NeurIPS 2022 Papers

A canonical noise distribution (CND) is an additive mechanism designed to satisfy $f$-differential privacy ($f$-DP), without any wasted privacy budget. $f$-DP is a hypothesis testing-based formulation of privacy phrased in terms of tradeoff functions, which captures the difficulty of a hypothesis test. In this paper, we consider the existence and construction of both log-concave CNDs and multivariate CNDs. Log-concave distributions are important to ensure that higher outputs of the mechanism correspond to higher input values, whereas multivariate noise distributions are important to ensure that a joint release of multiple outputs has a tight privacy characterization. We show that the existence and construction of CNDs for both types of problems is related to whether the tradeoff function can be decomposed by functional composition (related to group privacy) or mechanism composition. In particular, we show that pure $\epsilon$-DP cannot be decomposed in either way and that there is neither a log-concave CND nor any multivariate CND for $\epsilon$-DP. On the other hand, we show that Gaussian-DP, $(0,\delta)$-DP, and Laplace-DP each have both log-concave and multivariate CNDs.

CLIP yielded impressive results on zero-shot transfer learning tasks and is considered as a foundation model like BERT or GPT3. CLIP vision models that have a rich representation are pre-trained using the InfoNCE objective and natural language supervision before they are fine-tuned on particular tasks. Though CLIP excels at zero-shot transfer learning, it suffers from an explaining away problem, that is, it focuses on one or few features, while neglecting other relevant features. This problem is caused by insufficiently extracting the covariance structure in the original multi-modal data. We suggest to use modern Hopfield networks to tackle the problem of explaining away. Their retrieved embeddings have an enriched covariance structure derived from co-occurrences of features in the stored embeddings. However, modern Hopfield networks increase the saturation effect of the InfoNCE objective which hampers learning. We propose to use the InfoLOOB objective to mitigate this saturation effect. We introduce the novel "Contrastive Leave One Out Boost" (CLOOB), which uses modern Hopfield networks for covariance enrichment together with the InfoLOOB objective. In experiments we compare CLOOB to CLIP after pre-training on the Conceptual Captions and the YFCC dataset with respect to their zero-shot transfer learning performance on other datasets. CLOOB consistently outperforms CLIP at zero-shot transfer learning across all considered architectures and datasets.

Data augmentation is key to improving the generalization ability of deep learning models. Mixup is a simple and widely-used data augmentation technique that has proven effective in alleviating the problems of overfitting and data scarcity. Also, recent studies of saliency-aware Mixup in the image domain show that preserving discriminative parts is beneficial to improving the generalization performance. However, these Mixup-based data augmentations are underexplored in 3D vision, especially in point clouds. In this paper, we propose SageMix, a saliency-guided Mixup for point clouds to preserve salient local structures. Specifically, we extract salient regions from two point clouds and smoothly combine them into one continuous shape. With a simple sequential sampling by re-weighted saliency scores, SageMix preserves the local structure of salient regions. Extensive experiments demonstrate that the proposed method consistently outperforms existing Mixup methods in various benchmark point cloud datasets. With PointNet++, our method achieves an accuracy gain of 2.6% and 4.0% over standard training in ModelNet40 and ScanObjectNN, respectively. In addition to generalization performance, SageMix improves robustness and uncertainty calibration. Moreover, when adopting our method to various tasks including part segmentation and standard image classification, our method achieves competitive performance. Code is available at https://github.com/mlvlab/SageMix.

