NeurIPS 2020 Papers

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and k-means require individual components of the mixture to be somewhat spherical, and perform poorly when they are stretched. To overcome this issue, we propose a non-convex program seeking for an affine transform to turn the data into a one-dimensional point cloud concentrating around -1 and 1, after which clustering becomes easy. Our theoretical contributions are two-fold: (1) we show that the non-convex loss function exhibits desirable geometric properties when the sample size exceeds some constant multiple of the dimension, and (2) we leverage this to prove that an efficient first-order algorithm achieves near-optimal statistical precision without good initialization. We also propose a general methodology for clustering with flexible choices of feature transforms and loss objectives.

Spectral clustering and $k$-means, both as two major traditional clustering methods, are still attracting a lot of attention, although a variety of novel clustering algorithms have been proposed in recent years. Firstly, a unified framework of $k$-means and ratio-cut is revisited, and a novel and efficient clustering algorithm is then proposed based on this framework. The time and space complexity of our method are both linear with respect to the number of samples, and are independent of the number of clusters to construct, more importantly. These properties mean that it is easily scalable and applicable to large practical problems. Extensive experiments on 12 real-world benchmark and 8 facial datasets validate the advantages of the proposed algorithms compared to the state-of-the-art clustering algorithms. In particular, over 15x and 7x speed-up can be obtained with respect to $k$-means on the synthetic dataset of 1 million samples and the benchmark dataset (CelebA) of 200k samples, respectively [GitHub].

Modern machine learning workloads use large models, with complex structures, that are very expensive to execute. The devices that execute complex models are becoming increasingly heterogeneous as we see a flourishing of Domain Specific Architectures (DSAs) being offered as hardware accelerators in addition to CPUs. These trends necessitate distributing the workload across multiple devices. Recent work has shown that significant gains can be obtained with model parallelism, i.e, partitioning a neural network's computational graph onto multiple devices. In particular, this form of parallelism assumes a pipeline of devices, which is fed a stream of samples and yields high throughput for training and inference of DNNs. However, for such settings (large models and multiple heterogeneous devices), we require automated algorithms and toolchains that can partition the ML workload across devices.

Exploration is a key problem in reinforcement learning, since agents can only learn from data they acquire in the environment. With that in mind, maintaining a population of agents is an attractive method, as it allows data be collected with a diverse set of behaviors. This behavioral diversity is often boosted via multi-objective loss functions. However, those approaches typically leverage mean field updates based on pairwise distances, which makes them susceptible to cycling behaviors and increased redundancy. In addition, explicitly boosting diversity often has a detrimental impact on optimizing already fruitful behaviors for rewards. As such, the reward-diversity trade off typically relies on heuristics. Finally, such methods require behavioral representations, often handcrafted and domain specific. In this paper, we introduce an approach to optimize all members of a population simultaneously. Rather than using pairwise distance, we measure the volume of the entire population in a behavioral manifold, defined by task-agnostic behavioral embeddings. In addition, our algorithm Diversity via Determinants (DvD), adapts the degree of diversity during training using online learning techniques. We introduce both evolutionary and gradient-based instantiations of DvD and show they effectively improve exploration without reducing performance when better exploration is not required.

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT). While current randomized solvers for least-squares optimization prescribe an embedding dimension at least greater than the data dimension, we show that the embedding dimension can be reduced to the effective dimension of the optimization problem, and still preserve high-probability convergence guarantees. In this regard, we derive sharp matrix deviation inequalities over ellipsoids for both Gaussian and SRHT embeddings. Specifically, we improve on the constant of a classical Gaussian concentration bound whereas, for SRHT embeddings, our deviation inequality involves a novel technical approach. Leveraging these bounds, we are able to design a practical and adaptive algorithm which does not require to know the effective dimension beforehand. Our method starts with an initial embedding dimension equal to 1 and, over iterations, increases the embedding dimension up to the effective one at most. Hence, our algorithm improves the state-of-the-art computational complexity for solving regularized least-squares problems. Further, we show numerically that it outperforms standard iterative solvers such as the conjugate gradient method and its pre-conditioned version on several standard machine learning datasets.

