OpenRaiser/Intern-Atlas huggingface dataset:
A Game Theoretic Analysis of Additive Adversarial Attacks and Defenses
Venue: Conference NeurIPS 2020
Year: 2020

Research in adversarial learning follows a cat and mouse game between attackers and defenders where attacks are proposed, they are mitigated by new defenses, and subsequently new attacks are proposed that break earlier defenses, and so on. However, it has remained unclear as to whether there are conditions under which no better attacks or defenses can be proposed. In this paper, we propose a game-theoretic framework for studying attacks and defenses which exist in equilibrium. Under a locally linear decision boundary model for the underlying binary classifier, we prove that the Fast Gradient Method attack and the Randomized Smoothing defense form a Nash Equilibrium. We then show how this equilibrium defense can be approximated given finitely many samples from a data-generating distribution, and derive a generalization bound for the performance of our approximation.
Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts
Venue: Conference NeurIPS 2020
Year: 2020

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in- and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.
Recurrent Quantum Neural Networks
Venue: Conference NeurIPS 2020
Year: 2020

Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. In contrast, applied quantum computing is in its infancy. Nevertheless there already exist quantum machine learning models such as variational quantum eigensolvers which have been used successfully e.g. in the context of energy minimization tasks. In this work we construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks such as sequence learning and integer digit classification. The QRNN cell is built from parametrized quantum neurons, which, in conjunction with amplitude amplification, create a nonlinear activation of polynomials of its inputs and cell state, and allow the extraction of a probability distribution over predicted classes at each step. To study the model's performance, we provide an implementation in pytorch, which allows the relatively efficient optimization of parametrized quantum circuits with thousands of parameters. We establish a QRNN training setup by benchmarking optimization hyperparameters, and analyse suitable network topologies for simple memorisation and sequence prediction tasks from Elman's seminal paper (1990) on temporal structure learning. We then proceed to evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step. Finally, we analyse to what extent the unitary nature of the network counteracts the vanishing gradient problem that plagues many existing quantum classifiers and classical RNNs.
No-Regret Learning and Mixed Nash Equilibria: They Do Not Mix
Venue: Conference NeurIPS 2020
Year: 2020

Understanding the behavior of no-regret dynamics in general $N$-player games is a fundamental question in online learning and game theory. A folk result in the field states that, in finite games, the empirical frequency of play under no-regret learning converges to the game's set of coarse correlated equilibria. By contrast, our understanding of how the day-to-day behavior of the dynamics correlates to the game's Nash equilibria is much more limited, and only partial results are known for certain classes of games (such as zero-sum or congestion games). In this paper, we study the dynamics of "follow-the-regularized-leader" (FTRL), arguably the most well-studied class of no-regret dynamics, and we establish a sweeping negative result showing that the notion of mixed Nash equilibrium is antithetical to no-regret learning. Specifically, we show that any Nash equilibrium which is not strict (in that every player has a unique best response) cannot be stable and attracting under the dynamics of FTRL. This result has significant implications for predicting the outcome of a learning process as it shows unequivocally that only strict (and hence, pure) Nash equilibria can emerge as stable limit points thereof.
A Unifying View of Optimism in Episodic Reinforcement Learning
Venue: Conference NeurIPS 2020
Year: 2020

The principle of optimism in the face of uncertainty underpins many theoretically successful reinforcement learning algorithms. In this paper we provide a general framework for designing, analyzing and implementing such algorithms in the episodic reinforcement learning problem. This framework is built upon Lagrangian duality, and demonstrates that every model-optimistic algorithm that constructs an optimistic MDP has an equivalent representation as a value-optimistic dynamic programming algorithm. Typically, it was thought that these two classes of algorithms were distinct, with model-optimistic algorithms benefiting from a cleaner probabilistic analysis while value-optimistic algorithms are easier to implement and thus more practical. With the framework developed in this paper, we show that it is possible to get the best of both worlds by providing a class of algorithms which have a computationally efficient dynamic-programming implementation and also a simple probabilistic analysis. Besides being able to capture many existing algorithms in the tabular setting, our framework can also address largescale problems under realizable function approximation, where it enables a simple model-based analysis of some recently proposed methods.
Continuous Submodular Maximization: Beyond DR-Submodularity
Venue: Conference NeurIPS 2020
Year: 2020