Hierarchical reinforcement learning (HRL) has been proven to be effective for tasks with sparse rewards, for it can improve the agent's exploration efficiency by discovering high-quality hierarchical structures (e.g., subgoals or options). However, automatically discovering high-quality hierarchical structures is still a great challenge. Previous HRL methods can only find the hierarchical structures in simple environments, as they are mainly achieved through the randomness of agent's policies during exploration. In complicated environments, such a randomness-driven exploration paradigm can hardly discover high-quality hierarchical structures because of the low exploration efficiency. In this paper, we propose CDHRL, a causality-driven hierarchical reinforcement learning framework, to build high-quality hierarchical structures efficiently in complicated environments. The key insight is that the causalities among environment variables are naturally fit for modeling reachable subgoals and their dependencies; thus, the causality is suitable to be the guidance in building high-quality hierarchical structures. Roughly, we build the hierarchy of subgoals based on causality autonomously, and utilize the subgoal-based policies to unfold further causality efficiently. Therefore, CDHRL leverages a causality-driven discovery instead of a randomness-driven exploration for high-quality hierarchical structure construction. The results in two complex environments, 2D-Minecraft and Eden, show that CDHRL can discover high-quality hierarchical structures and significantly enhance exploration efficiency.

We propose generative multitask learning (GMTL), a simple and scalable approach to causal machine learning in the multitask setting. Our approach makes a minor change to the conventional multitask inference objective, and improves robustness to target shift. Since GMTL only modifies the inference objective, it can be used with existing multitask learning methods without requiring additional training. The improvement in robustness comes from mitigating unobserved confounders that cause the targets, but not the input. We refer to them as \emph{target-causing confounders}. These confounders induce spurious dependencies between the input and targets. This poses a problem for conventional multitask learning, due to its assumption that the targets are conditionally independent given the input. GMTL mitigates target-causing confounding at inference time, by removing the influence of the joint target distribution, and predicting all targets jointly. This removes the spurious dependencies between the input and targets, where the degree of removal is adjustable via a single hyperparameter. This flexibility is useful for managing the trade-off between in- and out-of-distribution generalization. Our results on the Attributes of People and Taskonomy datasets reflect an improved robustness to target shift across four multitask learning methods.

We consider the problem of training a neural network to store a set of patterns with maximal noise robustness. A solution, in terms of optimal weights and state update rules, is derived by training each individual neuron to perform either kernel classification or interpolation with a minimum weight norm. By applying this method to feed-forward and recurrent networks, we derive optimal models, termed kernel memory networks, that include, as special cases, many of the hetero- and auto-associative memory models that have been proposed over the past years, such as modern Hopfield networks and Kanerva's sparse distributed memory. We modify Kanerva's model and demonstrate a simple way to design a kernel memory network that can store an exponential number of continuous-valued patterns with a finite basin of attraction. The framework of kernel memory networks offers a simple and intuitive way to understand the storage capacity of previous memory models, and allows for new biological interpretations in terms of dendritic non-linearities and synaptic cross-talk.

High-quality data is necessary for modern machine learning. However, the acquisition of such data is difficult due to noisy and ambiguous annotations of humans. The aggregation of such annotations to determine the label of an image leads to a lower data quality. We propose a data-centric image classification benchmark with nine real-world datasets and multiple annotations per image to allow researchers to investigate and quantify the impact of such data quality issues. With the benchmark we can study the impact of annotation costs and (semi-)supervised methods on the data quality for image classification by applying a novel methodology to a range of different algorithms and diverse datasets. Our benchmark uses a two-phase approach via a data label improvement method in the first phase and a fixed evaluation model in the second phase. Thereby, we give a measure for the relation between the input labeling effort and the performance of (semi-)supervised algorithms to enable a deeper insight into how labels should be created for effective model training. Across thousands of experiments, we show that one annotation is not enough and that the inclusion of multiple annotations allows for a better approximation of the real underlying class distribution. We identify that hard labels can not capture the ambiguity of the data and this might lead to the common issue of overconfident models. Based on the presented datasets, benchmarked methods, and analysis, we create multiple research opportunities for the future directed at the improvement of label noise estimation approaches, data annotation schemes, realistic (semi-)supervised learning, or more reliable image collection.

