision-making process on a set of feasible reactions. While the majority of recent works focus on the prediction of feasible reactions at each step, there have been limited attempts toward improving the sequential decision-making policy. Existing strategies rely on either the expensive and high-variance value estimation by online rollout, or a settled value estimation neural network pre-trained with simulated pathways of limited diversity and no negative feedback. Besides, how to return multiple candidate pathways that are not only diverse but also desirable for chemists (e.g., affordable building block materials) remains an open challenge. To this end, we propose a Goal-dRiven Actor-critic retroSynthetic Planning (GRASP) framework, where we identify the policy that performs goal-driven retrosynthesis navigation toward a user-demand objective. Our experiments on the benchmark Pistachio dataset and a chemists-designed dataset demonstrate that the framework outperforms state-of-the-art approaches by up to 32.2% on search efficiency and 5.6% on quality. Remarkably, our user studies show that GRASP successfully plans pathways that accomplish the goal prescribed with a designated goal (building block materials).
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Yemin Yu, Ying Wei, Kun Kuang, Zhengxing Huang, Huaxiu Yao, Fei Wu
| null | null | 2,022 |
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Temporal Latent Bottleneck: Synthesis of Fast and Slow Processing Mechanisms in Sequence Learning
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Recurrent neural networks have a strong inductive bias towards learning temporally compressed representations, as the entire history of a sequence is represented by a single vector. By contrast, Transformers have little inductive bias towards learning temporally compressed representations, as they allow for attention over all previously computed elements in a sequence. Having a more compressed representation of a sequence may be beneficial for generalization, as a high-level representation may be more easily re-used and re-purposed and will contain fewer irrelevant details. At the same time, excessive compression of representations comes at the cost of expressiveness. We propose a solution which divides computation into two streams. A slow stream that is recurrent in nature aims to learn a specialized and compressed representation, by forcing chunks of $K$ time steps into a single representation which is divided into multiple vectors. At the same time, a fast stream is parameterized as a Transformer to process chunks consisting of $K$ time-steps conditioned on the information in the slow-stream. In the proposed approach we hope to gain the expressiveness of the Transformer, while encouraging better compression and structuring of representations in the slow stream. We show the benefits of the proposed method in terms of improved sample efficiency and generalization performance as compared to various competitive baselines for visual perception and sequential decision making tasks.
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Aniket Didolkar, Kshitij Gupta, Anirudh Goyal, Nitesh Bharadwaj Gundavarapu, Alex M. Lamb, Nan Rosemary Ke, Yoshua Bengio
| null | null | 2,022 |
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Near-Optimal Private and Scalable $k$-Clustering
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We study the differentially private (DP) $k$-means and $k$-median clustering problems of $n$ points in $d$-dimensional Euclidean space in the massively parallel computation (MPC) model. We provide two near-optimal algorithms where the near-optimality is in three aspects: they both achieve (1). $O(1)$ parallel computation rounds, (2). near-linear in $n$ and polynomial in $k$ total computational work (i.e., near-linear running time when $n$ is a sufficient polynomial in $k$), (3). $O(1)$ relative approximation and $\text{poly}(k, d)$ additive error. Note that $\Omega(1)$ relative approximation is provably necessary even for any polynomial-time non-private algorithm, and $\Omega(k)$ additive error is a provable lower bound for any polynomial-time DP $k$-means/median algorithm. Our two algorithms provide a tradeoff between the relative approximation and the additive error: the first has $O(1)$ relative approximation and $\sim (k^{2.5} + k^{1.01} \sqrt{d})$ additive error, and the second one achieves $(1+\gamma)$ relative approximation to the optimal non-private algorithm for an arbitrary small constant $\gamma>0$ and with $\text{poly}(k, d)$ additive error for a larger polynomial dependence on $k$ and $d$. To achieve our result, we develop a general framework which partitions the data and reduces the DP clustering problem for the entire dataset to the DP clustering problem for each part. To control the blow-up of the additive error introduced by each part, we develop a novel charging argument which might be of independent interest.
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Vincent Cohen-Addad, Alessandro Epasto, Vahab Mirrokni, Shyam Narayanan, Peilin Zhong
| null | null | 2,022 |
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Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching
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In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/DeformationBasis.