Effective intersection control can play an important role in reducing traffic congestion and associated vehicular emissions. This is vitally needed in developing countries, where air pollution is reaching life threatening levels. This paper presents EcoLight intersection control for developing regions, where budget is constrained and network connectivity is very poor. EcoLight learns effective control offline using state-of-the-art Deep Reinforcement Learning methods, but deploys highly efficient runtime control algorithms on low cost embedded devices that work stand-alone on road without server connectivity. EcoLight optimizes both average case and worst case values of throughput, travel time and other metrics, as evaluated on open-source datasets from New York and on a custom developing region dataset.

We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classification tasks, which exploits the progress of the early learning phase. In contrast with existing approaches, which use the model output during early learning to detect the examples with clean labels, and either ignore or attempt to correct the false labels, we take a different route and instead capitalize on early learning via regularization. There are two key elements to our approach. First, we leverage semi-supervised learning techniques to produce target probabilities based on the model outputs. Second, we design a regularization term that steers the model towards these targets, implicitly preventing memorization of the false labels. The resulting framework is shown to provide robustness to noisy annotations on several standard benchmarks and real-world datasets, where it achieves results comparable to the state of the art.

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides a prototype of a non-convex loss landscape with interpolating regimes and a large generalization gap. We define a particular stochastic process for which SGD can be extended to a continuous-time limit that we call stochastic gradient flow. In the full-batch limit we recover the standard gradient flow. We apply dynamical mean-field theory from statistical physics to track the dynamics of the algorithm in the high-dimensional limit via a self-consistent stochastic process. We explore the performance of the algorithm as a function of control parameters shedding light on how it navigates the loss landscape.

Biological brains are inherently limited in their capacity to process and store information, but are nevertheless capable of solving complex tasks with apparent ease. Intelligent behavior is related to these limitations, since resource constraints drive the need to generalize and assign importance differentially to features in the environment or memories of past experiences. Recently, there have been parallel efforts in reinforcement learning and neuroscience to understand strategies adopted by artificial and biological agents to circumvent limitations in information storage. However, the two threads have been largely separate. In this article, we propose a dynamical framework to maximize expected reward under constraints of limited resources, which we implement with a cost function that penalizes precise representations of action-values in memory, each of which may vary in its precision. We derive from first principles an algorithm, Dynamic Resource Allocator (DRA), which we apply to two standard tasks in reinforcement learning and a model-based planning task, and find that it allocates more resources to items in memory that have a higher impact on cumulative rewards. Moreover, DRA learns faster when starting with a higher resource budget than what it eventually allocates for performing well on tasks, which may explain why frontal cortical areas in biological brains appear more engaged in early stages of learning before settling to lower asymptotic levels of activity. Our work provides a normative solution to the problem of learning how to allocate costly resources to a collection of uncertain memories in a manner that is capable of adapting to changes in the environment.

One of the basic primitives in the class of submodular optimization problems is the submodular maximization under a cardinality constraint. Here we are given a ground set $V$ that is endowed with a monotone submodular function $f: 2^V \rightarrow \REAL^+$ and a parameter $0 < k \le n$ and the goal is to return an optimal set $S \subseteq V$ of at most $k$ elements, i.e., $f(S)$ is maximum among all subsets of $V$ of size at most $k$. This basic primitive has many applications in machine learning as well as combinatorial optimization. Example applications are agglomerative clustering, exemplar-based clustering, categorical feature compression, document and corpus summarization, recommender systems, search result diversification, data subset selection, minimum spanning tree, max flow, global minimum cut, maximum matching, traveling salesman problem, max clique, max cut, set cover and knapsack, among the others. In this paper, we propose the first dynamic algorithm for this problem. Given a stream of inserts and deletes of elements of an underlying ground set $V$, we develop a dynamic algorithm that with high probability, maintains a $(\frac{1}{2} - \epsilon)$-approximation of a cardinality-constrained monotone submodular maximization for any sequence of $z$ updates (inserts and deletes) in time $O(k^2z\epsilon^{-3}\cdot \log^5 n)$, where $n$ is the maximum size of $V$ at any time. That is, the amortized update time of our algorithm is $O(k^2\epsilon^{-3}\cdot \log^5 n)$.