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for node- and graph-level perturbations are derived; the vertex-set non-preserving case is treated by utilizing recently developed mathematical-physics based tools. Energy propagation through the network layers is investigated and related to truncation stability. New methods of graph-level feature aggregation are introduced and stability of the resulting composite scattering architectures is established. Finally, scattering transforms are extended to edge- and higher order tensorial input. Theoretical results are complemented by numerical investigations: Suitably chosen scattering networks conforming to the developed theory perform better than traditional graph-wavelet based scattering approaches in social network graph classification tasks and significantly outperform other graph-based learning approaches to regression of quantum-chemical energies on QM$7$.

We investigate the parameterization of deep neural networks that by design satisfy the continuity equation, a fundamental conservation law. This is enabled by the observation that any solution of the continuity equation can be represented as a divergence-free vector field. We hence propose building divergence-free neural networks through the concept of differential forms, and with the aid of automatic differentiation, realize two practical constructions. As a result, we can parameterize pairs of densities and vector fields that always satisfy the continuity equation by construction, foregoing the need for extra penalty methods or expensive numerical simulation. Furthermore, we prove these models are universal and so can be used to represent any divergence-free vector field. Finally, we experimentally validate our approaches by computing neural network-based solutions to fluid equations, solving for the Hodge decomposition, and learning dynamical optimal transport maps.

Knowledge distillation can be generally divided into offline and online categories according to whether teacher model is pre-trained and persistent during the distillation process. Offline distillation can employ existing models yet always demonstrates inferior performance than online ones. In this paper, we first empirically show that the essential factor for their performance gap lies in the reversed distillation from student to teacher, rather than the training fashion. Offline distillation can achieve competitive performance gain by fine-tuning pre-trained teacher to adapt student with such reversed distillation. However, this fine-tuning process still costs lots of training budgets. To alleviate this dilemma, we propose SHAKE, a simple yet effective SHAdow KnowlEdge transfer framework to bridge offline and online distillation, which trades the accuracy with efficiency. Specifically, we build an extra shadow head on the backbone to mimic the predictions of pre-trained teacher as its shadow. Then, this shadow head is leveraged as a proxy teacher to perform bidirectional distillation with student on the fly. In this way, SHAKE not only updates this student-aware proxy teacher with the knowledge of pre-trained model, but also greatly optimizes costs of augmented reversed distillation. Extensive experiments on classification and object detection tasks demonstrate that our technique achieves state-of-the-art results with different CNNs and Vision Transformer models. Additionally, our method shows strong compatibility with multi-teacher and augmentation strategies by gaining additional performance improvement. Code is made publicly available at https://lilujunai.github.io/SHAKE/.

For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM estimation is potentially very sensitive to outliers. Robustified GMM estimators have been developed in the past, but suffer from several drawbacks: computational intractability, poor dimension-dependence, and no quantitative recovery guarantees in the presence of a constant fraction of outliers. In this work, we develop the first computationally efficient GMM estimator (under intuitive assumptions) that can tolerate a constant $\epsilon$ fraction of adversarially corrupted samples, and that has an $\ell_2$ recovery guarantee of $O(\sqrt{\epsilon})$. To achieve this, we draw upon and extend a recent line of work on algorithmic robust statistics for related but simpler problems such as mean estimation, linear regression and stochastic optimization. As a special case, we apply our algorithm to instrumental variables linear regression with heterogeneous treatment effects, and experimentally demonstrate that it can tolerate as much as $10$ -- $15\%$ corruption, significantly improving upon baseline methods.

We consider representation learning on periodic graphs encoding crystal materials. Different from regular graphs, periodic graphs consist of a minimum unit cell repeating itself on a regular lattice in 3D space. How to effectively encode these periodic structures poses unique challenges not present in regular graph representation learning. In addition to being E(3) invariant, periodic graph representations need to be periodic invariant. That is, the learned representations should be invariant to shifts of cell boundaries as they are artificially imposed. Furthermore, the periodic repeating patterns need to be captured explicitly as lattices of different sizes and orientations may correspond to different materials. In this work, we propose a transformer architecture, known as Matformer, for periodic graph representation learning. Our Matformer is designed to be invariant to periodicity and can capture repeating patterns explicitly. In particular, Matformer encodes periodic patterns by efficient use of geometric distances between the same atoms in neighboring cells. Experimental results on multiple common benchmark datasets show that our Matformer outperforms baseline methods consistently. In addition, our results demonstrate the importance of periodic invariance and explicit repeating pattern encoding for crystal representation learning. Our code is publicly available at https://github.com/YKQ98/Matformer.