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Ramana Subramanyam Sundararaman, Riccardo Marin, Emanuele Rodolà, Maks Ovsjanikov
| null | null | 2,022 |
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Minimax Optimal Algorithms for Fixed-Budget Best Arm Identification
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We consider the fixed-budget best arm identification problem where the goal is to find the arm of the largest mean with a fixed number of samples. It is known that the probability of misidentifying the best arm is exponentially small to the number of rounds. However, limited characterizations have been discussed on the rate (exponent) of this value. In this paper, we characterize the minimax optimal rate as a result of an optimization over all possible parameters. We introduce two rates, $R^{\mathrm{go}}$ and $R^{\mathrm{go}}_{\infty}$, corresponding to lower bounds on the probability of misidentification, each of which is associated with a proposed algorithm. The rate $R^{\mathrm{go}}$ is associated with $R^{\mathrm{go}}$-tracking, which can be efficiently implemented by a neural network and is shown to outperform existing algorithms. However, this rate requires a nontrivial condition to be achievable. To address this issue, we introduce the second rate $R^{\mathrm{go}}_\infty$. We show that this rate is indeed achievable by introducing a conceptual algorithm called delayed optimal tracking (DOT).
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Junpei Komiyama, Taira Tsuchiya, Junya Honda
| null | null | 2,022 |
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Modeling Transitivity and Cyclicity in Directed Graphs via Binary Code Box Embeddings
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Modeling directed graphs with differentiable representations is a fundamental requirement for performing machine learning on graph-structured data. Geometric embedding models (e.g. hyperbolic, cone, and box embeddings) excel at this task, exhibiting useful inductive biases for directed graphs. However, modeling directed graphs that both contain cycles and some element of transitivity, two properties common in real-world settings, is challenging. Box embeddings, which can be thought of as representing the graph as an intersection over some learned super-graphs, have a natural inductive bias toward modeling transitivity, but (as we prove) cannot model cycles. To this end, we propose binary code box embeddings, where a learned binary code selects a subset of graphs for intersection. We explore several variants, including global binary codes (amounting to a union over intersections) and per-vertex binary codes (allowing greater flexibility) as well as methods of regularization. Theoretical and empirical results show that the proposed models not only preserve a useful inductive bias of transitivity but also have sufficient representational capacity to model arbitrary graphs, including graphs with cycles.
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Dongxu Zhang, Michael Boratko, Cameron Musco, Andrew McCallum
| null | null | 2,022 |
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Revisiting Sparse Convolutional Model for Visual Recognition
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Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be expressed by a linear combination of a few elements from a convolutional dictionary, are powerful tools for analyzing natural images with good theoretical interpretability and biological plausibility. However, such principled models have not demonstrated competitive performance when compared with empirically designed deep networks. This paper revisits the sparse convolutional modeling for image classification and bridges the gap between good empirical performance (of deep learning) and good interpretability (of sparse convolutional models). Our method uses differentiable optimization layers that are defined from convolutional sparse coding as drop-in replacements of standard convolutional layers in conventional deep neural networks. We show that such models have equally strong empirical performance on CIFAR-10, CIFAR-100 and ImageNet datasets when compared to conventional neural networks. By leveraging stable recovery property of sparse modeling, we further show that such models can be much more robust to input corruptions as well as adversarial perturbations in testing through a simple proper trade-off between sparse regularization and data reconstruction terms.
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xili dai, Mingyang Li, Pengyuan Zhai, Shengbang Tong, Xingjian Gao, Shao-Lun Huang, Zhihui Zhu, Chong You, Yi Ma
| null | null | 2,022 |
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Generalization Bounds for Gradient Methods via Discrete and Continuous Prior
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Proving algorithm-dependent generalization error bounds for gradient-type optimization methods has attracted significant attention recently in learning theory. However, most existing trajectory-based analyses require either restrictive assumptions on the learning rate (e.g., fast decreasing learning rate), or continuous injected noise (such as the Gaussian noise in Langevin dynamics). In this paper, we introduce a new discrete data-dependent prior to the PAC-Bayesian framework, and prove a high probability generalization bound of order $O(\frac{1}{n}\cdot \sum_{t=1}^T(\gamma_t/\varepsilon_t)^2\left\|{\mathrm{g}_t}\right\|^2)$ for Floored GD (i.e. a version of gradient descent with precision level $\varepsilon_t$), where $n$ is the number of training samples, $\gamma_t$ is the learning rate at step $t$, $\mathrm{g}_t$ is roughly the difference of the gradient computed using all samples and that using only prior samples. $\left\|{\mathrm{g}_t}\right\|$ is upper bounded by and and typical much smaller than the gradient norm $\left\|{\nabla f(W_t)}\right\|$. We remark that our bound holds for nonconvex and nonsmooth scenarios. Moreover, our theoretical results provide numerically favorable upper bounds of testing errors (e.g., $0.037$ on MNIST). Using similar technique, we can also obtain new generalization bounds for a certain variant of SGD. Furthermore, we study the generalization bounds for gradient Langevin Dynamics (GLD). Using the same framework with a carefully constructed continuous prior, we show a new high probability generalization bound of order $O(\frac{1}{n} + \frac{L^2}{n^2}\sum_{t=1}^T(\gamma_t/\sigma_t)^2)$ for GLD. The new $1/n^2$ rate is due to the concentration of the difference between the gradient of training samples and that of the prior.
