The increasing scale of data propels the popularity of leveraging parallelism to speed up the optimization. Minibatch stochastic gradient descent (minibatch SGD) and local SGD are two popular methods for parallel optimization. The existing theoretical studies show a linear speedup of these methods with respect to the number of machines, which, however, is measured by optimization errors. As a comparison, the stability and generalization of these methods are much less studied. In this paper, we study the stability and generalization analysis of minibatch and local SGD to understand their learnability by introducing a novel expectation-variance decomposition. We incorporate training errors into the stability analysis, which shows how small training errors help generalization for overparameterized models. We show both minibatch and local SGD achieve a linear speedup to attain the optimal risk bounds.

Graph clustering is a fundamental task in graph analysis, and recent advances in utilizing graph neural networks (GNNs) have shown impressive results. Despite the success of existing GNN-based graph clustering methods, they often overlook the quality of graph structure, which is inherent in real-world graphs due to their sparse and multifarious nature, leading to subpar performance. Graph structure learning allows refining the input graph by adding missing links and removing spurious connections. However, previous endeavors in graph structure learning have predominantly centered around supervised settings, and cannot be directly applied to our specific clustering tasks due to the absence of ground-truth labels. To bridge the gap, we propose a novel method called \textbf{ho}mophily-enhanced structure \textbf{le}arning for graph clustering (HoLe). Our motivation stems from the observation that subtly enhancing the degree of homophily within the graph structure can significantly improve GNNs and clustering outcomes. To realize this objective, we develop two clustering-oriented structure learning modules, i.e., hierarchical correlation estimation and cluster-aware sparsification. The former module enables a more accurate estimation of pairwise node relationships by leveraging guidance from latent and clustering spaces, while the latter one generates a sparsified structure based on the similarity matrix and clustering assignments. Additionally, we devise a joint optimization approach alternating between training the homophily-enhanced structure learning and GNN-based clustering, thereby enforcing their reciprocal effects. Extensive experiments on seven benchmark datasets of various types and scales, across a range of clustering metrics, demonstrate the superiority of HoLe against state-of-the-art baselines.

Modern image classification is based upon directly predicting classes via large discriminative networks, which do not directly contain information about the intuitive visual features that may constitute a classification decision. Recently, work in vision-language models (VLM) such as CLIP has provided ways to specify natural language descriptions of image classes, but typically focuses on providing single descriptions for each class. In this work, we demonstrate that an alternative approach, in line with humans' understanding of multiple visual features per class, can also provide compelling performance in the robust few-shot learning setting. In particular, we introduce a novel method, \textit{SLR-AVD (Sparse Logistic Regression using Augmented Visual Descriptors)}. This method first automatically generates multiple visual descriptions of each class via a large language model (LLM), then uses a VLM to translate these descriptions to a set of visual feature embeddings of each image, and finally uses sparse logistic regression to select a relevant subset of these features to classify each image. Core to our approach is the fact that, information-theoretically, these descriptive features are more invariant to domain shift than traditional image embeddings, even though the VLM training process is not explicitly designed for invariant representation learning. These invariant descriptive features also compose a better input compression scheme. When combined with finetuning, we show that SLR-AVD is able to outperform existing state-of-the-art finetuning approaches on both in-distribution and out-of-distribution performance.

Video self-supervised learning (VSSL) has made significant progress in recent years. However, the exact behavior and dynamics of these models under different forms of distribution shift are not yet known. In this paper, we comprehensively study the behavior of six popular self-supervised methods (v-SimCLR, v-MoCo, v-BYOL, v-SimSiam, v-DINO, v-MAE) in response to various forms of natural distribution shift, i.e., (i) context shift, (ii) viewpoint shift, (iii) actor shift, (iv) source shift, (v) generalizability to unknown classes (zero-shot), and (vi) open-set recognition. To perform this extensive study, we carefully craft a test bed consisting of 17 in-distribution and out-of-distribution benchmark pairs using available public datasets and a series of evaluation protocols to stress-test the different methods under the intended shifts. Our study uncovers a series of intriguing findings and interesting behaviors of VSSL methods. For instance, we observe that while video models generally struggle with context shifts, v-MAE and supervised learning exhibit more robustness. Moreover, our study shows that v-MAE is a strong temporal learner, whereas contrastive methods, v-SimCLR and v-MoCo, exhibit strong performances against viewpoint shifts. When studying the notion of open-set recognition, we notice a trade-off between closed-set and open-set recognition performance if the pretrained VSSL encoders are used without finetuning. We hope that our work will contribute to the development of robust video representation learning frameworks for various real-world scenarios. The project page and code are available at: https://pritamqu.github.io/OOD-VSSL.

