About contrastive unsupervised representation learning for classification and its convergence

TL;DR

This paper extends theoretical understanding of contrastive unsupervised representation learning, providing convergence guarantees and analyzing its effectiveness for multi-class classification with multiple negatives.

Contribution

It introduces new theoretical results on convergence and performance guarantees for contrastive learning with multiple negatives and multiway classification.

Findings

Convergence guarantees for contrastive training with gradient descent.

Performance bounds for multi-class classification.

Numerical experiments supporting theoretical results.

Abstract

Contrastive representation learning has been recently proved to be very efficient for self-supervised training. These methods have been successfully used to train encoders which perform comparably to supervised training on downstream classification tasks. A few works have started to build a theoretical framework around contrastive learning in which guarantees for its performance can be proven. We provide extensions of these results to training with multiple negative samples and for multiway classification. Furthermore, we provide convergence guarantees for the minimization of the contrastive training error with gradient descent of an overparametrized deep neural encoder, and provide some numerical experiments that complement our theoretical findings