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Xuanyuan Luo, Bei Luo, Jian Li
| null | null | 2,022 |
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REVIVE: Regional Visual Representation Matters in Knowledge-Based Visual Question Answering
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This paper revisits visual representation in knowledge-based visual question answering (VQA) and demonstrates that using regional information in a better way can significantly improve the performance. While visual representation is extensively studied in traditional VQA, it is under-explored in knowledge-based VQA even though these two tasks share the common spirit, i.e., rely on visual input to answer the question. Specifically, we observe in most state-of-the-art knowledge-based VQA methods: 1) visual features are extracted either from the whole image or in a sliding window manner for retrieving knowledge, and the important relationship within/among object regions is neglected; 2) visual features are not well utilized in the final answering model, which is counter-intuitive to some extent. Based on these observations, we propose a new knowledge-based VQA method REVIVE, which tries to utilize the explicit information of object regions not only in the knowledge retrieval stage but also in the answering model. The key motivation is that object regions and inherent relationship are important for knowledge-based VQA. We perform extensive experiments on the standard OK-VQA dataset and achieve new state-of the-art performance, i.e., 58.0 accuracy, surpassing previous state-of-the-art method by a large margin (+3.6%). We also conduct detailed analysis and show the necessity of regional information in different framework components for knowledge-based VQA. Code is publicly available at https://github.com/yzleroy/REVIVE.
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Yuanze Lin, Yujia Xie, Dongdong Chen, Yichong Xu, Chenguang Zhu, Lu Yuan
| null | null | 2,022 |
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On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds
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Deep generative models have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that deep generative networks can efficiently generate high-dimensional complex data from a low-dimensional easy-to-sample distribution. However, this phenomenon can not be justified by existing theories. The widely held manifold hypothesis speculates that real-world data sets, such as natural images and signals, exhibit low-dimensional geometric structures. In this paper, we take such low-dimensional data structures into consideration by assuming that data distributions are supported on a low-dimensional manifold. We prove approximation and estimation theories of deep generative networks for estimating distributions on a low-dimensional manifold under the Wasserstein-1 loss. We show that the Wasserstein-1 loss converges to zero at a fast rate depending on the intrinsic dimension instead of the ambient data dimension. Our theory leverages the low-dimensional geometric structures in data sets and justifies the practical power of deep generative models. We require no smoothness assumptions on the data distribution which is desirable in practice.
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Biraj Dahal, Alexander Havrilla, Minshuo Chen, Tuo Zhao, Wenjing Liao
| null | null | 2,022 |
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Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Media
| null |
Recent years have witnessed the rise of misinformation campaigns that spread specific narratives on social media to manipulate public opinions on different areas, such as politics and healthcare. Consequently, an effective and efficient automatic methodology to estimate the influence of the misinformation on user beliefs and activities is needed. However, existing works on misinformation impact estimation either rely on small-scale psychological experiments or can only discover the correlation between user behaviour and misinformation. To address these issues, in this paper, we build up a causal framework that model the causal effect of misinformation from the perspective of temporal point process. To adapt the large-scale data, we design an efficient yet precise way to estimate the \textbf{Individual Treatment Effect} (ITE) via neural temporal point process and gaussian mixture models. Extensive experiments on synthetic dataset verify the effectiveness and efficiency of our model. We further apply our model on a real-world dataset of social media posts and engagements about COVID-19 vaccines. The experimental results indicate that our model recognized identifiable causal effect of misinformation that hurts people's subjective emotions toward the vaccines.
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Yizhou Zhang, Defu Cao, Yan Liu
| null | null | 2,022 |
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A Near-Optimal Primal-Dual Method for Off-Policy Learning in CMDP
| null |
As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish an $\Omega\left(\frac{\min\left\{|\mathcal{S}||\mathcal{A}|,|\mathcal{S}|+I\right\} C^*}{(1-\gamma)^3\epsilon^2}\right)$ sample complexity lower bound for the offline CMDP problem, where $I$ stands for the number of constraints. By introducing a simple but novel deviation control mechanism, we propose a near-optimal primal-dual learning algorithm called DPDL. This algorithm provably guarantees zero constraint violation and its sample complexity matches the above lower bound except for an $\tilde{\mathcal{O}}((1-\gamma)^{-1})$ factor. Comprehensive discussion on how to deal with the unknown constant $C^*$ and the potential asynchronous structure on the offline dataset are also included.