Self-supervised methods received tremendous attention thanks to their seemingly heuristic approach to learning representations that respect the semantics of the data without any apparent supervision in the form of labels. A growing body of literature is already being published in an attempt to build a coherent and theoretically grounded understanding of the workings of a zoo of losses used in modern self-supervised representation learning methods. In this paper, we attempt to provide an understanding from the perspective of a Laplace operator and connect the inductive bias stemming from the augmentation process to a low-rank matrix completion problem. To this end, we leverage the results from low-rank matrix completion to provide theoretical analysis on the convergence of modern SSL methods and a key property that affects their downstream performance.

While most machine learning models can provide confidence in their predictions, confidence is insufficient to understand a prediction's reliability. For instance, the model may have a low confidence prediction if the input is not well-represented in the training dataset or if the input is inherently ambiguous. In this work, we investigate the relationship between how atypical (rare) a sample or a class is and the reliability of a model's predictions. We first demonstrate that atypicality is strongly related to miscalibration and accuracy. In particular, we empirically show that predictions for atypical inputs or atypical classes are more overconfident and have lower accuracy. Using these insights, we show incorporating atypicality improves uncertainty quantification and model performance for discriminative neural networks and large language models. In a case study, we show that using atypicality improves the performance of a skin lesion classifier across different skin tone groups without having access to the group attributes. Overall, we propose that models should use not only confidence but also atypicality to improve uncertainty quantification and performance. Our results demonstrate that simple post-hoc atypicality estimators can provide significant value.

Transformer architecture has shown impressive performance in multiple research domains and has become the backbone of many neural network models. However, there is limited understanding on how it works. In particular, with a simple predictive loss, how the representation emerges from the gradient \emph{training dynamics} remains a mystery. In this paper, for 1-layer transformer with one self-attention layer plus one decoder layer, we analyze its SGD training dynamics for the task of next token prediction in a mathematically rigorous manner. We open the black box of the dynamic process of how the self-attention layer combines input tokens, and reveal the nature of underlying inductive bias. More specifically, with the assumption (a) no positional encoding, (b) long input sequence, and (c) the decoder layer learns faster than the self-attention layer, we prove that self-attention acts as a \emph{discriminative scanning algorithm}: starting from uniform attention, it gradually attends more to distinct key tokens for a specific next token to be predicted, and pays less attention to common key tokens that occur across different next tokens. Among distinct tokens, it progressively drops attention weights, following the order of low to high co-occurrence between the key and the query token in the training set. Interestingly, this procedure does not lead to winner-takes-all, but decelerates due to a \emph{phase transition} that is controllable by the learning rates of the two layers, leaving (almost) fixed token combination. We verify this \textbf{\emph{scan and snap}} dynamics on synthetic and real-world data (WikiText).

To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.

Actor-critic (AC) methods are widely used in reinforcement learning (RL) and benefit from the flexibility of using any policy gradient method as the actor and value-based method as the critic. The critic is usually trained by minimizing the TD error, an objective that is potentially decorrelated with the true goal of achieving a high reward with the actor. We address this mismatch by designing a joint objective for training the actor and critic in a decision-aware fashion. We use the proposed objective to design a generic, AC algorithm that can easily handle any function approximation. We explicitly characterize the conditions under which the resulting algorithm guarantees monotonic policy improvement, regardless of the choice of the policy and critic parameterization. Instantiating the generic algorithm results in an actor that involves maximizing a sequence of surrogate functions (similar to TRPO, PPO) and a critic that involves minimizing a closely connected objective. Using simple bandit examples, we provably establish the benefit of the proposed critic objective over the standard squared error. Finally, we empirically demonstrate the benefit of our decision-aware actor-critic framework on simple RL problems.

Due to the high communication overhead when training machine learning models in a distributed environment, modern algorithms invariably rely on lossy communication compression. However, when untreated, the errors caused by compression propagate, and can lead to severely unstable behavior, including exponential divergence. Almost a decade ago, Seide et al [2014] proposed an error feedback (EF) mechanism, which we refer to as EF14, as an immensely effective heuristic for mitigating this issue. However, despite steady algorithmic and theoretical advances in the EF field in the last decade, our understanding is far from complete. In this work we address one of the most pressing issues. In particular, in the canonical nonconvex setting, all known variants of EF rely on very large batch sizes to converge, which can be prohibitive in practice. We propose a surprisingly simple fix which removes this issue both theoretically, and in practice: the application of Polyak's momentum to the latest incarnation of EF due to Richt\'{a}rik et al. [2021] known as EF21. Our algorithm, for which we coin the name EF21-SGDM, improves the communication and sample complexities of previous error feedback algorithms under standard smoothness and bounded variance assumptions, and does not require any further strong assumptions such as bounded gradient dissimilarity. Moreover, we propose a double momentum version of our method that improves the complexities even further. Our proof seems to be novel even when compression is removed from the method, and as such, our proof technique is of independent interest in the study of nonconvex stochastic optimization enriched with Polyak's momentum.