Towards the Generalization of Contrastive Self-Supervised Learning

TL;DR

This paper provides a theoretical framework for understanding the generalization of contrastive self-supervised learning, linking it to data augmentation, representation alignment, and class divergence, supported by empirical validation.

Contribution

It introduces a $(\sigma,\delta)$-measure to quantify data augmentation and derives an upper bound on classification error, connecting theoretical insights with practical contrastive loss functions.

Findings

Generalization depends on data augmentation, representation alignment, and class divergence.

InfoNCE and cross-correlation losses achieve key representation properties.

Stronger data concentration correlates with better downstream performance.

Abstract

Recently, self-supervised learning has attracted great attention, since it only requires unlabeled data for model training. Contrastive learning is one popular method for self-supervised learning and has achieved promising empirical performance. However, the theoretical understanding of its generalization ability is still limited. To this end, we define a kind of $(\sigma,\delta)$-measure to mathematically quantify the data augmentation, and then provide an upper bound of the downstream classification error rate based on the measure. It reveals that the generalization ability of contrastive self-supervised learning is related to three key factors: alignment of positive samples, divergence of class centers, and concentration of augmented data. The first two factors are properties of learned representations, while the third one is determined by pre-defined data augmentation. We further investigate two canonical contrastive losses, InfoNCE and cross-correlation, to show how they provably achieve the first two factors. Moreover, we conduct experiments to study the third factor, and observe a strong correlation between downstream performance and the concentration of augmented data.