ICML 2021 Papers

We consider a stochastic contextual bandit problem where the dimension $d$ of the feature vectors is potentially large, however, only a sparse subset of features of cardinality $s_0 \ll d$ affect the reward function. Essentially all existing algorithms for sparse bandits require a priori knowledge of the value of the sparsity index $s_0$. This knowledge is almost never available in practice, and misspecification of this parameter can lead to severe deterioration in the performance of existing methods. The main contribution of this paper is to propose an algorithm that does not require prior knowledge of the sparsity index $s_0$ and establish tight regret bounds on its performance under mild conditions. We also comprehensively evaluate our proposed algorithm numerically and show that it consistently outperforms existing methods, even when the correct sparsity index is revealed to them but is kept hidden from our algorithm.

Sparsifying deep neural networks is of paramount interest in many areas, especially when those networks have to be implemented on low-memory devices. In this article, we propose a new formulation of the problem of generating sparse weights for a pre-trained neural network. By leveraging the properties of standard nonlinear activation functions, we show that the problem is equivalent to an approximate subdifferential inclusion problem. The accuracy of the approximation controls the sparsity. We show that the proposed approach is valid for a broad class of activation functions (ReLU, sigmoid, softmax). We propose an iterative optimization algorithm to induce sparsity whose convergence is guaranteed. Because of the algorithm flexibility, the sparsity can be ensured from partial training data in a minibatch manner. To demonstrate the effectiveness of our method, we perform experiments on various networks in different applicative contexts: image classification, speech recognition, natural language processing, and time-series forecasting.

Transformer-based models are popularly used in natural language processing (NLP). Its core component, self-attention, has aroused widespread interest. To understand the self-attention mechanism, a direct method is to visualize the attention map of a pre-trained model. Based on the patterns observed, a series of efficient Transformers with different sparse attention masks have been proposed. From a theoretical perspective, universal approximability of Transformer-based models is also recently proved. However, the above understanding and analysis of self-attention is based on a pre-trained model. To rethink the importance analysis in self-attention, we study the significance of different positions in attention matrix during pre-training. A surprising result is that diagonal elements in the attention map are the least important compared with other attention positions. We provide a proof showing that these diagonal elements can indeed be removed without deteriorating model performance. Furthermore, we propose a Differentiable Attention Mask (DAM) algorithm, which further guides the design of the SparseBERT. Extensive experiments verify our interesting findings and illustrate the effect of the proposed algorithm.

Approximations to Gaussian processes (GPs) based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini-batch based learning. In this work, we further push the limits of scalability of sparse GPs by allowing large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

Sparse adversarial attacks can fool deep neural networks (DNNs) by only perturbing a few pixels (regularized by $\ell_0$ norm). Recent efforts combine it with another $\ell_\infty$ imperceptible on the perturbation magnitudes. The resultant sparse and imperceptible attacks are practically relevant, and indicate an even higher vulnerability of DNNs that we usually imagined. However, such attacks are more challenging to generate due to the optimization difficulty by coupling the $\ell_0$ regularizer and box constraints with a non-convex objective. In this paper, we address this challenge by proposing a homotopy algorithm, to jointly tackle the sparsity and the perturbation bound in one unified framework. Each iteration, the main step of our algorithm is to optimize an $\ell_0$-regularized adversarial loss, by leveraging the nonmonotone Accelerated Proximal Gradient Method (nmAPG) for nonconvex programming; it is followed by an $\ell_0$ change control step, and an optional post-attack step designed to escape bad local minima. We also extend the algorithm to handling the structural sparsity regularizer. We extensively examine the effectiveness of our proposed \textbf{homotopy attack} for both targeted and non-targeted attack scenarios, on CIFAR-10 and ImageNet datasets. Compared to state-of-the-art methods, our homotopy attack leads to significantly fewer perturbations, e.g., reducing 42.91% on CIFAR-10 and 75.03% on ImageNet (average case, targeted attack), at similar maximal perturbation magnitudes, when still achieving 100% attack success rates. Our codes are available at: {\small\url{https://github.com/VITA-Group/SparseADV_Homotopy}}.

This paper provides a statistical analysis of high-dimensional batch reinforcement learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that sparsity-aware methods can make batch RL more sample efficient. We first consider the off-policy policy evaluation problem. To evaluate a new target policy, we analyze a Lasso fitted Q-evaluation method and establish a finite-sample error bound that has no polynomial dependence on the ambient dimension. To reduce the Lasso bias, we further propose a post model-selection estimator that applies fitted Q-evaluation to the features selected via group Lasso. Under an additional signal strength assumption, we derive a sharper instance-dependent error bound that depends on a divergence function measuring the distribution mismatch between the data distribution and occupancy measure of the target policy. Further, we study the Lasso fitted Q-iteration for batch policy optimization and establish a finite-sample error bound depending on the ratio between the number of relevant features and restricted minimal eigenvalue of the data’s covariance. In the end, we complement the results with minimax lower bounds for batch-data policy evaluation/optimization that nearly match our upper bounds. The results suggest that having well-conditioned data is crucial for sparse batch policy learning.

Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance parameter goes to zero, RMP exhibits a surprising connection to Stepwise Regression. Further, we derive novel guarantees for Stepwise Regression algorithms, which also shed light on RMP. Our guarantees for Forward Regression improve on deterministic and probabilistic results for Orthogonal Matching Pursuit with noise. Our analysis of Backward Regression culminates in a bound on the residual of the optimal solution to the subset selection problem that, if satisfied, guarantees the optimality of the result. To our knowledge, this bound is the first that can be computed in polynomial time and depends chiefly on the smallest singular value of the matrix. We report numerical experiments using a variety of feature selection algorithms. Notably, RMP and its limiting variant are both efficient and maintain strong performance with correlated features.

We present a new framework SoundDet, which is an end-to-end trainable and light-weight framework, for polyphonic moving sound event detection and localization. Prior methods typically approach this problem by preprocessing raw waveform into time-frequency representations, which is more amenable to process with well-established image processing pipelines. Prior methods also detect in segment-wise manner, leading to incomplete and partial detections. SoundDet takes a novel approach and directly consumes the raw, multichannel waveform and treats the spatio-temporal sound event as a complete “sound-object" to be detected. Specifically, SoundDet consists of a backbone neural network and two parallel heads for temporal detection and spatial localization, respectively. Given the large sampling rate of raw waveform, the backbone network first learns a set of phase-sensitive and frequency-selective bank of filters to explicitly retain direction-of-arrival information, whilst being highly computationally and parametrically efficient than standard 1D/2D convolution. A dense sound event proposal map is then constructed to handle the challenges of predicting events with large varying temporal duration. Accompanying the dense proposal map are a temporal overlapness map and a motion smoothness map that measure a proposal’s confidence to be an event from temporal detection accuracy and movement consistency perspective. Involving the two maps guarantees SoundDet to be trained in a spatio-temporally unified manner. Experimental results on the public DCASE dataset show the advantage of SoundDet on both segment-based evaluation and our newly proposed event-based evaluation system.

High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the curse of dimensionality. In this paper, we argue that tensor trains provide an appealing approximation framework for parabolic PDEs: the combination of reformulations in terms of backward stochastic differential equations and regression-type methods in the tensor format holds the promise of leveraging latent low-rank structures enabling both compression and efficient computation. Following this paradigm, we develop novel iterative schemes, involving either explicit and fast or implicit and accurate updates. We demonstrate in a number of examples that our methods achieve a favorable trade-off between accuracy and computational efficiency in comparison with state-of-the-art neural network based approaches.

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.

Training agents to autonomously control anthropomorphic robotic hands has the potential to lead to systems capable of performing a multitude of complex manipulation tasks in unstructured and uncertain environments. In this work, we first introduce a suite of challenging simulated manipulation tasks where current reinforcement learning and trajectory optimisation techniques perform poorly. These include environments where two simulated hands have to pass or throw objects between each other, as well as an environment where the agent must learn to spin a long pen between its fingers. We then introduce a simple trajectory optimisation algorithm that performs significantly better than existing methods on these environments. Finally, on the most challenging “PenSpin" task, we combine sub-optimal demonstrations generated through trajectory optimisation with off-policy reinforcement learning, obtaining performance that far exceeds either of these approaches individually. Videos of all of our results are available at: https://dexterous-manipulation.github.io

Quantization is one of the core components in lossy image compression. For neural image compression, end-to-end optimization requires differentiable approximations of quantization, which can generally be grouped into three categories: additive uniform noise, straight-through estimator and soft-to-hard annealing. Training with additive uniform noise approximates the quantization error variationally but suffers from the train-test mismatch. The other two methods do not encounter this mismatch but, as shown in this paper, hurt the rate-distortion performance since the latent representation ability is weakened. We thus propose a novel soft-then-hard quantization strategy for neural image compression that first learns an expressive latent space softly, then closes the train-test mismatch with hard quantization. In addition, beyond the fixed integer-quantization, we apply scaled additive uniform noise to adaptively control the quantization granularity by deriving a new variational upper bound on actual rate. Experiments demonstrate that our proposed methods are easy to adopt, stable to train, and highly effective especially on complex compression models.

Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from data, recent work has proposed smoothing out local irregularities in the measured distributions via convolution with a Gaussian kernel. Motivated by the scalability of this framework to high dimensions, we investigate the structural and statistical behavior of the Gaussian-smoothed $p$-Wasserstein distance $\mathsf{W}_p^{(\sigma)}$, for arbitrary $p\geq 1$. After establishing basic metric and topological properties of $\mathsf{W}_p^{(\sigma)}$, we explore the asymptotic statistical properties of $\mathsf{W}_p^{(\sigma)}(\hat{\mu}_n,\mu)$, where $\hat{\mu}_n$ is the empirical distribution of $n$ independent observations from $\mu$. We prove that $\mathsf{W}_p^{(\sigma)}$ enjoys a parametric empirical convergence rate of $n^{-1/2}$, which contrasts the $n^{-1/d}$ rate for unsmoothed $\Wp$ when $d \geq 3$. Our proof relies on controlling $\mathsf{W}_p^{(\sigma)}$ by a $p$th-order smooth Sobolev distance $\mathsf{d}_p^{(\sigma)}$ and deriving the limit distribution of $\sqrt{n}\,\mathsf{d}_p^{(\sigma)}(\hat{\mu}_n,\mu)$ for all dimensions $d$. As applications, we provide asymptotic guarantees for two-sample testing and minimum distance estimation using $\mathsf{W}_p^{(\sigma)}$, with experiments for $p=2$ using a maximum mean discrepancy formulation of $\mathsf{d}_2^{(\sigma)}$.