Electroencephalography (EEG) provides access to neuronal dynamics non-invasively with millisecond resolution, rendering it a viable method in neuroscience and healthcare. However, its utility is limited as current EEG technology does not generalize well across domains (i.e., sessions and subjects) without expensive supervised re-calibration. Contemporary methods cast this transfer learning (TL) problem as a multi-source/-target unsupervised domain adaptation (UDA) problem and address it with deep learning or shallow, Riemannian geometry aware alignment methods. Both directions have, so far, failed to consistently close the performance gap to state-of-the-art domain-specific methods based on tangent space mapping (TSM) on the symmetric, positive definite (SPD) manifold. Here, we propose a machine learning framework that enables, for the first time, learning domain-invariant TSM models in an end-to-end fashion. To achieve this, we propose a new building block for geometric deep learning, which we denote SPD domain-specific momentum batch normalization (SPDDSMBN). A SPDDSMBN layer can transform domain-specific SPD inputs into domain-invariant SPD outputs, and can be readily applied to multi-source/-target and online UDA scenarios. In extensive experiments with 6 diverse EEG brain-computer interface (BCI) datasets, we obtain state-of-the-art performance in inter-session and -subject TL with a simple, intrinsically interpretable network architecture, which we denote TSMNet. Code: https://github.com/rkobler/TSMNet

We consider the stochastic gradient descent (SGD) algorithm driven by a general stochastic sequence, including i.i.d noise and random walk on an arbitrary graph, among others; and analyze it in the asymptotic sense. Specifically, we employ the notion of `efficiency ordering', a well-analyzed tool for comparing the performance of Markov Chain Monte Carlo (MCMC) samplers, for SGD algorithms in the form of Loewner ordering of covariance matrices associated with the scaled iterate errors in the long term. Using this ordering, we show that input sequences that are more efficient for MCMC sampling also lead to smaller covariance of the errors for SGD algorithms in the limit. This also suggests that an arbitrarily weighted MSE of SGD iterates in the limit becomes smaller when driven by more efficient chains. Our finding is of particular interest in applications such as decentralized optimization and swarm learning, where SGD is implemented in a random walk fashion on the underlying communication graph for cost issues and/or data privacy. We demonstrate how certain non-Markovian processes, for which typical mixing-time based non-asymptotic bounds are intractable, can outperform their Markovian counterparts in the sense of efficiency ordering for SGD. We show the utility of our method by applying it to gradient descent with shuffling and mini-batch gradient descent, reaffirming key results from existing literature under a unified framework. Empirically, we also observe efficiency ordering for variants of SGD such as accelerated SGD and Adam, open up the possibility of extending our notion of efficiency ordering to a broader family of stochastic optimization algorithms.

