Optimal VC Dimension of Contrastive Learning with Margin

תקציר מקורי באנגליתarXiv: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 question. Recently, \citet*{alon2024optimal} proved that, for PAC-learning $d$-dimensional Euclidean representations of $n$-point datasets, $\Theta(\min(nd, n^2))$ triplets are necessary and sufficient, while they posed as an open question whether their VC dimension bounds for the more realistic setting