NeurIPS 2021 Papers

Training neural networks with batch normalization and weight decay has become a common practice in recent years. In this work, we show that their combined use may result in a surprising periodic behavior of optimization dynamics: the training process regularly exhibits destabilizations that, however, do not lead to complete divergence but cause a new period of training. We rigorously investigate the mechanism underlying the discovered periodic behavior from both empirical and theoretical points of view and analyze the conditions in which it occurs in practice. We also demonstrate that periodic behavior can be regarded as a generalization of two previously opposing perspectives on training with batch normalization and weight decay, namely the equilibrium presumption and the instability presumption.

Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse tensors. We propose a fast and accurate sketched ALS algorithm for Tucker decomposition, which solves a sequence of sketched rank-constrained linear least squares subproblems. Theoretical sketch size upper bounds are provided to achieve $O(\epsilon)$ relative error for each subproblem with two sketching techniques, TensorSketch and leverage score sampling. Experimental results show that this new ALS algorithm, combined with a new initialization scheme based on the randomized range finder, yields decomposition accuracy comparable to the standard higher-order orthogonal iteration (HOOI) algorithm. The new algorithm achieves up to $22.0\%$ relative decomposition residual improvement compared to the state-of-the-art sketched randomized algorithm for Tucker decomposition of various synthetic and real datasets. This Tucker-ALS algorithm is further used to accelerate CP decomposition, by using randomized Tucker compression followed by CP decomposition of the Tucker core tensor. Experimental results show that this algorithm not only converges faster, but also yields more accurate CP decompositions.

Chamfer Distance (CD) and Earth Mover’s Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by global distribution while overlooks the fidelity of detailed structures. Besides, their unbounded value range induces a heavy influence from the outliers. These defects prevent them from providing a consistent evaluation. To tackle these problems, we propose a new similarity measure named Density-aware Chamfer Distance (DCD). It is derived from CD and benefits from several desirable properties: 1) it can detect disparity of density distributions and is thus a more intensive measure of similarity compared to CD; 2) it is stricter with detailed structures and significantly more computationally efficient than EMD; 3) the bounded value range encourages a more stable and reasonable evaluation over the whole test set. We adopt DCD to evaluate the point cloud completion task, where experimental results show that DCD pays attention to both the overall structure and local geometric details and provides a more reliable evaluation even when CD and EMD contradict each other. We can also use DCD as the training loss, which outperforms the same model trained with CD loss on all three metrics. In addition, we propose a novel point discriminator module that estimates the priority for another guided down-sampling step, and it achieves noticeable improvements under DCD together with competitive results for both CD and EMD. We hope our work could pave the way for a more comprehensive and practical point cloud similarity evaluation. Our code will be available at https://github.com/wutong16/Density_aware_Chamfer_Distance.

Sampling-based inference and learning techniques, especially Bayesian inference, provide an essential approach to handling uncertainty in machine learning (ML). As these techniques are increasingly used in daily life, it becomes essential to safeguard the ML systems with various trustworthy-related constraints, such as fairness, safety, interpretability. Mathematically, enforcing these constraints in probabilistic inference can be cast into sampling from intractable distributions subject to general nonlinear constraints, for which practical efficient algorithms are still largely missing. In this work, we propose a family of constrained sampling algorithms which generalize Langevin Dynamics (LD) and Stein Variational Gradient Descent (SVGD) to incorporate a moment constraint specified by a general nonlinear function. By exploiting the gradient flow structure of LD and SVGD, we derive two types of algorithms for handling constraints, including a primal-dual gradient approach and the constraint controlled gradient descent approach. We investigate the continuous-time mean-field limit of these algorithms and show that they have O(1/t) convergence under mild conditions. Moreover, the LD variant converges linearly assuming that a log Sobolev like inequality holds. Various numerical experiments are conducted to demonstrate the efficiency of our algorithms in trustworthy settings.

Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussian i.i.d. input data underlying the canonical teacher-student model may, however, be perceived as too restrictive to capture the behaviour of realistic data sets. In this paper, we introduce a Gaussian covariate generalisation of the model where the teacher and student can act on different spaces, generated with fixed, but generic feature maps. While still solvable in a closed form, this generalization is able to capture the learning curves for a broad range of realistic data sets, thus redeeming the potential of the teacher-student framework. Our contribution is then two-fold: first, we prove a rigorous formula for the asymptotic training loss and generalisation error. Second, we present a number of situations where the learning curve of the model captures the one of a realistic data set learned with kernel regression and classification, with out-of-the-box feature maps such as random projections or scattering transforms, or with pre-learned ones - such as the features learned by training multi-layer neural networks. We discuss both the power and the limitations of the framework.

Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models, as the chosen kernel determines both the inductive biases and prior support of functions under the GP prior. This work addresses the challenge of constructing custom kernel functions for high-dimensional GP regression models. Drawing inspiration from recent progress in deep learning, we introduce a novel approach named KITT: Kernel Identification Through Transformers. KITT exploits a transformer-based architecture to generate kernel recommendations in under 0.1 seconds, which is several orders of magnitude faster than conventional kernel search algorithms. We train our model using synthetic data generated from priors over a vocabulary of known kernels. By exploiting the nature of the self-attention mechanism, KITT is able to process datasets with inputs of arbitrary dimension. We demonstrate that kernels chosen by KITT yield strong performance over a diverse collection of regression benchmarks.

The goal of understanding decision-making behaviours in clinical environments is of paramount importance if we are to bring the strengths of machine learning to ultimately improve patient outcomes. Mainstream development of algorithms is often geared towards optimal performance in tasks that do not necessarily translate well into the medical regime---due to several factors including the lack of public availability of realistic data, the intrinsically offline nature of the problem, as well as the complexity and variety of human behaviours. We therefore present a new benchmarking suite designed specifically for medical sequential decision modelling: the Medkit-Learn(ing) Environment, a publicly available Python package providing simple and easy access to high-fidelity synthetic medical data. While providing a standardised way to compare algorithms in a realistic medical setting, we employ a generating process that disentangles the policy and environment dynamics to allow for a range of customisations, thus enabling systematic evaluation of algorithms’ robustness against specific challenges prevalent in healthcare.

We present a neural analysis and synthesis (NANSY) framework that can manipulate the voice, pitch, and speed of an arbitrary speech signal. Most of the previous works have focused on using information bottleneck to disentangle analysis features for controllable synthesis, which usually results in poor reconstruction quality. We address this issue by proposing a novel training strategy based on information perturbation. The idea is to perturb information in the original input signal (e.g., formant, pitch, and frequency response), thereby letting synthesis networks selectively take essential attributes to reconstruct the input signal. Because NANSY does not need any bottleneck structures, it enjoys both high reconstruction quality and controllability. Furthermore, NANSY does not require any labels associated with speech data such as text and speaker information, but rather uses a new set of analysis features, i.e., wav2vec feature and newly proposed pitch feature, Yingram, which allows for fully self-supervised training. Taking advantage of fully self-supervised training, NANSY can be easily extended to a multilingual setting by simply training it with a multilingual dataset. The experiments show that NANSY can achieve significant improvement in performance in several applications such as zero-shot voice conversion, pitch shift, and time-scale modification.

Multi-person pose estimation in crowded scenes is challenging because overlapping and occlusions make it difficult to detect person bounding boxes and infer pose cues from individual keypoints. To address those issues, this paper proposes a direct pose-level inference strategy that is free of bounding box detection and keypoint grouping. Instead of inferring individual keypoints, the Pose-level Inference Network (PINet) directly infers the complete pose cues for a person from his/her visible body parts. PINet first applies the Part-based Pose Generation (PPG) to infer multiple coarse poses for each person from his/her body parts. Those coarse poses are refined by the Pose Refinement module through incorporating pose priors, and finally are fused in the Pose Fusion module. PINet relies on discriminative body parts to differentiate overlapped persons, and applies visual body cues to infer the global pose cues. Experiments on several crowded scenes pose estimation benchmarks demonstrate the superiority of PINet. For instance, it achieves 59.8% AP on the OCHuman dataset, outperforming the recent works by a large margin.

As predictive models are increasingly being deployed in high-stakes decision making (e.g., loan approvals), there has been growing interest in post-hoc techniques which provide recourse to affected individuals. These techniques generate recourses under the assumption that the underlying predictive model does not change. However, in practice, models are often regularly updated for a variety of reasons (e.g., dataset shifts), thereby rendering previously prescribed recourses ineffective.To address this problem, we propose a novel framework, RObust Algorithmic Recourse (ROAR), that leverages adversarial training for finding recourses that are robust to model shifts. To the best of our knowledge, this work proposes the first ever solution to this critical problem. We also carry out theoretical analysis which underscores the importance of constructing recourses that are robust to model shifts: 1) We quantify the probability of invalidation for recourses generated without accounting for model shifts. 2) We prove that the additional cost incurred due to the robust recourses output by our framework is bounded. Experimental evaluation on multiple synthetic and real-world datasets demonstrates the efficacy of the proposed framework.

