Year: 2025
Type: preprint
Abstract: We study contrastive learning under the PAC learning framework. While a series of recent works have shown statistical results for learning under contrastive loss, based either on the VC-dimension or Rademacher complexity, their algorithms are inherently inefficient or not implying PAC guarantees. In this paper, we consider contrastive learning of the fundamental concept of linear representations. Surprisingly, even under such basic setting, the existence of efficient PAC learners is largely open. We first show that the problem of contrastive PAC learning of linear representations is intractable to solve in general. We then show that it can be relaxed to a semi-definite program when the distance between contrastive samples is measured by the $\ell_2$-norm. We then establish generalization guarantees based on Rademacher complexity, and connect it to PAC guarantees under certain contrastive large-margin conditions. To the best of our knowledge, this is the first efficient PAC learning algorithm for contrastive learning.
Source: arXiv (Cornell University)
Author: Shen, Jie
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414836571
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