NeurIPS 2021 Papers

We provide a first-order oracle complexity lower bound for finding stationary points of min-max optimization problems where the objective function is smooth, nonconvex in the minimization variable, and strongly concave in the maximization variable. We establish a lower bound of $\Omega\left(\sqrt{\kappa}\epsilon^{-2}\right)$ for deterministic oracles, where $\epsilon$ defines the level of approximate stationarity and $\kappa$ is the condition number. Our lower bound matches the best existing upper bound in the $\epsilon$ and $\kappa$ dependence up to logarithmic factors. For stochastic oracles, we provide a lower bound of $\Omega\left(\sqrt{\kappa}\epsilon^{-2} + \kappa^{1/3}\epsilon^{-4}\right)$. It suggests that there is a gap between the best existing upper bound $\mathcal{O}(\kappa^3 \epsilon^{-4})$ and our lower bound in the condition number dependence.

Invariant Risk Minimization (IRM) is a recently proposed framework for out-of-distribution (o.o.d) generalization. Most of the studies on IRM so far have focused on theoretical results, toy problems, and simple models. In this work, we investigate the applicability of IRM to bias mitigation-a special case of o.o.d generalization-in increasingly naturalistic settings and deep models. Using natural language inference (NLI) as a test case, we start with a setting where both the dataset and the bias are synthetic, continue with a natural dataset and synthetic bias, and end with a fully realistic setting with natural datasets and bias. Our results show that in naturalistic settings, learning complex features in place of the bias proves to be difficult, leading to a rather small improvement over empirical risk minimization. Moreover, we find that in addition to being sensitive to random seeds, the performance of IRM also depends on several critical factors, notably dataset size, bias prevalence, and bias strength, thus limiting IRM's advantage in practical scenarios. Our results highlight key challenges in applying IRM to real-world scenarios, calling for a more naturalistic characterization of the problem setup for o.o.d generalization.

In the stochastic linear contextual bandit setting there exist several minimax procedures for exploration with policies that are reactive to the data being acquired. In practice, there can be a significant engineering overhead to deploy these algorithms, especially when the dataset is collected in a distributed fashion or when a human in the loop is needed to implement a different policy. Exploring with a single non-reactive policy is beneficial in such cases. Assuming some batch contexts are available, we design a single stochastic policy to collect a good dataset from which a near-optimal policy can be extracted. We present a theoretical analysis as well as numerical experiments on both synthetic and real-world datasets.

We study the problem of inferring time-varying Gaussian Markov random fields, where the underlying graphical model is both sparse and changes {sparsely} over time. Most of the existing methods for the inference of time-varying Markov random fields (MRFs) rely on the \textit{regularized maximum likelihood estimation} (MLE), that typically suffer from weak statistical guarantees and high computational time. Instead, we introduce a new class of constrained optimization problems for the inference of sparsely-changing Gaussian MRFs (GMRFs). The proposed optimization problem is formulated based on the exact $\ell_0$ regularization, and can be solved in near-linear time and memory. Moreover, we show that the proposed estimator enjoys a provably small estimation error. We derive sharp statistical guarantees in the high-dimensional regime, showing that such problems can be learned with as few as one sample per time period. Our proposed method is extremely efficient in practice: it can accurately estimate sparsely-changing GMRFs with more than 500 million variables in less than one hour.

Few-shot object detection (FSOD) aims to detect new objects based on few annotated samples. To alleviate the impact of few samples, enhancing the generalization and discrimination abilities of detectors on new objects plays an important role. In this paper, we explore employing Singular Value Decomposition (SVD) to boost both the generalization and discrimination abilities. In specific, we propose a novel method, namely, SVD-Dictionary enhancement, to build two separated spaces based on the sorted singular values. Concretely, the eigenvectors corresponding to larger singular values are used to build the generalization space in which localization is performed, as these eigenvectors generally suppress certain variations (e.g., the variation of styles) and contain intrinsical characteristics of objects. Meanwhile, since the eigenvectors corresponding to relatively smaller singular values may contain richer category-related information, we can utilize them to build the discrimination space in which classification is performed. Dictionary learning is further leveraged to capture high-level discriminative information from the discrimination space, which is beneficial for improving detection accuracy. In the experiments, we separately verify the effectiveness of our method on PASCAL VOC and COCO benchmarks. Particularly, for the 2-shot case in VOC split1, our method significantly outperforms the baseline by 6.2\%. Moreover, visualization analysis shows that our method is instrumental in doing FSOD.