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Fan Chen, Junyu Zhang, Zaiwen Wen
| null | null | 2,022 |
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FedAvg with Fine Tuning: Local Updates Lead to Representation Learning
| null |
The Federated Averaging (FedAvg) algorithm, which consists of alternating between a few local stochastic gradient updates at client nodes, followed by a model averaging update at the server, is perhaps the most commonly used method in Federated Learning. Notwithstanding its simplicity, several empirical studies have illustrated that the model output by FedAvg leads to a model that generalizes well to new unseen tasks after a few fine-tuning steps. This surprising performance of such a simple method, however, is not fully understood from a theoretical point of view. In this paper, we formally investigate this phenomenon in the multi-task linear regression setting. We show that the reason behind the generalizability of the FedAvg output is FedAvg’s power in learning the common data representation among the clients’ tasks, by leveraging the diversity among client data distributions via multiple local updates between communication rounds. We formally establish the iteration complexity required by the clients for proving such result in the setting where the underlying shared representation is a linear map. To the best of our knowledge, this is the first result showing that FedAvg learns an expressive representation in any setting. Moreover, we show that multiple local updates between communication rounds are necessary for representation learning, as distributed gradient methods that make only one local update between rounds provably cannot recover the ground-truth representation in the linear setting, and empirically yield neural network representations that generalize drastically worse to new clients than those learned by FedAvg trained on heterogeneous image classification datasets.
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Liam Collins, Hamed Hassani, Aryan Mokhtari, Sanjay Shakkottai
| null | null | 2,022 |
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BackdoorBench: A Comprehensive Benchmark of Backdoor Learning
| null |
Backdoor learning is an emerging and vital topic for studying deep neural networks' vulnerability (DNNs). Many pioneering backdoor attack and defense methods are being proposed, successively or concurrently, in the status of a rapid arms race. However, we find that the evaluations of new methods are often unthorough to verify their claims and accurate performance, mainly due to the rapid development, diverse settings, and the difficulties of implementation and reproducibility. Without thorough evaluations and comparisons, it is not easy to track the current progress and design the future development roadmap of the literature. To alleviate this dilemma, we build a comprehensive benchmark of backdoor learning called BackdoorBench. It consists of an extensible modular-based codebase (currently including implementations of 8 state-of-the-art (SOTA) attacks and 9 SOTA defense algorithms) and a standardized protocol of complete backdoor learning. We also provide comprehensive evaluations of every pair of 8 attacks against 9 defenses, with 5 poisoning ratios, based on 5 models and 4 datasets, thus 8,000 pairs of evaluations in total. We present abundant analysis from different perspectives about these 8,000 evaluations, studying the effects of different factors in backdoor learning. All codes and evaluations of BackdoorBench are publicly available at https://backdoorbench.github.io.
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Baoyuan Wu, Hongrui Chen, Mingda Zhang, Zihao Zhu, Shaokui Wei, Danni Yuan, Chao Shen
| null | null | 2,022 |
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Memory Efficient Continual Learning with Transformers
| null |
In many real-world scenarios, data to train machine learning models becomes available over time. Unfortunately, these models struggle to continually learn new concepts without forgetting what has been learnt in the past. This phenomenon is known as catastrophic forgetting and it is difficult to prevent due to practical constraints. For instance, the amount of data that can be stored or the computational resources that can be used might be limited. Moreover, applications increasingly rely on large pre-trained neural networks, such as pre-trained Transformers, since compute or data might not be available in sufficiently large quantities to practitioners to train from scratch. In this paper, we devise a method to incrementally train a model on a sequence of tasks using pre-trained Transformers and extending them with Adapters. Different than the existing approaches, our method is able to scale to a large number of tasks without significant overhead and allows sharing information across tasks. On both image and text classification tasks, we empirically demonstrate that our method maintains a good predictive performance without retraining the model or increasing the number of model parameters over time. The resulting model is also significantly faster at inference time compared to Adapter-based state-of-the-art methods.
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Beyza Ermis, Giovanni Zappella, Martin Wistuba, Aditya Rawal, Cedric Archambeau
| null | null | 2,022 |
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DReS-FL: Dropout-Resilient Secure Federated Learning for Non-IID Clients via Secret Data Sharing
| null |
Federated learning (FL) strives to enable collaborative training of machine learning models without centrally collecting clients' private data. Different from centralized training, the local datasets across clients in FL are non-independent and identically distributed (non-IID). In addition, the data-owning clients may drop out of the training process arbitrarily. These characteristics will significantly degrade the training performance. This paper proposes a Dropout-Resilient Secure Federated Learning (DReS-FL) framework based on Lagrange coded computing (LCC) to tackle both the non-IID and dropout problems. The key idea is to utilize Lagrange coding to secretly share the private datasets among clients so that each client receives an encoded version of the global dataset, and the local gradient computation over this dataset is unbiased. To correctly decode the gradient at the server, the gradient function has to be a polynomial in a finite field, and thus we construct polynomial integer neural networks (PINNs) to enable our framework. Theoretical analysis shows that DReS-FL is resilient to client dropouts and provides privacy protection for the local datasets. Furthermore, we experimentally demonstrate that DReS-FL consistently leads to significant performance gains over baseline methods.
