Self-Supervised Contrastive Learning is Approximately Supervised Contrastive Learning

• URL: http://arxiv.org/abs/2506.04411v1
• Date: Wed, 04 Jun 2025 19:43:36 GMT
• Title: Self-Supervised Contrastive Learning is Approximately Supervised Contrastive Learning
• Authors: Achleshwar Luthra, Tianbao Yang, Tomer Galanti,
• Abstract summary: We show that standard self-supervised contrastive learning objectives implicitly approximate a supervised variant we call the negatives-only supervised contrastive loss (NSCL)<n>We prove that the gap between the CL and NSCL losses vanishes as the number of semantic classes increases, under a bound that is both label-agnostic and architecture-independent.
• Score: 48.11265601808718
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite its empirical success, the theoretical foundations of self-supervised contrastive learning (CL) are not yet fully established. In this work, we address this gap by showing that standard CL objectives implicitly approximate a supervised variant we call the negatives-only supervised contrastive loss (NSCL), which excludes same-class contrasts. We prove that the gap between the CL and NSCL losses vanishes as the number of semantic classes increases, under a bound that is both label-agnostic and architecture-independent. We characterize the geometric structure of the global minimizers of the NSCL loss: the learned representations exhibit augmentation collapse, within-class collapse, and class centers that form a simplex equiangular tight frame. We further introduce a new bound on the few-shot error of linear-probing. This bound depends on two measures of feature variability--within-class dispersion and variation along the line between class centers. We show that directional variation dominates the bound and that the within-class dispersion's effect diminishes as the number of labeled samples increases. These properties enable CL and NSCL-trained representations to support accurate few-shot label recovery using simple linear probes. Finally, we empirically validate our theoretical findings: the gap between CL and NSCL losses decays at a rate of $\mathcal{O}(\frac{1}{\#\text{classes}})$; the two losses are highly correlated; minimizing the CL loss implicitly brings the NSCL loss close to the value achieved by direct minimization; and the proposed few-shot error bound provides a tight estimate of probing performance in practice.

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