From Pixels to Components: Eigenvector Masking for Visual Representation Learning

Predicting masked from visible parts of an image is a powerful self-supervised approach for visual representation learning. However, the common practice of masking random patches of pixels exhibits certain failure modes, which can prevent learning meaningful high-level features, as required for downstream tasks. We propose an alternative masking strategy that operates on a suitable transformation of the data rather than on the raw pixels. Specifically, we perform principal component analysis and then randomly mask a subset of components, which accounts for a fixed ratio of the data variance. The learning task then amounts to reconstructing the masked components from the visible ones. Compared to local patches of pixels, the principal components of images carry more global information. We thus posit that predicting masked from visible components involves more high-level features, allowing our masking strategy to extract more useful representations. This is corroborated by our empirical findings which demonstrate improved image classification performance for component over pixel masking. Our method thus constitutes a simple and robust data-driven alternative to traditional masked image modeling approaches.

Cross-Entropy Is All You Need To Invert the Data Generating Process

Supervised learning has become a cornerstone of modern machine learning, yet a comprehensive theory explaining its effectiveness remains elusive. Empirical phenomena, such as neural analogy-making and the linear representation hypothesis, suggest that supervised models can learn interpretable factors of variation in a linear fashion. Recent advances in self-supervised learning, particularly nonlinear Independent Component Analysis, have shown that these methods can recover latent structures by inverting the data generating process. We extend these identifiability results to parametric instance discrimination, then show how insights transfer to the ubiquitous setting of supervised learning with cross-entropy minimization. We prove that even in standard classification tasks, models learn representations of ground-truth factors of variation up to a linear transformation. We corroborate our theoretical contribution with a series of empirical studies. First, using simulated data matching our theoretical assumptions, we demonstrate successful disentanglement of latent factors. Second, we show that on DisLib, a widely-used disentanglement benchmark, simple classification tasks recover latent structures up to linear transformations. Finally, we reveal that models trained on ImageNet encode representations that permit linear decoding of proxy factors of variation. Together, our theoretical findings and experiments offer a compelling explanation for recent observations of linear representations, such as superposition in neural networks. This work takes a significant step toward a cohesive theory that accounts for the unreasonable effectiveness of supervised deep learning.

A Probabilistic Model to explain Self-Supervised Representation Learning

Self-supervised learning (SSL) learns representations by leveraging an auxiliary unsupervised task, such as classifying semantically related samples, e.g. different data augmentations or modalities. Of the many approaches to SSL, contrastive methods, e.g. SimCLR, CLIP and VicREG, have gained attention for learning representations that achieve downstream performance close to that of supervised learning. However, a theoretical understanding of the mechanism behind these methods eludes. We propose a generative latent variable model for the data and show that several families of discriminative self-supervised algorithms, including contrastive methods, approximately induce its latent structure over representations, providing a unifying theoretical framework. We also justify links to mutual information and the use of a projection head. Fitting our model generatively, as SimVE, improves performance over previous VAE methods on common benchmarks (e.g. FashionMNIST, CIFAR10, CelebA), narrows the gap to discriminative methods on _content_ classification and, as our analysis predicts, outperforms them where _style_ information is required, taking a step toward task-agnostic representations.

Identifiability Results for Multimodal Contrastive Learning

Contrastive learning is a cornerstone underlying recent progress in multi-view and multimodal learning, e.g., in representation learning with image/caption pairs. While its effectiveness is not yet fully understood, a line of recent work reveals that contrastive learning can invert the data generating process and recover ground truth latent factors shared between views. In this work, we present new identifiability results for multimodal contrastive learning, showing that it is possible to recover shared factors in a more general setup than the multi-view setting studied previously. Specifically, we distinguish between the multi-view setting with one generative mechanism (e.g., multiple cameras of the same type) and the multimodal setting that is characterized by distinct mechanisms (e.g., cameras and microphones). Our work generalizes previous identifiability results by redefining the generative process in terms of distinct mechanisms with modality-specific latent variables. We prove that contrastive learning can block-identify latent factors shared between modalities, even when there are nontrivial dependencies between factors. We empirically verify our identifiability results with numerical simulations and corroborate our findings on a complex multimodal dataset of image/text pairs. Zooming out, our work provides a theoretical basis for multimodal representation learning and explains in which settings multimodal contrastive learning can be effective in practice.