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Jiawei Shao, Yuchang Sun, Songze Li, Jun Zhang
| null | null | 2,022 |
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Convergence beyond the over-parameterized regime using Rayleigh quotients
| null |
In this paper, we present a new strategy to prove the convergence of Deep Learning architectures to a zero training (or even testing) loss by gradient flow. Our analysis is centered on the notion of Rayleigh quotients in order to prove Kurdyka-Lojasiewicz inequalities for a broader set of neural network architectures and loss functions. We show that Rayleigh quotients provide a unified view for several convergence analysis techniques in the literature. Our strategy produces a proof of convergence for various examples of parametric learning. In particular, our analysis does not require the number of parameters to tend to infinity, nor the number of samples to be finite, thus extending to test loss minimization and beyond the over-parameterized regime.
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David A. R. Robin, Kevin Scaman, marc lelarge
| null | null | 2,022 |
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Symbolic Distillation for Learned TCP Congestion Control
| null |
Recent advances in TCP congestion control (CC) have achieved tremendous success with deep reinforcement learning (RL) approaches, which use feedforward neural networks (NN) to learn complex environment conditions and make better decisions. However, such ``black-box'' policies lack interpretability and reliability, and often, they need to operate outside the traditional TCP datapath due to the use of complex NNs. This paper proposes a novel two-stage solution to achieve the best of both worlds: first to train a deep RL agent, then distill its (over-)parameterized NN policy into white-box, light-weight rules in the form of symbolic expressions that are much easier to understand and to implement in constrained environments. At the core of our proposal is a novel symbolic branching algorithm that enables the rule to be aware of the context in terms of various network conditions, eventually converting the NN policy into a symbolic tree. The distilled symbolic rules preserve and often improve performance over state-of-the-art NN policies while being faster and simpler than a standard neural network. We validate the performance of our distilled symbolic rules on both simulation and emulation environments. Our code is available at https://github.com/VITA-Group/SymbolicPCC.
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S P Sharan, Wenqing Zheng, Kuo-Feng Hsu, Jiarong Xing, Ang Chen, Zhangyang Wang
| null | null | 2,022 |
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A Probabilistic Graph Coupling View of Dimension Reduction
| null |
Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full understanding of their properties and limitations. To that extent, we introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. These graphs induce a Markov random field dependency structure among the observations in both input and latent spaces. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Moreover this reveals that these methods relying on shift-invariant kernels suffer from a statistical degeneracy that explains poor performances in conserving coarse-grain dependencies. New links are drawn with PCA which appears as a non-degenerate graph coupling model.
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Hugues Van Assel, Thibault Espinasse, Julien Chiquet, Franck Picard
| null | null | 2,022 |
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Temporally-Consistent Survival Analysis
| null |
We study survival analysis in the dynamic setting: We seek to model the time to an event of interest given sequences of states. Taking inspiration from temporal-difference learning, a central idea in reinforcement learning, we develop algorithms that estimate a discrete-time survival model by exploiting a temporal-consistency condition. Intuitively, this condition captures the fact that the survival distribution at consecutive states should be similar, accounting for the delay between states. Our method can be combined with any parametric survival model and naturally accommodates right-censored observations. We demonstrate empirically that it achieves better sample-efficiency and predictive performance compared to approaches that directly regress the observed survival outcome.
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Lucas Maystre, Daniel Russo
| null | null | 2,022 |
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On Convergence of FedProx: Local Dissimilarity Invariant Bounds, Non-smoothness and Beyond
| null |
The \FedProx~algorithm is a simple yet powerful distributed proximal point optimization method widely used for federated learning (FL) over heterogeneous data. Despite its popularity and remarkable success witnessed in practice, the theoretical understanding of FedProx is largely underinvestigated: the appealing convergence behavior of \FedProx~is so far characterized under certain non-standard and unrealistic dissimilarity assumptions of local functions, and the results are limited to smooth optimization problems. In order to remedy these deficiencies, we develop a novel local dissimilarity invariant convergence theory for \FedProx~and its minibatch stochastic extension through the lens of algorithmic stability. As a result, we contribute to derive several new and deeper insights into \FedProx~for non-convex federated optimization including: 1) convergence guarantees invariant to certain stringent local dissimilarity conditions; 2) convergence guarantees for non-smooth FL problems; and 3) linear speedup with respect to size of minibatch and number of sampled devices. Our theory for the first time reveals that local dissimilarity and smoothness are not must-have for \FedProx~to get favorable complexity bounds.
