Although theoretical properties such as expressive power and over-smoothing of graph neural networks (GNN) have been extensively studied recently, its convergence property is a relatively new direction. In this paper, we investigate the convergence of one powerful GNN, Invariant Graph Network (IGN) over graphs sampled from graphons. We first prove the stability of linear layers for general $k$-IGN (of order $k$) based on a novel interpretation of linear equivariant layers. Building upon this result, we prove the convergence of $k$-IGN under the model of \citet{ruiz2020graphon}, where we access the edge weight but the convergence error is measured for graphon inputs. Under the more natural (and more challenging) setting of \citet{keriven2020convergence} where one can only access 0-1 adjacency matrix sampled according to edge probability, we first show a negative result that the convergence of any IGN is not possible. We then obtain the convergence of a subset of IGNs, denoted as IGN-small, after the edge probability estimation. We show that IGN-small still contains function class rich enough that can approximate spectral GNNs arbitrarily well. Lastly, we perform experiments on various graphon models to verify our statements.

There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. We propose to initialize the networks with a rich representation containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. Such a representation is constructed with the Rich Feature Construction (RFC) algorithm, also called the Bonsai algorithm, which consists of a succession of training episodes. During discovery episodes, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During synthesis episodes, we use knowledge distillation to force the network to simultaneously represent all the previously discovered features. Initializing the networks with Bonsai representations consistently helps six OoD methods achieve top performance on ColoredMNIST benchmark. The same technique substantially outperforms comparable results on the Wilds Camelyon17 task, eliminates the high result variance that plagues other methods, and makes hyperparameter tuning and model selection more reliable.

Pretrained language models have become the standard approach for many NLP tasks due to strong performance, but they are very expensive to train. We propose a simple and efficient learning framework, TLM, that does not rely on large-scale pretraining. Given some labeled task data and a large general corpus, TLM uses task data as queries to retrieve a tiny subset of the general corpus and jointly optimizes the task objective and the language modeling objective from scratch. On eight classification datasets in four domains, TLM achieves results better than or similar to pretrained language models (e.g., RoBERTa-Large) while reducing the training FLOPs by two orders of magnitude. With high accuracy and efficiency, we hope TLM will contribute to democratizing NLP and expediting its development.

The rise of Federated Learning (FL) is bringing machine learning to edge computing by utilizing data scattered across edge devices. However, the heterogeneity of edge network topologies and the uncertainty of wireless transmission are two major obstructions of FL's wide application in edge computing, leading to prohibitive convergence time and high communication cost. In this work, we propose an FL scheme to address both challenges simultaneously. Specifically, we enable edge devices to learn self-distilled neural networks that are readily prunable to arbitrary sizes, which capture the knowledge of the learning domain in a nested and progressive manner. Not only does our approach tackle system heterogeneity by serving edge devices with varying model architectures, but it also alleviates the issue of connection uncertainty by allowing transmitting part of the model parameters under faulty network connections, without wasting the contributing knowledge of the transmitted parameters. Extensive empirical studies show that under system heterogeneity and network instability, our approach demonstrates significant resilience and higher communication efficiency compared to the state-of-the-art.

Supervised learning can improve the design of state-of-the-art solvers for combinatorial problems, but labelling large numbers of combinatorial instances is often impractical due to exponential worst-case complexity. Inspired by the recent success of contrastive pre-training for images, we conduct a scientific study of the effect of augmentation design on contrastive pre-training for the Boolean satisfiability problem. While typical graph contrastive pre-training uses label-agnostic augmentations, our key insight is that many combinatorial problems have well-studied invariances, which allow for the design of label-preserving augmentations. We find that label-preserving augmentations are critical for the success of contrastive pre-training. We show that our representations are able to achieve comparable test accuracy to fully-supervised learning while using only 1% of the labels. We also demonstrate that our representations are more transferable to larger problems from unseen domains. Our code is available at https://github.com/h4duan/contrastive-sat.

In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel solution for inductive relation prediction, an important learning task for knowledge graph completion. To predict the relation between two entities, one can use the existence of rules, namely a sequence of relations. Previous works view rules as paths and primarily focus on the searching of paths between entities. The space of rules is huge, and one has to sacrifice either efficiency or accuracy. In this paper, we consider rules as cycles and show that the space of cycles has a unique structure based on the mathematics of algebraic topology. By exploring the linear structure of the cycle space, we can improve the searching efficiency of rules. We propose to collect cycle bases that span the space of cycles. We build a novel GNN framework on the collected cycles to learn the representations of cycles, and to predict the existence/non-existence of a relation. Our method achieves state-of-the-art performance on benchmarks.