In this paper, we propose the first continuous optimization algorithms that achieve a constant factor approximation guarantee for the problem of monotone continuous submodular maximization subject to a linear constraint. We first prove that a simple variant of the vanilla coordinate ascent, called Coordinate-Ascent+, achieves a $(\frac{e-1}{2e-1}-\varepsilon)$-approximation guarantee while performing $O(n/\varepsilon)$ iterations, where the computational complexity of each iteration is roughly $O(n/\sqrt{\varepsilon}+n\log n)$ (here, $n$ denotes the dimension of the optimization problem). We then propose Coordinate-Ascent++, that achieves the tight $(1-1/e-\varepsilon)$-approximation guarantee while performing the same number of iterations, but at a higher computational complexity of roughly $O(n^3/\varepsilon^{2.5} + n^3 \log n / \varepsilon^2)$ per iteration. However, the computation of each round of Coordinate-Ascent++ can be easily parallelized so that the computational cost per machine scales as $O(n/\sqrt{\varepsilon}+n\log n)$.
An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits
Venue: Conference NeurIPS 2020
Year: 2020

In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving asymptotically optimal algorithms from problem-dependent regret lower bounds and we introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We build on a reformulation of the lower bound, where context distribution and exploration policy are decoupled, and we obtain an algorithm robust to unbalanced context distributions. Then, using an incremental primal-dual approach to solve the Lagrangian relaxation of the lower bound, we obtain a scalable and computationally efficient algorithm. Finally, we remove forced exploration and build on confidence intervals of the optimization problem to encourage a minimum level of exploration that is better adapted to the problem structure. We demonstrate the asymptotic optimality of our algorithm, while providing both problem-dependent and worst-case finite-time regret guarantees. Our bounds scale with the logarithm of the number of arms, thus avoiding the linear dependence common in all related prior works. Notably, we establish minimax optimality for any learning horizon in the special case of non-contextual linear bandits. Finally, we verify that our algorithm obtains better empirical performance than state-of-the-art baselines.
On the Similarity between the Laplace and Neural Tangent Kernels
Venue: Conference NeurIPS 2020
Year: 2020

Recent theoretical work has shown that massively overparameterized neural networks are equivalent to kernel regressors that use Neural Tangent Kernels(NTK). Experiments show that these kernel methods perform similarly to real neural networks. Here we show that NTK for fully connected networks is closely related to the standard Laplace kernel. We show theoretically that for normalized data on the hypersphere both kernels have the same eigenfunctions and their eigenvalues decay polynomially at the same rate, implying that their Reproducing Kernel Hilbert Spaces (RKHS) include the same sets of functions. This means that both kernels give rise to classes of functions with the same smoothness properties. The two kernels differ for data off the hypersphere, but experiments indicate that when data is properly normalized these differences are not significant. Finally, we provide experiments on real data comparing NTK and the Laplace kernel, along with a larger class ofγ-exponential kernels. We show that these perform almost identically. Our results suggest that much insight about neural networks can be obtained from analysis of the well-known Laplace kernel, which has a simple closed-form.
A causal view of compositional zero-shot recognition
Venue: Conference NeurIPS 2020
Year: 2020