Audio-visual source localization is a challenging task that aims to predict the location of visual sound sources in a video. Since collecting ground-truth annotations of sounding objects can be costly, a plethora of weakly-supervised localization methods that can learn from datasets with no bounding-box annotations have been proposed in recent years, by leveraging the natural co-occurrence of audio and visual signals. Despite significant interest, popular evaluation protocols have two major flaws. First, they allow for the use of a fully annotated dataset to perform early stopping, thus significantly increasing the annotation effort required for training. Second, current evaluation metrics assume the presence of sound sources at all times. This is of course an unrealistic assumption, and thus better metrics are necessary to capture the model's performance on (negative) samples with no visible sound sources. To accomplish this, we extend the test set of popular benchmarks, Flickr SoundNet and VGG-Sound Sources, in order to include negative samples, and measure performance using metrics that balance localization accuracy and recall. Using the new protocol, we conducted an extensive evaluation of prior methods, and found that most prior works are not capable of identifying negatives and suffer from significant overfitting problems (rely heavily on early stopping for best results). We also propose a new approach for visual sound source localization that addresses both these problems. In particular, we found that, through extreme visual dropout and the use of momentum encoders, the proposed approach combats overfitting effectively, and establishes a new state-of-the-art performance on both Flickr SoundNet and VGG-Sound Source. Code and pre-trained models are available at https://github.com/stoneMo/SLAVC.

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in imbalanced binary classification, where data are dominated by samples from one of two classes. The first part of this paper derives a novel generalization of the Bayes-optimal classifier from accuracy to any performance metric computed from the confusion matrix. Specifically, this result (a) demonstrates that stochastic classifiers sometimes outperform the best possible deterministic classifier and (b) removes an empirically unverifiable absolute continuity assumption that is poorly understood but pervades existing results. We then demonstrate how to use this generalized Bayes classifier to obtain regret bounds in terms of the error of estimating regression functions under uniform loss. Finally, we use these results to develop some of the first finite-sample statistical guarantees specific to imbalanced binary classification. Specifically, we demonstrate that optimal classification performance depends on properties of class imbalance, such as a novel notion called Uniform Class Imbalance, that have not previously been formalized. We further illustrate these contributions numerically in the case of $k$-nearest neighbor classification.

Given data from diverse sets of distinct distributions, domain generalization aims to learn models that generalize to unseen distributions. A common approach is designing a data-driven surrogate penalty to capture generalization and minimize the empirical risk jointly with the penalty. We argue that a significant failure mode of this recipe is an excess risk due to an erroneous penalty or hardness in joint optimization. We present an approach that eliminates this problem. Instead of jointly minimizing empirical risk with the penalty, we minimize the penalty under the constraint of optimality of the empirical risk. This change guarantees that the domain generalization penalty cannot impair optimization of the empirical risk, \ie, in-distribution performance. To solve the proposed optimization problem, we demonstrate an exciting connection to rate-distortion theory and utilize its tools to design an efficient method. Our approach can be applied to any penalty-based domain generalization method, and we demonstrate its effectiveness by applying it to three examplar methods from the literature, showing significant improvements.

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.

We propose a series of computationally efficient, nonparametric tests for the two-sample, independence and goodness-of-fit problems, using the Maximum Mean Discrepancy (MMD), Hilbert Schmidt Independence Criterion (HSIC), and Kernel Stein Discrepancy (KSD), respectively. Our test statistics are incomplete $U$-statistics, with a computational cost that interpolates between linear time in the number of samples, and quadratic time, as associated with classical $U$-statistic tests. The three proposed tests aggregate over several kernel bandwidths to detect departures from the null on various scales: we call the resulting tests MMDAggInc, HSICAggInc and KSDAggInc. This procedure provides a solution to the fundamental kernel selection problem as we can aggregate a large number of kernels with several bandwidths without incurring a significant loss of test power. For the test thresholds, we derive a quantile bound for wild bootstrapped incomplete $U$-statistics, which is of independent interest. We derive non-asymptotic uniform separation rates for MMDAggInc and HSICAggInc, and quantify exactly the trade-off between computational efficiency and the attainable rates: this result is novel for tests based on incomplete $U$-statistics, to our knowledge. We further show that in the quadratic-time case, the wild bootstrap incurs no penalty to test power over more widespread permutation-based approaches, since both attain the same minimax optimal rates (which in turn match the rates that use oracle quantiles). We support our claims with numerical experiments on the trade-off between computational efficiency and test power. In all three testing frameworks, our proposed linear-time tests outperform the current linear-time state-of-the-art tests (or at least match their test power).