Generalization Analysis for Contrastive Representation Learning
This work addresses a theoretical gap for researchers in machine learning, providing more meaningful generalization guarantees for contrastive representation learning, though it is incremental as it builds on existing analysis methods.
The paper tackles the problem of limited generalization analysis in contrastive learning by establishing novel generalization bounds that do not depend on the number of negative examples, up to logarithmic terms, and improves these bounds for self-bounding Lipschitz loss functions to achieve fast rates under low noise conditions.
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.