People easily recognize new visual categories that are new combinations of known components. This compositional generalization capacity is critical for learning in real-world domains like vision and language because the long tail of new combinations dominates the distribution. Unfortunately, learning systems struggle with compositional generalization because they often build on features that are correlated with class labels even if they are not "essential" for the class. This leads to consistent misclassification of samples from a new distribution, like new combinations of known components. Here we describe an approach for compositional generalization that builds on causal ideas. First, we describe compositional zero-shot learning from a causal perspective, and propose to view zero-shot inference as finding "which intervention caused the image?". Second, we present a causal-inspired embedding model that learns disentangled representations of elementary components of visual objects from correlated (confounded) training data. We evaluate this approach on two datasets for predicting new combinations of attribute-object pairs: A well-controlled synthesized images dataset and a real-world dataset which consists of fine-grained types of shoes. We show improvements compared to strong baselines.
HiPPO: Recurrent Memory with Optimal Polynomial Projections
Venue: Conference NeurIPS 2020
Year: 2020

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.
CASTLE: Regularization via Auxiliary Causal Graph Discovery
Venue: Conference NeurIPS 2020
Year: 2020

Regularization improves generalization of supervised models to out-of-sample data. Prior works have shown that prediction in the causal direction (effect from cause) results in lower testing error than the anti-causal direction. However, existing regularization methods are agnostic of causality. We introduce Causal Structure Learning (CASTLE) regularization and propose to regularize a neural network by jointly learning the causal relationships between variables. CASTLE learns the causal directed acyclical graph (DAG) as an adjacency matrix embedded in the neural network's input layers, thereby facilitating the discovery of optimal predictors. Furthermore, CASTLE efficiently reconstructs only the features in the causal DAG that have a causal neighbor, whereas reconstruction-based regularizers suboptimally reconstruct all input features. We provide a theoretical generalization bound for our approach and conduct experiments on a plethora of synthetic and real publicly available datasets demonstrating that CASTLE consistently leads to better out-of-sample predictions as compared to other popular benchmark regularizers.
Neural Networks Fail to Learn Periodic Functions and How to Fix It
Venue: Conference NeurIPS 2020
Year: 2020

Previous literature offers limited clues on how to learn a periodic function using modern neural networks. We start with a study of the extrapolation properties of neural networks; we prove and demonstrate experimentally that the standard activations functions, such as ReLU, tanh, sigmoid, along with their variants, all fail to learn to extrapolate simple periodic functions. We hypothesize that this is due to their lack of a "periodic" inductive bias. As a fix of this problem, we propose a new activation, namely, $x + \sin^2(x)$, which achieves the desired periodic inductive bias to learn a periodic function while maintaining a favorable optimization property of the ReLU-based activations. Experimentally, we apply the proposed method to temperature and financial data prediction.
Distribution Matching for Crowd Counting
Venue: Conference NeurIPS 2020
Year: 2020

In crowd counting, each training image contains multiple people, where each person is annotated by a dot. Existing crowd counting methods need to use a Gaussian to smooth each annotated dot or to estimate the likelihood of every pixel given the annotated point. In this paper, we show that imposing Gaussians to annotations hurts generalization performance. Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count). In DM-Count, we use Optimal Transport (OT) to measure the similarity between the normalized predicted density map and the normalized ground truth density map. To stabilize OT computation, we include a Total Variation loss in our model. We show that the generalization error bound of DM-Count is tighter than that of the Gaussian smoothed methods. In terms of Mean Absolute Error, DM-Count outperforms the previous state-of-the-art methods by a large margin on two large-scale counting datasets, UCF-QNRF and NWPU, and achieves the state-of-the-art results on the ShanghaiTech and UCF-CC50 datasets. DM-Count reduced the error of the state-of-the-art published result by approximately 16%. Code is available at https://github.com/cvlab-stonybrook/DM-Count.
Correspondence learning via linearly-invariant embedding
Venue: Conference NeurIPS 2020
Year: 2020