In contrast to traditional weight optimization in a continuous space, we demonstrate the existence of effective random networks whose weights are never updated. By selecting a weight among a fixed set of random values for each individual connection, our method uncovers combinations of random weights that match the performance of traditionally-trained networks of the same capacity. We refer to our networks as "slot machines" where each reel (connection) contains a fixed set of symbols (random values). Our backpropagation algorithm "spins" the reels to seek "winning" combinations, i.e., selections of random weight values that minimize the given loss. Quite surprisingly, we find that allocating just a few random values to each connection (e.g., 8 values per connection) yields highly competitive combinations despite being dramatically more constrained compared to traditionally learned weights. Moreover, finetuning these combinations often improves performance over the trained baselines. A randomly initialized VGG-19 with 8 values per connection contains a combination that achieves 91% test accuracy on CIFAR-10. Our method also achieves an impressive performance of 98.2% on MNIST for neural networks containing only random weights.

We develop an iterative (greedy) deep learning (DL) algorithm which is able to transform an arbitrary probability distribution function (PDF) into the target PDF. The model is based on iterative Optimal Transport of a series of 1D slices, matching on each slice the marginal PDF to the target. The axes of the orthogonal slices are chosen to maximize the PDF difference using Wasserstein distance at each iteration, which enables the algorithm to scale well to high dimensions. As special cases of this algorithm, we introduce two sliced iterative Normalizing Flow (SINF) models, which map from the data to the latent space (GIS) and vice versa (SIG). We show that SIG is able to generate high quality samples of image datasets, which match the GAN benchmarks, while GIS obtains competitive results on density estimation tasks compared to the density trained NFs, and is more stable, faster, and achieves higher p(x) when trained on small training sets. SINF approach deviates significantly from the current DL paradigm, as it is greedy and does not use concepts such as mini-batching, stochastic gradient descent and gradient back-propagation through deep layers.

We introduce a new skill-discovery algorithm that builds a discrete graph representation of large continuous MDPs, where nodes correspond to skill subgoals and the edges to skill policies. The agent constructs this graph during an unsupervised training phase where it interleaves discovering skills and planning using them to gain coverage over ever-increasing portions of the state-space. Given a novel goal at test time, the agent plans with the acquired skill graph to reach a nearby state, then switches to learning to reach the goal. We show that the resulting algorithm, Deep Skill Graphs, outperforms both flat and existing hierarchical reinforcement learning methods on four difficult continuous control tasks.

Training convolutional neural networks with a Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients, stable training, etc. While 1-Lipschitz networks can be designed by imposing a 1-Lipschitz constraint on each layer, training such networks requires each layer to be gradient norm preserving (GNP) to prevent gradients from vanishing. However, existing GNP convolutions suffer from slow training, lead to significant reduction in accuracy and provide no guarantees on their approximations. In this work, we propose a GNP convolution layer called \textbf{S}kew \textbf{O}rthogonal \textbf{C}onvolution (SOC) that uses the following mathematical property: when a matrix is {\it Skew-Symmetric}, its exponential function is an {\it orthogonal} matrix. To use this property, we first construct a convolution filter whose Jacobian is Skew-Symmetric. Then, we use the Taylor series expansion of the Jacobian exponential to construct the SOC layer that is orthogonal. To efficiently implement SOC, we keep a finite number of terms from the Taylor series and provide a provable guarantee on the approximation error. Our experiments on CIFAR-10 and CIFAR-100 show that SOC allows us to train provably Lipschitz, large convolutional neural networks significantly faster than prior works while achieving significant improvements for both standard and certified robust accuracies.

Sketch drawings capture the salient information of visual concepts. Previous work has shown that neural networks are capable of producing sketches of natural objects drawn from a small number of classes. While earlier approaches focus on generation quality or retrieval, we explore properties of image representations learned by training a model to produce sketches of images. We show that this generative, class-agnostic model produces informative embeddings of images from novel examples, classes, and even novel datasets in a few-shot setting. Additionally, we find that these learned representations exhibit interesting structure and compositionality.

In general, graph representation learning methods assume that the train and test data come from the same distribution. In this work we consider an underexplored area of an otherwise rapidly developing field of graph representation learning: The task of out-of-distribution (OOD) graph classification, where train and test data have different distributions, with test data unavailable during training. Our work shows it is possible to use a causal model to learn approximately invariant representations that better extrapolate between train and test data. Finally, we conclude with synthetic and real-world dataset experiments showcasing the benefits of representations that are invariant to train/test distribution shifts.