The conventional recipe for maximizing model accuracy is to (1) train multiple models with various hyperparameters and (2) pick the individual model which performs best on a held-out validation set, discarding the remainder. In this paper, we revisit the second step of this procedure in the context of fine-tuning large pre-trained models, where fine-tuned models often appear to lie in a single low error basin. We show that averaging the weights of multiple models fine-tuned with different hyperparameter configurations often improves accuracy and robustness. Unlike a conventional ensemble, we may average many models without incurring any additional inference or memory costs---we call the results “model soups.” When fine-tuning large pre-trained models such as CLIP, ALIGN, and a ViT-G pre-trained on JFT, our soup recipe provides significant improvements over the best model in a hyperparameter sweep on ImageNet. The resulting ViT-G model, which attains 90.94% top-1 accuracy on ImageNet, achieved a new state of the art. Furthermore, we show that the model soup approach extends to multiple image classification and natural language processing tasks, improves out-of-distribution performance, and improves zero-shot performance on new downstream tasks. Finally, we analytically relate the performance similarity of weight-averaging and logit-ensembling to flatness of the loss and confidence of the predictions, and validate this relation empirically. Code is available at https://github.com/mlfoundations/model-soups.

Recent investigations in noise contrastive estimation suggest, both empirically as well as theoretically, that while having more negative samples'' in the contrastive loss improves downstream classification performance initially, beyond a threshold, it hurts downstream performance due to acollision-coverage'' trade-off. But is such a phenomenon inherent in contrastive learning?We show in a simple theoretical setting, where positive pairs are generated by sampling from the underlying latent class (introduced by Saunshi et al. (ICML 2019)), that the downstream performance of the representation optimizing the (population) contrastive loss in fact does not degrade with the number of negative samples. Along the way, we give a structural characterization of the optimal representation in our framework, for noise contrastive estimation. We also provide empirical support for our theoretical results on CIFAR-10 and CIFAR-100 datasets.

What matters for contrastive learning? We argue that contrastive learning heavily relies on informative features, or ``hard'' (positive or negative) features. Early works include more informative features by applying complex data augmentations and large batch size or memory bank, and recent works design elaborate sampling approaches to explore informative features. The key challenge toward exploring such features is that the source multi-view data is generated by applying random data augmentations, making it infeasible to always add useful information in the augmented data. Consequently, the informativeness of features learned from such augmented data is limited. In response, we propose to directly augment the features in latent space, thereby learning discriminative representations without a large amount of input data. We perform a meta learning technique to build the augmentation generator that updates its network parameters by considering the performance of the encoder. However, insufficient input data may lead the encoder to learn collapsed features and therefore malfunction the augmentation generator. A new margin-injected regularization is further added in the objective function to avoid the encoder learning a degenerate mapping. To contrast all features in one gradient back-propagation step, we adopt the proposed optimization-driven unified contrastive loss instead of the conventional contrastive loss. Empirically, our method achieves state-of-the-art results on several benchmark datasets.

Self-supervised Contrastive Learning (CL) has been recently shown to be very effective in preventing deep networks from overfitting noisy labels. Despite its empirical success, the theoretical understanding of the effect of contrastive learning on boosting robustness is very limited. In this work, we rigorously prove that the representation matrix learned by contrastive learning boosts robustness, by having: (i) one prominent singular value corresponding to each sub-class in the data, and significantly smaller remaining singular values; and (ii) a large alignment between the prominent singular vectors and the clean labels of each sub-class. The above properties enable a linear layer trained on such representations to effectively learn the clean labels without overfitting the noise. We further show that the low-rank structure of the Jacobian of deep networks pre-trained with contrastive learning allows them to achieve a superior performance initially, when fine-tuned on noisy labels. Finally, we demonstrate that the initial robustness provided by contrastive learning enables robust training methods to achieve state-of-the-art performance under extreme noise levels, e.g., an average of 27.18% and 15.58% increase in accuracy on CIFAR-10 and CIFAR-100 with 80% symmetric noisy labels, and 4.11% increase in accuracy on WebVision.

Self-supervised learning has achieved a great success in the representation learning of visual and textual data. However, the current methods are mainly validated on the well-curated datasets, which do not exhibit the real-world long-tailed distribution. Recent attempts to consider self-supervised long-tailed learning are made by rebalancing in the loss perspective or the model perspective, resembling the paradigms in the supervised long-tailed learning. Nevertheless, without the aid of labels, these explorations have not shown the expected significant promise due to the limitation in tail sample discovery or the heuristic structure design. Different from previous works, we explore this direction from an alternative perspective, i.e., the data perspective, and propose a novel Boosted Contrastive Learning (BCL) method. Specifically, BCL leverages the memorization effect of deep neural networks to automatically drive the information discrepancy of the sample views in contrastive learning, which is more efficient to enhance the long-tailed learning in the label-unaware context. Extensive experiments on a range of benchmark datasets demonstrate the effectiveness of BCL over several state-of-the-art methods. Our code is available at https://github.com/MediaBrain-SJTU/BCL.

