A Probabilistic Model for Non-Contrastive Learning

TL;DR

This paper introduces a probabilistic model for self-supervised learning that explains how different data augmentation strategies influence the learned representations, connecting SSL loss functions to statistical models like PCA.

Contribution

It proposes a latent variable statistical model for SSL that links the maximum likelihood estimate to PCA or a simple non-contrastive loss based on data augmentation quality.

Findings

MLE reduces to PCA with informative augmentations

MLE approaches a non-contrastive loss with less informative augmentations

Empirical results support the theoretical analysis

Abstract

Self-supervised learning (SSL) aims to find meaningful representations from unlabeled data by encoding semantic similarities through data augmentations. Despite its current popularity, theoretical insights about SSL are still scarce. For example, it is not yet known whether commonly used SSL loss functions can be related to a statistical model, much in the same as OLS, generalized linear models or PCA naturally emerge as maximum likelihood estimates of an underlying generative process. In this short paper, we consider a latent variable statistical model for SSL that exhibits an interesting property: Depending on the informativeness of the data augmentations, the MLE of the model either reduces to PCA, or approaches a simple non-contrastive loss. We analyze the model and also empirically illustrate our findings.