Logistic regression remains one of the most widely used tools in applied statistics, machine learning and data science. However, in moderately high-dimensional problems, where the number of features $d$ is a non-negligible fraction of the sample size $n$, the logistic regression maximum likelihood estimator (MLE), and statistical procedures based the large-sample approximation of its distribution, behave poorly. Recently, Sur and Candès (2019) showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this high-dimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of the \emph{signal strength}, which is a function of the underlying parameters $\beta$ of the logistic regression. To address this issue, we propose SLOE, a fast and straightforward approach to estimate the signal strength in logistic regression. The key insight of SLOE is that the Sur and Candès (2019) correction can be reparameterized in terms of the corrupted signal strength, which is only a function of the estimated parameters $\widehat \beta$. We propose an estimator for this quantity, prove that it is consistent in the relevant high-dimensional regime, and show that dimensionality correction using SLOE is accurate in finite samples. Compared to the existing ProbeFrontier heuristic, SLOE is conceptually simpler and orders of magnitude faster, making it suitable for routine use. We demonstrate the importance of routine dimensionality correction in the Heart Disease dataset from the UCI repository, and a genomics application using data from the UK Biobank.

Existing convolutional neural networks (CNNs) often use global average pooling (GAP) to aggregate feature maps into a single representation. However, GAP cannot well characterize complex distributive patterns of spatial features while such patterns play an important role in texture-oriented applications, e.g., material recognition and ground terrain classification. In the context of texture representation, this paper addressed the issue by proposing Fractal Encoding (FE), a feature encoding module grounded by multi-fractal geometry. Considering a CNN feature map as a union of level sets of points lying in the 2D space, FE characterizes their spatial layout via a local-global hierarchical fractal analysis which examines the multi-scale power behavior on each level set. This enables a CNN to encode the regularity on the spatial arrangement of image features, leading to a robust yet discriminative spectrum descriptor. In addition, FE has trainable parameters for data adaptivity and can be easily incorporated into existing CNNs for end-to-end training. We applied FE to ResNet-based texture classification and retrieval, and demonstrated its effectiveness on several benchmark datasets.

The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss functions, their behaviour in generically non-convex, high dimensional landscapes is poorly understood. In this work, we use dynamical mean field theory techniques to describe analytically the average dynamics of these methods in a prototypical non-convex model: the (spiked) matrix-tensor model. We derive a closed set of equations that describe the behaviour of heavy-ball momentum and Nesterov acceleration in the infinite dimensional limit. By numerical integration of these equations, we observe that these methods speed up the dynamics but do not improve the algorithmic threshold with respect to gradient descent in the spiked model.

If causal relationships are linear and acyclic and noise terms are independent and Gaussian, causal orientation is not identified from observational data --- even if faithfulness is satisfied (Spirtes et al., 2002). Shimizu et al. (2006) showed that acyclic, linear, {\bf non}-Gaussian (LiNGAM) causal models {\em are} identified from observational data, so long as no latent confounders are present. That holds even when faithfulness fails. Genin and Mayo-Wilson (2020) refine that result: not only are causal relationships identified, but causal orientation is {\em statistically decidable}. That means that for every $\epsilon>0,$ there is a method that converges in probability to the correct orientation and, at every sample size, outputs an incorrect orientation with probability less than $\epsilon.$ These results naturally raise questions about what happens in the presence of latent confounders. Hoyer et al. (2008) and Salehkaleybar et al. (2020) show that, although the causal model is not uniquely identified, causal orientation among observed variables is identified in the presence of latent confounders, so long as faithfulness is satisfied. This paper refines these results: although it is possible to converge to the right orientation in the limit, causal orientation is no longer statistically decidable---it is not possible to converge to the correct orientation with finite-sample bounds on the probability of orientation errors, even if faithfulness is satisfied. However, that limiting result suggests several adjustments to the LiNGAM model that may recover decidability.

Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck in the distributed setting. Gradient compression methods can be used to alleviate this problem, and a recent line of work shows that SGD augmented with gradient compression converges to an $\varepsilon$-first-order stationary point. In this paper we extend these results to convergence to an $\varepsilon$-second-order stationary point ($\varepsilon$-SOSP), which is to the best of our knowledge the first result of this type. In addition, we show that, when the stochastic gradient is not Lipschitz, compressed SGD with RandomK compressor converges to an $\varepsilon$-SOSP with the same number of iterations as uncompressed SGD [Jin et al.,2021] (JACM), while improving the total communication by a factor of $\tilde \Theta(\sqrt{d} \varepsilon^{-3/4})$, where $d$ is the dimension of the optimization problem. We present additional results for the cases when the compressor is arbitrary and when the stochastic gradient is Lipschitz.

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm distributional gradient matching (DGM) jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.

The memorization effect of deep neural network (DNN) plays a pivotal role in many state-of-the-art label-noise learning methods. To exploit this property, the early stopping trick, which stops the optimization at the early stage of training, is usually adopted. Current methods generally decide the early stopping point by considering a DNN as a whole. However, a DNN can be considered as a composition of a series of layers, and we find that the latter layers in a DNN are much more sensitive to label noise, while their former counterparts are quite robust. Therefore, selecting a stopping point for the whole network may make different DNN layers antagonistically affect each other, thus degrading the final performance. In this paper, we propose to separate a DNN into different parts and progressively train them to address this problem. Instead of the early stopping which trains a whole DNN all at once, we initially train former DNN layers by optimizing the DNN with a relatively large number of epochs. During training, we progressively train the latter DNN layers by using a smaller number of epochs with the preceding layers fixed to counteract the impact of noisy labels. We term the proposed method as progressive early stopping (PES). Despite its simplicity, compared with the traditional early stopping, PES can help to obtain more promising and stable results. Furthermore, by combining PES with existing approaches on noisy label training, we achieve state-of-the-art performance on image classification benchmarks. The code is made public at https://github.com/tmllab/PES.