In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead of using the Laplace-Beltrami eigenfunctions as done in virtually all previous works in this domain, we demonstrate that learning the basis from data can both improve robustness and lead to better accuracy in challenging settings. We interpret the basis as a learned embedding into a higher dimensional space. Following the functional map paradigm the optimal transformation in this embedding space must be linear and we propose a separate architecture aimed at estimating the transformation by learning optimal descriptor functions. This leads to the first end-to-end trainable functional map-based correspondence approach in which both the basis and the descriptors are learned from data. Interestingly, we also observe that learning a \emph{canonical} embedding leads to worse results, suggesting that leaving an extra linear degree of freedom to the embedding network gives it more robustness, thereby also shedding light onto the success of previous methods. Finally, we demonstrate that our approach achieves state-of-the-art results in challenging non-rigid 3D point cloud correspondence applications.
Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning
Venue: Conference NeurIPS 2020
Year: 2020

Priority dispatching rule (PDR) is widely used for solving real-world Job-shop scheduling problem (JSSP). However, the design of effective PDRs is a tedious task, requiring a myriad of specialized knowledge and often delivering limited performance. In this paper, we propose to automatically learn PDRs via an end-to-end deep reinforcement learning agent. We exploit the disjunctive graph representation of JSSP, and propose a Graph Neural Network based scheme to embed the states encountered during solving. The resulting policy network is size-agnostic, effectively enabling generalization on large-scale instances. Experiments show that the agent can learn high-quality PDRs from scratch with elementary raw features, and demonstrates strong performance against the best existing PDRs. The learned policies also perform well on much larger instances that are unseen in training.
On Adaptive Attacks to Adversarial Example Defenses
Venue: Conference NeurIPS 2020
Year: 2020

Adaptive attacks have (rightfully) become the de facto standard for evaluating defenses to adversarial examples. We find, however, that typical adaptive evaluations are incomplete. We demonstrate that thirteen defenses recently published at ICLR, ICML and NeurIPS---and chosen for illustrative and pedagogical purposes---can be circumvented despite attempting to perform evaluations using adaptive attacks. While prior evaluation papers focused mainly on the end result---showing that a defense was ineffective---this paper focuses on laying out the methodology and the approach necessary to perform an adaptive attack. We hope that these analyses will serve as guidance on how to properly perform adaptive attacks against defenses to adversarial examples, and thus will allow the community to make further progress in building more robust models.
Locally-Adaptive Nonparametric Online Learning
Venue: Conference NeurIPS 2020
Year: 2020

One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that are able to fit complex environments. Although such hard comparators and complex environments may exhibit local regularities, efficient algorithms, which can provably take advantage of these local patterns, are hardly known. We fill this gap by introducing efficient online algorithms (based on a single versatile master algorithm) each adapting to one of the following regularities: (i) local Lipschitzness of the competitor function, (ii) local metric dimension of the instance sequence, (iii) local performance of the predictor across different regions of the instance space. Extending previous approaches, we design algorithms that dynamically grow hierarchical $ε$-nets on the instance space whose prunings correspond to different "locality profiles" for the problem at hand. Using a technique based on tree experts, we simultaneously and efficiently compete against all such prunings, and prove regret bounds each scaling with a quantity associated with a different type of local regularity. When competing against "simple" locality profiles, our technique delivers regret bounds that are significantly better than those proven using the previous approach. On the other hand, the time dependence of our bounds is not worse than that obtained by ignoring any local regularities.
Compositional Generalization via Neural-Symbolic Stack Machines
Venue: Conference NeurIPS 2020
Year: 2020

Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this issue, we propose the Neural-Symbolic Stack Machine (NeSS). It contains a neural network to generate traces, which are then executed by a symbolic stack machine enhanced with sequence manipulation operations. NeSS combines the expressive power of neural sequence models with the recursion supported by the symbolic stack machine. Without training supervision on execution traces, NeSS achieves 100% generalization performance in four domains: the SCAN benchmark of language-driven navigation tasks, the task of few-shot learning of compositional instructions, the compositional machine translation benchmark, and context-free grammar parsing tasks.
Graphon Neural Networks and the Transferability of Graph Neural Networks
Venue: Conference NeurIPS 2020
Year: 2020

Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound vanishes with growing number of nodes if the graph convolutional filters are bandlimited in the graph spectral domain. This result establishes a tradeoff between discriminability and transferability of GNNs.