ICLR 2023 Papers

We develop and analyze DASHA: a new family of methods for nonconvex distributed optimization problems. When the local functions at the nodes have a finite-sum or an expectation form, our new methods, DASHA-PAGE, DASHA-MVR and DASHA-SYNC-MVR, improve the theoretical oracle and communication complexity of the previous state-of-the-art method MARINA by Gorbunov et al. (2020). In particular, to achieve an $\varepsilon$-stationary point, and considering the random sparsifier Rand$K$ as an example, our methods compute the optimal number of gradients $\mathcal{O}\left(\frac{\sqrt{m}}{\varepsilon\sqrt{n}}\right)$ and $\mathcal{O}\left(\frac{\sigma}{\varepsilon^{3/2}n}\right)$ in finite-sum and expectation form cases, respectively, while maintaining the SOTA communication complexity $\mathcal{O}\left(\frac{d}{\varepsilon \sqrt{n}}\right)$. Furthermore, unlike MARINA, the new methods DASHA, DASHA-PAGE and DASHA-MVR send compressed vectors only, which makes them more practical for federated learning. We extend our results to the case when the functions satisfy the Polyak-Lojasiewicz condition. Finally, our theory is corroborated in practice: we see a significant improvement in experiments with nonconvex classification and training of deep learning models.

We formally study how \emph{ensemble} of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using \emph{knowledge distillation}. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the \emph{same} architecture, trained using the \emph{same} algorithm on the \emph{same} data set, and they only differ by the random seeds used in the initialization. We show that ensemble/knowledge distillation in \emph{deep learning} works very differently from traditional learning theory (such as boosting or NTKs). We develop a theory showing that when data has a structure we refer to as ``multi-view'', then ensemble of independently trained neural networks can provably improve test accuracy, and such superior test accuracy can also be provably distilled into a single model. Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how the ``dark knowledge'' is hidden in the outputs of the ensemble and can be used in distillation.

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an explicit constant factor that holds true for the entire function class. Furthermore, in the stochastic setting, only a modified version of AdaGrad, different from the one commonly used in practice, in which the latest gradient is not used to update the stepsize, has been analyzed. Our paper aims at bridging these gaps and developing a deeper understanding of AdaGrad and its variants in the standard setting of smooth convex functions as well as the more general setting of quasar convex functions. First, we demonstrate new techniques to explicitly bound the convergence rate of the vanilla AdaGrad for unconstrained problems in both deterministic and stochastic settings. Second, we propose a variant of AdaGrad for which we can show the convergence of the last iterate, instead of the average iterate. Finally, we give new accelerated adaptive algorithms and their convergence guarantee in the deterministic setting with explicit dependency on the problem parameters, improving upon the asymptotic rate shown in previous works.

This paper addresses learning end-to-end models for time series data that include a temporal alignment step via dynamic time warping (DTW). Existing approaches to differentiable DTW either differentiate through a fixed warping path or apply a differentiable relaxation to the min operator found in the recursive steps used to solve the DTW problem. We instead propose a DTW layer based around bi-level optimisation and deep declarative networks, which we name DecDTW. By formulating DTW as a continuous, inequality constrained optimisation problem, we can compute gradients for the solution of the optimal alignment (with respect to the underlying time series) using implicit differentiation. An interesting byproduct of this formulation is that DecDTW outputs the optimal warping path between two time series as opposed to a soft approximation, recoverable from Soft-DTW. We show that this property is particularly useful for applications where downstream loss functions are defined on the optimal alignment path itself. This naturally occurs, for instance, when learning to improve the accuracy of predicted alignments against ground truth alignments. We evaluate DecDTW on two such applications, namely the audio-to-score alignment task in music information retrieval and the visual place recognition task in robotics, demonstrating state-of-the-art results in both.

Data heterogeneity is one of the most challenging issues in federated learning, which motivates a variety of approaches to learn personalized models for participating clients. One such approach in deep neural networks based tasks is employing a shared feature representation and learning a customized classifier head for each client. However, previous works do not utilize the global knowledge during local representation learning and also neglect the fine-grained collaboration between local classifier heads, which limits the model generalization ability. In this work, we conduct explicit local-global feature alignment by leveraging global semantic knowledge for learning a better representation. Moreover, we quantify the benefit of classifier combination for each client as a function of the combining weights and derive an optimization problem for estimating optimal weights. Finally, extensive evaluation results on benchmark datasets with various heterogeneous data scenarios demonstrate the effectiveness of our proposed method.