We consider reinforcement learning (RL) in episodic MDPs with adversarial full-information reward feedback and unknown fixed transition kernels. We propose two model-free policy optimization algorithms, POWER and POWER++, and establish guarantees for their dynamic regret. Compared with the classical notion of static regret, dynamic regret is a stronger notion as it explicitly accounts for the non-stationarity of environments. The dynamic regret attained by the proposed algorithms interpolates between different regimes of non-stationarity, and moreover satisfies a notion of adaptive (near-)optimality, in the sense that it matches the (near-)optimal static regret under slow-changing environments. The dynamic regret bound features two components, one arising from exploration, which deals with the uncertainty of transition kernels, and the other arising from adaptation, which deals with non-stationary environments. Specifically, we show that POWER++ improves over POWER on the second component of the dynamic regret by actively adapting to non-stationarity through prediction. To the best of our knowledge, our work is the first dynamic regret analysis of model-free RL algorithms in non-stationary environments.

We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length that essentially reflects the non-stationarity of environments, the state-of-the-art dynamic regret is $\mathcal{O}(\sqrt{T(1+P_T)})$. Although this bound is proved to be minimax optimal for convex functions, in this paper, we demonstrate that it is possible to further enhance the dynamic regret by exploiting the smoothness condition. Specifically, we propose novel online algorithms that are capable of leveraging smoothness and replace the dependence on $T$ in the dynamic regret by problem-dependent quantities: the variation in gradients of loss functions, the cumulative loss of the comparator sequence, and the minimum of the previous two terms. These quantities are at most $\mathcal{O}(T)$ while could be much smaller in benign environments. Therefore, our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and meanwhile guarantee the same rate in the worst case.

We propose to jointly analyze experts' eye movements and verbal narrations to discover important and interpretable knowledge patterns to better understand their decision-making processes. The discovered patterns can further enhance data-driven statistical models by fusing experts' domain knowledge to support complex human-machine collaborative decision-making. Our key contribution is a novel dynamic Bayesian nonparametric model that assigns latent knowledge patterns into key phases involved in complex decision-making. Each phase is characterized by a unique distribution of word topics discovered from verbal narrations and their dynamic interactions with eye movement patterns, indicating experts' special perceptual behavior within a given decision-making stage. A new split-merge-switch sampler is developed to efficiently explore the posterior state space with an improved mixing rate. Case studies on diagnostic error prediction and disease morphology categorization help demonstrate the effectiveness of the proposed model and discovered knowledge patterns.

The pre-trained language models like BERT, though powerful in many natural language processing tasks, are both computation and memory expensive. To alleviate this problem, one approach is to compress them for specific tasks before deployment. However, recent works on BERT compression usually compress the large BERT model to a fixed smaller size, and can not fully satisfy the requirements of different edge devices with various hardware performances. In this paper, we propose a novel dynamic BERT model (abbreviated as DynaBERT), which can flexibly adjust the size and latency by selecting adaptive width and depth. The training process of DynaBERT includes first training a width-adaptive BERT and then allowing both adaptive width and depth, by distilling knowledge from the full-sized model to small sub-networks. Network rewiring is also used to keep the more important attention heads and neurons shared by more sub-networks. Comprehensive experiments under various efficiency constraints demonstrate that our proposed dynamic BERT (or RoBERTa) at its largest size has comparable performance as BERT-base (or RoBERTa-base), while at smaller widths and depths consistently outperforms existing BERT compression methods. Code is available at https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/DynaBERT.

Tensor factorization based models have shown great power in knowledge graph completion (KGC). However, their performance usually suffers from the overfitting problem seriously. This motivates various regularizers---such as the squared Frobenius norm and tensor nuclear norm regulariers---while the limited applicability significantly limits their practical usage. To address this challenge, we propose a novel regularizer---namely, \textbf{DU}ality-induced \textbf{R}egul\textbf{A}rizer (DURA)---which is not only effective in improving the performance of existing models but widely applicable to various methods. The major novelty of DURA is based on the observation that, for an existing tensor factorization based KGC model (\textit{primal}), there is often another distance based KGC model (\textit{dual}) closely associated with it.