This paper is about the problem of learning a stochastic policy for generating an object (like a molecular graph) from a sequence of actions, such that the probability of generating an object is proportional to a given positive reward for that object. Whereas standard return maximization tends to converge to a single return-maximizing sequence, there are cases where we would like to sample a diverse set of high-return solutions. These arise, for example, in black-box function optimization when few rounds are possible, each with large batches of queries, where the batches should be diverse, e.g., in the design of new molecules. One can also see this as a problem of approximately converting an energy function to a generative distribution. While MCMC methods can achieve that, they are expensive and generally only perform local exploration. Instead, training a generative policy amortizes the cost of search during training and yields to fast generation. Using insights from Temporal Difference learning, we propose GFlowNet, based on a view of the generative process as a flow network, making it possible to handle the tricky case where different trajectories can yield the same final state, e.g., there are many ways to sequentially add atoms to generate some molecular graph. We cast the set of trajectories as a flow and convert the flow consistency equations into a learning objective, akin to the casting of the Bellman equations into Temporal Difference methods. We prove that any global minimum of the proposed objectives yields a policy which samples from the desired distribution, and demonstrate the improved performance and diversity of GFlowNet on a simple domain where there are many modes to the reward function, and on a molecule synthesis task.

In this work, we consider the optimization formulation for symmetric tensor decomposition recently introduced in the Subspace Power Method (SPM) of Kileel and Pereira. Unlike popular alternative functionals for tensor decomposition, the SPM objective function has the desirable properties that its maximal value is known in advance, and its global optima are exactly the rank-1 components of the tensor when the input is sufficiently low-rank. We analyze the non-convex optimization landscape associated with the SPM objective. Our analysis accounts for working with noisy tensors. We derive quantitative bounds such that any second-order critical point with SPM objective value exceeding the bound must equal a tensor component in the noiseless case, and must approximate a tensor component in the noisy case. For decomposing tensors of size $D^{\times m}$, we obtain a near-global guarantee up to rank $\widetilde{o}(D^{\lfloor m/2 \rfloor})$ under a random tensor model, and a global guarantee up to rank $\mathcal{O}(D)$ assuming deterministic frame conditions. This implies that SPM with suitable initialization is a provable, efficient, robust algorithm for low-rank symmetric tensor decomposition. We conclude with numerics that show a practical preferability for using the SPM functional over a more established counterpart.

We study online control of time-varying linear systems with unknown dynamics in the nonstochastic control model. At a high level, we demonstrate that this setting is \emph{qualitatively harder} than that of either unknown time-invariant or known time-varying dynamics, and complement our negative results with algorithmic upper bounds in regimes where sublinear regret is possible. More specifically, we study regret bounds with respect to common classes of policies: Disturbance Action (SLS), Disturbance Response (Youla), and linear feedback policies. While these three classes are essentially equivalent for LTI systems, we demonstrate that these equivalences break down for time-varying systems. We prove a lower bound that no algorithm can obtain sublinear regret with respect to the first two classes unless a certain measure of system variability also scales sublinearly in the horizon. Furthermore, we show that offline planning over the state linear feedback policies is NP-hard, suggesting hardness of the online learning problem. On the positive side, we give an efficient algorithm that attains a sublinear regret bound against the class of Disturbance Response policies up to the aforementioned system variability term. In fact, our algorithm enjoys sublinear \emph{adaptive} regret bounds, which is a strictly stronger metric than standard regret and is more appropriate for time-varying systems. We sketch extensions to Disturbance Action policies and partial observation, and propose an inefficient algorithm for regret against linear state feedback policies.

We study the algorithmic stability of Nesterov's accelerated gradient method. For convex quadratic objectives, Chen et al. (2018) proved that the uniform stability of the method grows quadratically with the number of optimization steps, and conjectured that the same is true for the general convex and smooth case. We disprove this conjecture and show, for two notions of algorithmic stability (including uniform stability), that the stability of Nesterov's accelerated method in fact deteriorates exponentially fast with the number of gradient steps. This stands in sharp contrast to the bounds in the quadratic case, but also to known results for non-accelerated gradient methods where stability typically grows linearly with the number of steps.