The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from $20.9\%$ to $39.3\%$ on a collection of mathematical competition problems.

While some state-of-the-art artificial neural network systems in computer vision are strikingly accurate models of the corresponding primate visual processing, there are still many discrepancies between these models and the behavior of primates on object recognition tasks. Many current models suffer from extreme sensitivity to adversarial attacks and often do not align well with the image-by-image behavioral error patterns observed in humans. Previous research has provided strong evidence that primate object recognition behavior can be very accurately predicted by neural population activity in the inferior temporal (IT) cortex, a brain area in the late stages of the visual processing hierarchy. Therefore, here we directly test whether making the late stage representations of models more similar to that of macaque IT produces new models that exhibit more robust, primate-like behavior. We conducted chronic, large-scale multi-electrode recordings across the IT cortex in six non-human primates (rhesus macaques). We then use these data to fine-tune (end-to-end) the model "IT" representations such that they are more aligned with the biological IT representations, while preserving accuracy on object recognition tasks. We generate a cohort of models with a range of IT similarity scores validated on held-out animals across two image sets with distinct statistics. Across a battery of optimization conditions, we observed a strong correlation between the models' IT-likeness and alignment with human behavior, as well as an increase in its adversarial robustness. We further assessed the limitations of this approach and find that the improvements in behavioral alignment and adversarial robustness generalize across different image statistics, but not to object categories outside of those covered in our IT training set. Taken together, our results demonstrate that building models that are more aligned with the primate brain leads to more robust and human-like behavior, and call for larger neural data-sets to further augment these gains.

Oversmoothing is a common phenomenon in a wide range of Graph Neural Networks (GNNs) and Transformers, where performance degenerates as the layer goes deeper. Instead of characterizing oversmoothing from the view of complete collapse in which representations converge to a single point, we dive into a more general perspective dimensional collapse in which representations lie in a narrow cone. Accordingly, inspired by the power of contrastive learning in preventing dimensional collapse, we propose a novel normalization layer ContraNorm. Intuitively, ContraNorm implicitly shatters representations in the embedding space, leading to a more uniform distribution and slighter dimensional collapse. On the theoretical analysis, we prove that ContraNorm can alleviate both complete collapse and dimensional collapse under some conditions. Our proposed normalization layer can be easily inserted into GNNs and Transformers with negligible parameter overhead. Experiments on various real-world datasets verify the effectiveness of our method.

Human visual perception can easily generalize to out-of-distributed visual data, which is far beyond the capability of modern machine learning models. Domain generalization (DG) aims to close this gap, with existing DG methods mainly focusing on the loss function design. In this paper, we propose to explore an orthogonal direction, i.e., the design of the backbone architecture. It is motivated by an empirical finding that transformer-based models trained with empirical risk minimization (ERM) outperform CNN-based models employing state-of-the-art (SOTA) DG algorithms on multiple DG datasets. We develop a formal framework to characterize a network's robustness to distribution shifts by studying its architecture's alignment with the correlations in the dataset. This analysis guides us to propose a novel DG model built upon vision transformers, namely \emph{Generalizable Mixture-of-Experts (GMoE)}. Extensive experiments on DomainBed demonstrate that GMoE trained with ERM outperforms SOTA DG baselines by a large margin. Moreover, GMoE is complementary to existing DG methods and its performance is substantially improved when trained with DG algorithms.

Today’s computer vision models achieve human or near-human level performance across a wide variety of vision tasks. However, their architectures, data, and learning algorithms differ in numerous ways from those that give rise to human vision. In this paper, we investigate the factors that affect the alignment between the representations learned by neural networks and human mental representations inferred from behavioral responses. We find that model scale and architecture have essentially no effect on the alignment with human behavioral responses, whereas the training dataset and objective function both have a much larger impact. These findings are consistent across three datasets of human similarity judgments collected using two different tasks. Linear transformations of neural network representations learned from behavioral responses from one dataset substantially improve alignment with human similarity judgments on the other two datasets. In addition, we find that some human concepts such as food and animals are well-represented by neural networks whereas others such as royal or sports-related objects are not. Overall, although models trained on larger, more diverse datasets achieve better alignment with humans than models trained on ImageNet alone, our results indicate that scaling alone is unlikely to be sufficient to train neural networks with conceptual representations that match those used by humans.