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Xiaotong Yuan, Ping Li
| null | null | 2,022 |
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Improved Imaging by Invex Regularizers with Global Optima Guarantees
| null |
Image reconstruction enhanced by regularizers, e.g., to enforce sparsity, low rank or smoothness priors on images, has many successful applications in vision tasks such as computer photography, biomedical and spectral imaging. It has been well accepted that non-convex regularizers normally perform better than convex ones in terms of the reconstruction quality. But their convergence analysis is only established to a critical point, rather than the global optima. To mitigate the loss of guarantees for global optima, we propose to apply the concept of invexity and provide the first list of proved invex regularizers for improving image reconstruction. Moreover, we establish convergence guarantees to global optima for various advanced image reconstruction techniques after being improved by such invex regularization. To the best of our knowledge, this is the first practical work applying invex regularization to improve imaging with global optima guarantees. To demonstrate the effectiveness of invex regularization, numerical experiments are conducted for various imaging tasks using benchmark datasets.
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Samuel Pinilla, Tingting Mu, Neil Bourne, Jeyan Thiyagalingam
| null | null | 2,022 |
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Curriculum Reinforcement Learning using Optimal Transport via Gradual Domain Adaptation
| null |
Curriculum Reinforcement Learning (CRL) aims to create a sequence of tasks, starting from easy ones and gradually learning towards difficult tasks. In this work, we focus on the idea of framing CRL as interpolations between a source (auxiliary) and a target task distribution. Although existing studies have shown the great potential of this idea, it remains unclear how to formally quantify and generate the movement between task distributions. Inspired by the insights from gradual domain adaptation in semi-supervised learning, we create a natural curriculum by breaking down the potentially large task distributional shift in CRL into smaller shifts. We propose GRADIENT which formulates CRL as an optimal transport problem with a tailored distance metric between tasks. Specifically, we generate a sequence of task distributions as a geodesic interpolation between the source and target distributions, which are actually the Wasserstein barycenter. Different from many existing methods, our algorithm considers a task-dependent contextual distance metric and is capable of handling nonparametric distributions in both continuous and discrete context settings. In addition, we theoretically show that GRADIENT enables smooth transfer between subsequent stages in the curriculum under certain conditions. We conduct extensive experiments in locomotion and manipulation tasks and show that our proposed GRADIENT achieves higher performance than baselines in terms of learning efficiency and asymptotic performance.
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Peide Huang, Mengdi Xu, Jiacheng Zhu, Laixi Shi, Fei Fang, DING ZHAO
| null | null | 2,022 |
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Hardness of Noise-Free Learning for Two-Hidden-Layer Neural Networks
| null |
We give superpolynomial statistical query (SQ) lower bounds for learning two-hidden-layer ReLU networks with respect to Gaussian inputs in the standard (noise-free) model. No general SQ lower bounds were known for learning ReLU networks of any depth in this setting: previous SQ lower bounds held only for adversarial noise models (agnostic learning) (Kothari and Klivans 2014, Goel et al. 2020a, Diakonikolas et al. 2020a) or restricted models such as correlational SQ (Goel et al. 2020b, Diakonikolas et al. 2020b). Prior work hinted at the impossibility of our result: Vempala and Wilmes (2019) showed that general SQ lower bounds cannot apply to any real-valued family of functions that satisfies a simple non-degeneracy condition. To circumvent their result, we refine a lifting procedure due to Daniely and Vardi (2021) that reduces Boolean PAC learning problems to Gaussian ones. We show how to extend their technique to other learning models and, in many well-studied cases, obtain a more efficient reduction. As such, we also prove new cryptographic hardness results for PAC learning two-hidden-layer ReLU networks, as well as new lower bounds for learning constant-depth ReLU networks from membership queries.
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Sitan Chen, Aravind Gollakota, Adam Klivans, Raghu Meka
| null | null | 2,022 |
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Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation
| null |
Causal discovery for quantitative data has been extensively studied but less is known for categorical data. We propose a novel causal model for categorical data based on a new classification model, termed classification with optimal label permutation (COLP). By design, COLP is a parsimonious classifier, which gives rise to a provably identifiable causal model. A simple learning algorithm via comparing likelihood functions of causal and anti-causal models suffices to learn the causal direction. Through experiments with synthetic and real data, we demonstrate the favorable performance of the proposed COLP-based causal model compared to state-of-the-art methods. We also make available an accompanying R package COLP, which contains the proposed causal discovery algorithm and a benchmark dataset of categorical cause-effect pairs.