We study online learning for optimal allocation when the resource to be allocated is time. An agent receives task proposals sequentially according to a Poisson process and can either accept or reject a proposed task. If she accepts the proposal, she is busy for the duration of the task and obtains a reward that depends on the task duration. If she rejects it, she remains on hold until a new task proposal arrives. We study the regret incurred by the agent first when she knows her reward function but does not know the distribution of the task duration, and then when she does not know her reward function, either. Faster rates are finally obtained by adding structural assumptions on the distribution of rides or on the reward function. This natural setting bears similarities with contextual (one-armed) bandits, but with the crucial difference that the normalized reward associated to a context depends on the whole distribution of contexts.

In this paper, we introduce spatiotemporal joint filter decomposition to decouple spatial and temporal learning, while preserving spatiotemporal dependency in a video. A 3D convolutional filter is now jointly decomposed over a set of spatial and temporal filter atoms respectively. In this way, a 3D convolutional layer becomes three: a temporal atom layer, a spatial atom layer, and a joint coefficient layer, all three remaining convolutional. One obvious arithmetic manipulation allowed in our joint decomposition is to swap spatial or temporal atoms with a set of atoms that have the same number but different sizes, while keeping the remaining unchanged. For example, as shown later, we can now achieve tempo-invariance by simply dilating temporal atoms only. To illustrate this useful atom-swapping property, we further demonstrate how such a decomposition permits the direct learning of 3D CNNs with full-size videos through iterations of two consecutive sub-stages of learning: In the temporal stage, full-temporal downsampled-spatial data are used to learn temporal atoms and joint coefficients while fixing spatial atoms. In the spatial stage, full-spatial downsampled-temporal data are used for spatial atoms and joint coefficients while fixing temporal atoms. We show empirically on multiple action recognition datasets that, the decoupled spatiotemporal learning significantly reduces the model memory footprints, and allows deep 3D CNNs to model high-spatial long-temporal dependency with limited computational resources while delivering comparable performance.

We propose a multi-agent variant of the classical multi-armed bandit problem, in which there are $N$ agents and $K$ arms, and pulling an arm generates a (possibly different) stochastic reward for each agent. Unlike the classical multi-armed bandit problem, the goal is not to learn the "best arm"; indeed, each agent may perceive a different arm to be the best for her personally. Instead, we seek to learn a fair distribution over the arms. Drawing on a long line of research in economics and computer science, we use the Nash social welfare as our notion of fairness. We design multi-agent variants of three classic multi-armed bandit algorithms and show that they achieve sublinear regret, which is now measured in terms of the lost Nash social welfare. We also extend a classical lower bound, establishing the optimality of one of our algorithms.

Mean estimation under differential privacy is a fundamental problem, but worst-case optimal mechanisms do not offer meaningful utility guarantees in practice when the global sensitivity is very large. Instead, various heuristics have been proposed to reduce the error on real-world data that do not resemble the worst-case instance. This paper takes a principled approach, yielding a mechanism that is instance-optimal in a strong sense. In addition to its theoretical optimality, the mechanism is also simple and practical, and adapts to a variety of data characteristics without the need of parameter tuning. It easily extends to the local and shuffle model as well.

Transformers with remarkable global representation capacities achieve competitive results for visual tasks, but fail to consider high-level local pattern information in input images. In this paper, we present a generic Dual-stream Network (DS-Net) to fully explore the representation capacity of local and global pattern features for image classification. Our DS-Net can simultaneously calculate fine-grained and integrated features and efficiently fuse them. Specifically, we propose an Intra-scale Propagation module to process two different resolutions in each block and an Inter-Scale Alignment module to perform information interaction across features at dual scales. Besides, we also design a Dual-stream FPN (DS-FPN) to further enhance contextual information for downstream dense predictions. Without bells and whistles, the proposed DS-Net outperforms DeiT-Small by 2.4\% in terms of top-1 accuracy on ImageNet-1k and achieves state-of-the-art performance over other Vision Transformers and ResNets. For object detection and instance segmentation, DS-Net-Small respectively outperforms ResNet-50 by 6.4\% and 5.5 \% in terms of mAP on MSCOCO 2017, and surpasses the previous state-of-the-art scheme, which significantly demonstrates its potential to be a general backbone in vision tasks. The code will be released soon.