Federated learning methods typically learn a model by iteratively sampling updates from a population of clients. In this work, we explore how the number of clients sampled at each round (the cohort size) impacts the quality of the learned model and the training dynamics of federated learning algorithms. Our work poses three fundamental questions. First, what challenges arise when trying to scale federated learning to larger cohorts? Second, what parallels exist between cohort sizes in federated learning, and batch sizes in centralized learning? Last, how can we design federated learning methods that effectively utilize larger cohort sizes? We give partial answers to these questions based on extensive empirical evaluation. Our work highlights a number of challenges stemming from the use of larger cohorts. While some of these (such as generalization issues and diminishing returns) are analogs of large-batch training challenges, others (including catastrophic training failures and fairness concerns) are unique to federated learning.

How can we make use of information parallelism in online decision-making problems while efficiently balancing the exploration-exploitation trade-off? In this paper, we introduce a batch Thompson Sampling framework for two canonical online decision-making problems with partial feedback, namely, stochastic multi-arm bandit and linear contextual bandit. Over a time horizon $T$, our batch Thompson Sampling policy achieves the same (asymptotic) regret bound of a fully sequential one while carrying out only $O(\log T)$ batch queries. To achieve this exponential reduction, i.e., reducing the number of interactions from $T$ to $O(\log T)$, our batch policy dynamically determines the duration of each batch in order to balance the exploration-exploitation trade-off. We also demonstrate experimentally that dynamic batch allocation outperforms natural baselines.

Recent advances in self-attention and pure multi-layer perceptrons (MLP) models for vision have shown great potential in achieving promising performance with fewer inductive biases. These models are generally based on learning interaction among spatial locations from raw data. The complexity of self-attention and MLP grows quadratically as the image size increases, which makes these models hard to scale up when high-resolution features are required. In this paper, we present the Global Filter Network (GFNet), a conceptually simple yet computationally efficient architecture, that learns long-term spatial dependencies in the frequency domain with log-linear complexity. Our architecture replaces the self-attention layer in vision transformers with three key operations: a 2D discrete Fourier transform, an element-wise multiplication between frequency-domain features and learnable global filters, and a 2D inverse Fourier transform. We exhibit favorable accuracy/complexity trade-offs of our models on both ImageNet and downstream tasks. Our results demonstrate that GFNet can be a very competitive alternative to transformer-style models and CNNs in efficiency, generalization ability and robustness. Code is available at https://github.com/raoyongming/GFNet

Multipartite ranking is a basic task in machine learning, where the Area Under the receiver operating characteristics Curve (AUC) is generally applied as the evaluation metric. Despite that AUC reflects the overall performance of the model, it is inconsistent with the expected performance in some application scenarios, where only a low False Positive Rate (FPR) is meaningful. To leverage high performance under low FPRs, we consider an alternative metric for multipartite ranking evaluating the True Positive Rate (TPR) at a given FPR, denoted as TPR@FPR. Unfortunately, the key challenge of direct TPR@FPR optimization is two-fold: \textbf{a)} the original objective function is not differentiable, making gradient backpropagation impossible; \textbf{b)} the loss function could not be written as a sum of independent instance-wise terms, making mini-batch based optimization infeasible. To address these issues, we propose a novel framework on top of the deep learning framework named \textit{Cross-Batch Approximation for Multipartite Ranking (CBA-MR)}. In face of \textbf{a)}, we propose a differentiable surrogate optimization problem where the instances having a short-time effect on FPR are rendered with different weights based on the random walk hypothesis. To tackle \textbf{b)}, we propose a fast ranking estimation method, where the full-batch loss evaluation is replaced by a delayed update scheme with the help of an embedding cache. Finally, experimental results on four real-world benchmarks are provided to demonstrate the effectiveness of the proposed method.

For many applications in image analysis, learning models that are invariant to translations and rotations is paramount. This is the case, for example, in medical imaging where the objects of interest can appear at arbitrary positions, with arbitrary orientations. As of today, Convolutional Neural Networks (CNN) are one of the most powerful tools for image analysis. They achieve, thanks to convolutions, an invariance with respect to translations. In this work, we present a new type of convolutional layer that takes advantage of Bessel functions, well known in physics, to build Bessel-CNNs (B-CNNs) that are invariant to all the continuous set of possible rotation angles by design.

We consider the problem where $n$ clients transmit $d$-dimensional real-valued vectors using $d(1+o(1))$ bits each, in a manner that allows the receiver to approximately reconstruct their mean. Such compression problems naturally arise in distributed and federated learning. We provide novel mathematical results and derive computationally efficient algorithms that are more accurate than previous compression techniques. We evaluate our methods on a collection of distributed and federated learning tasks, using a variety of datasets, and show a consistent improvement over the state of the art.

Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.