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Yang Ni
| null | null | 2,022 |
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Optimistic Posterior Sampling for Reinforcement Learning with Few Samples and Tight Guarantees
| null |
We consider reinforcement learning in an environment modeled by an episodic, tabular, step-dependent Markov decision process of horizon $H$ with $S$ states, and $A$ actions. The performance of an agent is measured by the regret after interacting with the environment for $T$ episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in $H$, $S$, $A$, and $T$ per state-action pair. For OPSRL we guarantee a high-probability regret bound of order at most $O(\sqrt{H^3SAT})$ ignoring $\text{poly}\log(HSAT)$ terms. The key novel technical ingredient is a new sharp anti-concentration inequality for linear forms of a Dirichlet random vector which may be of independent interest. Specifically, we extend the normal approximation-based lower bound for Beta distributions by Alfers and Dinges (1984) to Dirichlet distributions. Our bound matches the lower bound of order $\Omega(\sqrt{H^3SAT})$, thereby answering the open problems raised by Agrawal and Jia (2017) for the episodic setting.
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Daniil Tiapkin, Denis Belomestny, Daniele Calandriello, Eric Moulines, Remi Munos, Alexey Naumov, Mark Rowland, Michal Valko, Pierre Ménard
| null | null | 2,022 |
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Can Push-forward Generative Models Fit Multimodal Distributions?
| null |
Many generative models synthesize data by transforming a standard Gaussian random variable using a deterministic neural network. Among these models are the Variational Autoencoders and the Generative Adversarial Networks. In this work, we call them "push-forward" models and study their expressivity. We formally demonstrate that the Lipschitz constant of these generative networks has to be large in order to fit multimodal distributions. More precisely, we show that the total variation distance and the Kullback-Leibler divergence between the generated and the data distribution are bounded from below by a constant depending on the mode separation and the Lipschitz constant. Since constraining the Lipschitz constants of neural networks is a common way to stabilize generative models, there is a provable trade-off between the ability of push-forward models to approximate multimodal distributions and the stability of their training. We validate our findings on one-dimensional and image datasets and empirically show that the recently introduced diffusion models do not suffer of such limitation.
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Antoine Salmona, Valentin De Bortoli, Julie Delon, Agnes Desolneux
| null | null | 2,022 |
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Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis
| null |
Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although valuable learning signals can be provided by heterogeneous data from changing distributions, it is also known that learning under arbitrary (adversarial) changes is impossible. Causality provides a useful framework for modeling distribution shifts, since causal models encode both observational and interventional distributions. In this work, we explore the sparse mechanism shift hypothesis which posits that distribution shifts occur due to a small number of changing causal conditionals. Motivated by this idea, we apply it to learning causal structure from heterogeneous environments, where i.i.d. data only allows for learning an equivalence class of graphs without restrictive assumptions. We propose the Mechanism Shift Score (MSS), a score-based approach amenable to various empirical estimators, which provably identifies the entire causal structure with high probability if the sparse mechanism shifts hypothesis holds. Empirically, we verify behavior predicted by the theory and compare multiple estimators and score functions to identify the best approaches in practice. Compared to other methods, we show how MSS bridges a gap by both being nonparametric as well as explicitly leveraging sparse changes.
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Ronan Perry, Julius von Kügelgen, Bernhard Schölkopf
| null | null | 2,022 |
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Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Functions
| null |
We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with $1\le\alpha\le2$ which holds in a wide range of applications in machine learning and signal processing. This condition ensures that any first-order stationary point is a global optimum. We prove that the total sample complexity of SCRN in achieving $\epsilon$-global optimum is $\mathcal{O}(\epsilon^{-7/(2\alpha)+1})$ for $1\le\alpha< 3/2$ and $\mathcal{\tilde{O}}(\epsilon^{-2/(\alpha)})$ for $3/2\le\alpha\le 2$. SCRN improves the best-known sample complexity of stochastic gradient descent. Even under a weak version of gradient dominance property, which is applicable to policy-based reinforcement learning (RL), SCRN achieves the same improvement over stochastic policy gradient methods. Additionally, we show that the average sample complexity of SCRN can be reduced to ${\mathcal{O}}(\epsilon^{-2})$ for $\alpha=1$ using a variance reduction method with time-varying batch sizes. Experimental results in various RL settings showcase the remarkable performance of SCRN compared to first-order methods.
