Generalization Analysis for Contrastive Representation Learning
- URL: http://arxiv.org/abs/2302.12383v2
- Date: Tue, 28 Feb 2023 02:42:06 GMT
- Title: Generalization Analysis for Contrastive Representation Learning
- Authors: Yunwen Lei, Tianbao Yang, Yiming Ying, Ding-Xuan Zhou
- Abstract summary: Existing generalization error bounds depend linearly on the number $k$ of negative examples.
We establish novel generalization bounds for contrastive learning which do not depend on $k$, up to logarithmic terms.
- Score: 80.89690821916653
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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