Simplicial Embeddings (SEM) are representations learned through self-supervised learning (SSL), wherein a representation is projected into $L$ simplices of $V$ dimensions each using a \texttt{softmax} operation. This procedure conditions the representation onto a constrained space during pretraining and imparts an inductive bias for group sparsity. For downstream classification, we formally prove that the SEM representation leads to better generalization than an unnormalized representation. Furthermore, we empirically demonstrate that SSL methods trained with SEMs have improved generalization on natural image datasets such as CIFAR-100 and ImageNet. Finally, when used in a downstream classification task, we show that SEM features exhibit emergent semantic coherence where small groups of learned features are distinctly predictive of semantically-relevant classes.

Errors in labels obtained via human annotation adversely affect a trained model's performance. Existing approaches propose ways to mitigate the effect of label error on a model's downstream accuracy, yet little is known about its impact on a model's group-based disparity metrics\footnote{Group-based disparity metrics like subgroup calibration, false positive rate, false negative rate, equalized odds, and equal opportunity are more often known, colloquially, as \textit{fairness metrics} in the literature. We use the term group-based disparity metrics in this work.}. Here we study the effect of label error on a model's group-based disparity metrics like group calibration. We empirically characterize how varying levels of label error, in both training and test data, affect these disparity metrics. We find that group calibration and other metrics are sensitive to train-time and test-time label error---particularly for minority groups. For the same level of label error, the percentage change in group calibration error for the minority group is on average 1.5 times larger than the change for the majority group. Towards mitigating the impact of training-time label error, we present an approach to estimate how changing a single training input's label affects a model's group disparity metric on a test set. We empirically assess the proposed approach on a variety of datasets and find a 10-40\% improvement, compared to alternative approaches, in identifying training inputs that improve a model's disparity metric. The proposed approach can help surface training inputs that may need to be corrected for improving a model's group-based disparity metrics.

Language models have recently achieved strong performance across a wide range of NLP benchmarks. However, real world tasks are often poorly specified, and agents must deduce the intended behavior from a combination of context, instructions, and examples. We investigate how both humans and models behave in the face of such task ambiguity by proposing AmbiBench, a new benchmark of six ambiguously-specified classification tasks. We evaluate humans and models on AmbiBench by seeing how well they identify the intended task using 1) instructions with varying degrees of ambiguity, and 2) different numbers of labeled examples. We find that the combination of model scaling (to 175B parameters) and reinforcement learning from human feedback (RLHF) enables models to approach or exceed the accuracy of human participants across tasks, but that either one of these alone is not sufficient. In addition, we show how to dramatically improve the accuracy of language models trained without RLHF by finetuning on a small number of ambiguous in-context examples, providing a promising direction for teaching models to generalize well in the face of ambiguity.

We consider the problem of optimization of deep learning models with smooth activation functions. While there exist influential results on the problem from the ``near initialization'' perspective, we shed considerable new light on the problem. In particular, we make two key technical contributions for such models with $L$ layers, $m$ width, and $\sigma_0^2$ initialization variance. First, for suitable $\sigma_0^2$, we establish a $O(\frac{\text{poly}(L)}{\sqrt{m}})$ upper bound on the spectral norm of the Hessian of such models, considerably sharpening prior results. Second, we introduce a new analysis of optimization based on Restricted Strong Convexity (RSC) which holds as long as the squared norm of the average gradient of predictors is $\Omega(\frac{\text{poly}(L)}{\sqrt{m}})$ for the square loss. We also present results for more general losses. The RSC based analysis does not need the ``near initialization" perspective and guarantees geometric convergence for gradient descent (GD). To the best of our knowledge, ours is the first result on establishing geometric convergence of GD based on RSC for deep learning models, thus becoming an alternative sufficient condition for convergence that does not depend on the widely-used Neural Tangent Kernel (NTK). We share preliminary experimental results supporting our theoretical advances.