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Saeed Masiha, Saber Salehkaleybar, Niao He, Negar Kiyavash, Patrick Thiran
| null | null | 2,022 |
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Posterior and Computational Uncertainty in Gaussian Processes
| null |
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. Therefore in practice, GP models are often as much about the approximation method as they are about the data. Here, we develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended. The most common GP approximations map to an instance in this class, such as methods based on the Cholesky factorization, conjugate gradients, and inducing points. For any method in this class, we prove (i) convergence of its posterior mean in the associated RKHS, (ii) decomposability of its combined posterior covariance into mathematical and computational covariances, and (iii) that the combined variance is a tight worst-case bound for the squared error between the method's posterior mean and the latent function. Finally, we empirically demonstrate the consequences of ignoring computational uncertainty and show how implicitly modeling it improves generalization performance on benchmark datasets.
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Jonathan Wenger, Geoff Pleiss, Marvin Pförtner, Philipp Hennig, John P. Cunningham
| null | null | 2,022 |
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Phase transitions in when feedback is useful
| null |
Sensory observations about the world are invariably ambiguous. Inference about the world's latent variables is thus an important computation for the brain. However, computational constraints limit the performance of these computations. These constraints include energetic costs for neural activity and noise on every channel. Efficient coding is one prominent theory that describes how such limited resources can best be used. In one incarnation, this leads to a theory of predictive coding, where predictions are subtracted from signals, reducing the cost of sending something that is already known. This theory does not, however, account for the costs or noise associated with those predictions. Here we offer a theory that accounts for both feedforward and feedback costs, and noise in all computations. We formulate this inference problem as message-passing on a graph whereby feedback serves as an internal control signal aiming to maximize how well an inference tracks a target state while minimizing the costs of computation. We apply this novel formulation of inference as control to the canonical problem of inferring the hidden scalar state of a linear dynamical system with Gaussian variability. The best solution depends on architectural constraints, such as Dale's law, the ubiquitous law that each neuron makes solely excitatory or inhibitory postsynaptic connections. This biological structure can create asymmetric costs for feedforward and feedback channels. Under such conditions, our theory predicts the gain of optimal predictive feedback and how it is incorporated into the inference computation. We show that there is a non-monotonic dependence of optimal feedback gain as a function of both the computational parameters and the world dynamics, leading to phase transitions in whether feedback provides any utility in optimal inference under computational constraints.
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Lokesh Boominathan, Xaq Pitkow
| null | null | 2,022 |
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Learning Tractable Probabilistic Models from Inconsistent Local Estimates
| null |
Tractable probabilistic models such as cutset networks which admit exact linear time posterior marginal inference are often preferred in practice over intractable models such as Bayesian and Markov networks. This is because although tractable models, when learned from data, are slightly inferior to the intractable ones in terms of goodness-of-fit measures such as log-likelihood, they do not use approximate inference at prediction time and as a result exhibit superior predictive performance. In this paper, we consider the problem of improving a tractable model using a large number of local probability estimates, each defined over a small subset of variables that are either available from experts or via an external process. Given a model learned from fully-observed, but small amount of possibly noisy data, the key idea in our approach is to update the parameters of the model via a gradient descent procedure that seeks to minimize a convex combination of two quantities: one that enforces closeness via KL divergence to the local estimates and another that enforces closeness to the given model. We show that although the gradients are NP-hard to compute on arbitrary graphical models, they can be efficiently computed over tractable models. We show via experiments that our approach yields tractable models that are significantly superior to the ones learned from small amount of possibly noisy data, even when the local estimates are inconsistent.
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Shasha Jin, Vasundhara Komaragiri, Tahrima Rahman, Vibhav Gogate
| null | null | 2,022 |
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Deep Multi-Modal Structural Equations For Causal Effect Estimation With Unstructured Proxies
| null |
Estimating the effect of intervention from observational data while accounting for confounding variables is a key task in causal inference. Oftentimes, the confounders are unobserved, but we have access to large amounts of additional unstructured data (images, text) that contain valuable proxy signal about the missing confounders. This paper argues that leveraging this unstructured data can greatly improve the accuracy of causal effect estimation. Specifically, we introduce deep multi-modal structural equations, a generative model for causal effect estimation in which confounders are latent variables and unstructured data are proxy variables. This model supports multiple multimodal proxies (images, text) as well as missing data. We empirically demonstrate that our approach outperforms existing methods based on propensity scores and corrects for confounding using unstructured inputs on tasks in genomics and healthcare. Our methods can potentially support the use of large amounts of data that were previously not used in causal inference
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Shachi Deshpande, Kaiwen Wang, Dhruv Sreenivas, Zheng Li, Volodymyr Kuleshov
| null | null | 2,022 |
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