Generalization Analysis for Contrastive Representation Learning

TL;DR

This paper provides new theoretical generalization bounds for contrastive learning that are independent of the number of negative samples, addressing a key limitation in existing analyses.

Contribution

It introduces novel generalization bounds for contrastive learning that do not depend on the number of negative examples, using advanced complexity measures.

Findings

Generalization bounds independent of negative sample size

Improved bounds for Lipschitz loss functions with fast rates

Application to neural network representations

Abstract

Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular, the existing generalization error bounds depend linearly on the number $k$ of negative examples while it was widely shown in practice that choosing a large $k$ is necessary to guarantee good generalization of contrastive learning in downstream tasks. In this paper, we establish novel generalization bounds for contrastive learning which do not depend on $k$, up to logarithmic terms. Our analysis uses structural results on empirical covering numbers and Rademacher complexities to exploit the Lipschitz continuity of loss functions. For self-bounding Lipschitz loss functions, we further improve our results by developing optimistic bounds which imply fast rates in a low noise condition. We apply our results to learning with both linear representation and nonlinear representation by deep neural networks, for both of which we derive Rademacher complexity bounds to get improved generalization bounds.