Data augmentation is critical to contrastive self-supervised learning, whose goal is to distinguish a sample's augmentations (positives) from other samples (negatives). However, strong augmentations may change the sample-identity of the positives, while weak augmentation produces easy positives/negatives leading to nearly-zero loss and ineffective learning. In this paper, we study a simple adversarial augmentation method that can modify training data to be hard positives/negatives without distorting the key information about their original identities. In particular, we decompose a sample $x$ to be its variational auto-encoder (VAE) reconstruction $G(x)$ plus the residual $R(x)=x-G(x)$, where $R(x)$ retains most identity-distinctive information due to an information-theoretic interpretation of the VAE objective. We then adversarially perturb $G(x)$ in the VAE's bottleneck space and adds it back to the original $R(x)$ as an augmentation, which is therefore sufficiently challenging for contrastive learning and meanwhile preserves the sample identity intact. We apply this ``identity-disentangled adversarial augmentation (IDAA)'' to different self-supervised learning methods. On multiple benchmark datasets, IDAA consistently improves both their efficiency and generalization performance. We further show that IDAA learned on a dataset can be transferred to other datasets. Code is available at \href{https://github.com/kai-wen-yang/IDAA}{https://github.com/kai-wen-yang/IDAA}.

Contrastive learning (CL)-based self-supervised learning models learn visual representations in a pairwise manner. Although the prevailing CL model has achieved great progress, in this paper, we uncover an ever-overlooked phenomenon: When the CL model is trained with full images, the performance tested in full images is better than that in foreground areas; when the CL model is trained with foreground areas, the performance tested in full images is worse than that in foreground areas. This observation reveals that backgrounds in images may interfere with the model learning semantic information and their influence has not been fully eliminated. To tackle this issue, we build a Structural Causal Model (SCM) to model the background as a confounder. We propose a backdoor adjustment-based regularization method, namely \textit{Interventional Contrastive Learning with Meta Semantic Regularizer} (ICL-MSR), to perform causal intervention towards the proposed SCM. ICL-MSR can be incorporated into any existing CL methods to alleviate background distractions from representation learning. Theoretically, we prove that ICL-MSR achieves a tighter error bound. Empirically, our experiments on multiple benchmark datasets demonstrate that ICL-MSR is able to improve the performances of different state-of-the-art CL methods.

Contrastive representation learning encourages data representation to make semantically similar pairs closer than randomly drawn negative samples, which has been successful in various domains such as vision, language, and graphs.Recent theoretical studies have attempted to explain the benefit of the large negative sample size by upper-bounding the downstream classification loss with the contrastive loss.However, the previous surrogate bounds have two drawbacks: they are only legitimate for a limited range of negative sample sizes and prohibitively large even within that range.Due to these drawbacks, there still does not exist a consensus on how negative sample size theoretically correlates with downstream classification performance.Following the simplified setting where positive pairs are drawn from the true distribution (not generated by data augmentation; as supposed in previous studies),this study establishes surrogate upper and lower bounds for the downstream classification loss for all negative sample sizes that best explain the empirical observations on the negative sample size in the earlier studies.Our bounds suggest that the contrastive loss can be viewed as a surrogate objective of the downstream loss and larger negative sample sizes improve downstream classification because the surrogate gap between contrastive and supervised losses decays.We verify that our theory is consistent with experiments on synthetic, vision, and language datasets.

Avoiding feature collapse, when a Neural Network (NN) encoder maps all inputs to a constant vector, is a shared implicit desideratum of various methodological advances in self-supervised learning (SSL). To that end, whitened features have been proposed as an explicit objective to ensure uncollapsed features \cite{zbontar2021barlow,ermolov2021whitening,hua2021feature,bardes2022vicreg}. We identify power law behaviour in eigenvalue decay, parameterised by exponent $\beta{\geq}0$, as a spectrum that bridges between the collapsed & whitened feature extremes. We provide theoretical & empirical evidence highlighting the factors in SSL, like projection layers & regularisation strength, that influence eigenvalue decay rate, & demonstrate that the degree of feature whitening affects generalisation, particularly in label scarce regimes. We use our insights to motivate a novel method, PMP (PostMan-Pat), which efficiently post-processes a pretrained encoder to enforce eigenvalue decay rate with power law exponent $\beta$, & find that PostMan-Pat delivers improved label efficiency and transferability across a range of SSL methods and encoder architectures.