On the duality between contrastive and non-contrastive self-supervised learning

TL;DR

This paper explores the theoretical connections between contrastive and non-contrastive self-supervised learning methods, demonstrating their equivalence under certain conditions and showing how careful tuning can improve performance and unify state-of-the-art approaches.

Contribution

It establishes a theoretical equivalence between contrastive and non-contrastive criteria, and demonstrates how hyperparameter tuning can significantly enhance non-contrastive methods like SimCLR.

Findings

Contrastive and non-contrastive methods can be algebraically related and are often equivalent under limited assumptions.

Careful hyperparameter tuning can improve SimCLR's performance to match VICReg.

Large output dimensions are not necessary for effective non-contrastive learning.

Abstract

Recent approaches in self-supervised learning of image representations can be categorized into different families of methods and, in particular, can be divided into contrastive and non-contrastive approaches. While differences between the two families have been thoroughly discussed to motivate new approaches, we focus more on the theoretical similarities between them. By designing contrastive and covariance based non-contrastive criteria that can be related algebraically and shown to be equivalent under limited assumptions, we show how close those families can be. We further study popular methods and introduce variations of them, allowing us to relate this theoretical result to current practices and show the influence (or lack thereof) of design choices on downstream performance. Motivated by our equivalence result, we investigate the low performance of SimCLR and show how it can match VICReg's with careful hyperparameter tuning, improving significantly over known baselines. We also challenge the popular assumption that non-contrastive methods need large output dimensions. Our theoretical and quantitative results suggest that the numerical gaps between contrastive and non-contrastive methods in certain regimes can be closed given better network design choices and hyperparameter tuning. The evidence shows that unifying different SOTA methods is an important direction to build a better understanding of self-supervised learning.