We introduce LilNetX, an end-to-end trainable technique for neural networks that enables learning models with specified accuracy-rate-computation trade-off. Prior works approach these problems one at a time and often require post-processing or multistage training which become less practical and do not scale very well for large datasets or architectures. Our method constructs a joint training objective that penalizes the self information of network parameters in a latent representation space to encourage small model size while also introducing priors to increase structured sparsity in the parameter space to reduce computation. When compared with existing state-of-the-art model compression methods, we achieve up to 50% smaller model size and 98% model sparsity on ResNet-20 on the CIFAR-10 dataset as well as 37% smaller model size and 71% structured sparsity on ResNet-50 trained on ImageNet while retaining the same accuracy as those methods. We show that the resulting sparsity can improve the inference time of the models by almost 1.8 times the dense ResNet-50 baseline model. Code is available at https://github.com/Sharath-girish/LilNetX.

The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately limiting their generalization performance. To address this limitation, we devise a method that endows CNNs with simultaneous equivariance with respect to translation, rotation, and scaling. Our approach defines a convolution-like operation and ensures equivariance based on our proposed scalable Fourier-Argand representation. The method maintains similar efficiency as a traditional network and hardly introduces any additional learnable parameters, since it does not face the computational issue that often occurs in group-convolution operators. We validate the efficacy of our approach in the image classification task, demonstrating its robustness and the generalization ability to both scaled and rotated inputs.

Contrastive learning is widely used in areas such as visual representation learning (VRL) and sentence representation learning (SRL). Considering the differences between VRL and SRL in terms of negative sample size and evaluation focus, we believe that the solid findings obtained in VRL may not be entirely carried over to SRL. In this work, we consider the suitability of the decoupled form of contrastive loss, i.e., alignment and uniformity, in SRL. We find a performance gap between sentence representations obtained by jointly optimizing alignment and uniformity on the STS task and those obtained using contrastive loss. Further, we find that the joint optimization of alignment and uniformity during training is prone to overfitting, which does not occur on the contrastive loss. Analyzing them based on the variation of the gradient norms, we find that there is a property of ``gradient dissipation'' in contrastive loss and believe that it is the key to preventing overfitting. We simulate similar "gradient dissipation" of contrastive loss on four optimization objectives of two forms, and achieve the same or even better performance than contrastive loss on the STS tasks, confirming our hypothesis.

An oft-cited challenge of federated learning is the presence of heterogeneity. \emph{Data heterogeneity} refers to the fact that data from different clients may follow very different distributions. \emph{System heterogeneity} refers to client devices having different system capabilities. A considerable number of federated optimization methods address this challenge. In the literature, empirical evaluations usually start federated training from random initialization. However, in many practical applications of federated learning, the server has access to proxy data for the training task that can be used to pre-train a model before starting federated training. Using four standard federated learning benchmark datasets, we empirically study the impact of starting from a pre-trained model in federated learning. Unsurprisingly, starting from a pre-trained model reduces the training time required to reach a target error rate and enables the training of more accurate models (up to 40\%) than is possible when starting from random initialization. Surprisingly, we also find that starting federated learning from a pre-trained initialization reduces the effect of both data and system heterogeneity. We recommend future work proposing and evaluating federated optimization methods to evaluate the performance when starting from random and pre-trained initializations. This study raises several questions for further work on understanding the role of heterogeneity in federated optimization.

Invariant risk minimization (IRM) has received increasing attention as a way to acquire environment-agnostic data representations and predictions, and also a principled solution for preventing spurious correlations from being learned and improving models’ out-of-distribution generalization. Yet, recent works have found that the optimality of the originally-proposed IRM optimization (IRMV1) may be compromised in practice or could be impossible to achieve in some scenarios. Therefore, a series of advanced IRM algorithms have been developed that show practical improvement over IRMV1. In this work, we revisit these recent IRM advancements and identify and resolve three practical limitations in IRM training and evaluation. First, we find that the effect of batch size during training has been chronically overlooked in previous studies, leaving room for further improvement. We propose small-batch training and highlight the improvements over a set of large-batch optimization techniques. Second, we find that improper selection of evaluation environments could give a false sense of invariance for IRM. To alleviate this effect, we leverage diversified test-time environments to precisely characterize the invariance of IRM when applied in practice. Third, we revisit Ahuja et al. (2020)’s proposal to convert IRM into an ensemble game and identify a limitation when a single invariant predictor is desired instead of an ensemble of individual predictors. We propose a new IRM variant to address this limitation based on a novel viewpoint of ensemble IRM games as consensus-constrained bi-level optimization. Lastly, we conduct extensive experiments (covering 7 existing IRM variants and 7 datasets) to justify the practical significance of revisiting IRM training and evaluation in a principled manner.