We tackle the problem of establishing dense pixel-wise correspondences between a pair of images. In this work, we introduce Dual-Resolution Correspondence Networks (DualRC-Net), to obtain pixel-wise correspondences in a coarse-to-fine manner. DualRC-Net extracts both coarse- and fine- resolution feature maps. The coarse maps are used to produce a full but coarse 4D correlation tensor, which is then refined by a learnable neighbourhood consensus module. The fine-resolution feature maps are used to obtain the final dense correspondences guided by the refined coarse 4D correlation tensor. The selected coarse-resolution matching scores allow the fine-resolution features to focus only on a limited number of possible matches with high confidence. In this way, DualRC-Net dramatically increases matching reliability and localisation accuracy, while avoiding to apply the expensive 4D convolution kernels on fine-resolution feature maps. We comprehensively evaluate our method on large-scale public benchmarks including HPatches, InLoc, and Aachen Day-Night. It achieves state-of-the-art results on all of them.

We consider the problem of training machine learning models on distributed data in a decentralized way. For finite-sum problems, fast single-machine algorithms for large datasets rely on stochastic updates combined with variance reduction. Yet, existing decentralized stochastic algorithms either do not obtain the full speedup allowed by stochastic updates, or require oracles that are more expensive than regular gradients. In this work, we introduce a Decentralized stochastic algorithm with Variance Reduction called DVR. DVR only requires computing stochastic gradients of the local functions, and is computationally as fast as a standard stochastic variance-reduced algorithms run on a $1/n$ fraction of the dataset, where $n$ is the number of nodes. To derive DVR, we use Bregman coordinate descent on a well-chosen dual problem, and obtain a dual-free algorithm using a specific Bregman divergence. We give an accelerated version of DVR based on the Catalyst framework, and illustrate its effectiveness with simulations on real data.

The transition matrix, denoting the transition relationship from clean labels to noisy labels, is essential to build statistically consistent classifiers in label-noise learning. Existing methods for estimating the transition matrix rely heavily on estimating the noisy class posterior. However, the estimation error for noisy class posterior could be large because of the randomness of label noise. The estimation error would lead the transition matrix to be poorly estimated. Therefore in this paper, we aim to solve this problem by exploiting the divide-and-conquer paradigm. Specifically, we introduce an intermediate class to avoid directly estimating the noisy class posterior. By this intermediate class, the original transition matrix can then be factorized into the product of two easy-to-estimated transition matrices. We term the proposed method as the dual $T$-estimator. Both theoretical analyses and empirical results illustrate the effectiveness of the dual $T$-estimator for estimating transition matrices, leading to better classification performances.

Adversarial training is a popular defense strategy against attack threat models with bounded Lp norms. However, it often degrades the model performance on normal images and more importantly, the defense does not generalize well to novel attacks. Given the success of deep generative models such as GANs and VAEs in characterizing the underlying manifold of images, we investigate whether or not the aforementioned deficiencies of adversarial training can be remedied by exploiting the underlying manifold information. To partially answer this question, we consider the scenario when the manifold information of the underlying data is available. We use a subset of ImageNet natural images where an approximate underlying manifold is learned using StyleGAN. We also construct an ``On-Manifold ImageNet'' (OM-ImageNet) dataset by projecting the ImageNet samples onto the learned manifold. For OM-ImageNet, the underlying manifold information is exact. Using OM-ImageNet, we first show that on-manifold adversarial training improves both standard accuracy and robustness to on-manifold attacks. However, since no out-of-manifold perturbations are realized, the defense can be broken by Lp adversarial attacks. We further propose Dual Manifold Adversarial Training (DMAT) where adversarial perturbations in both latent and image spaces are used in robustifying the model. Our DMAT improves performance on normal images, and achieves comparable robustness to the standard adversarial training against Lp attacks. In addition, we observe that models defended by DMAT achieve improved robustness against novel attacks which manipulate images by global color shifts or various types of image filtering. Interestingly, similar improvements are also achieved when the defended models are tested on (out-of-manifold) natural images. These results demonstrate the potential benefits of using manifold information in enhancing robustness of deep learning models against various types of novel adversarial attacks.