Optimal VC Dimension of Contrastive Learning with Margin

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arXiv:2609.38834v1 Announce Type: cross Abstract: Contrastive learning is a successful paradigm for learning $d$-dimensional geometric representations from a collection of ``anchor--positive--negative'' triplets $(i,j^{+},k^{-})$, indicating that ``item $i$ is closer to $j$ than to $k$.'' Despite its success, understanding why contrastive learning leads to representations of high \textit{generalization} quality---beyond the often pessimistic predictions from PAC-learning---remains a central ques