An Information Theory Perspective on Variance-Invariance-Covariance Regularization

Ravid Shwartz-Ziv, Randall Balestriero, Kenji Kawaguchi, Tim G. J. Rudner, Yann LeCun

Keywords: Self-Supervised Learning, Generalization Bounds, Information-Theory, Deep Neural Networks

TL;DR: This paper provides an information-theoretic analysis of the VICReg method in self-supervised learning, introduces a family of improved SSL techniques based on these principles, and sets the stage for enhanced transfer learning research.

Abstract: Variance-Invariance-Covariance Regularization (VICReg) is a self-supervised learning (SSL) method that has shown promising results on a variety of tasks. However, the fundamental mechanisms underlying VICReg remain unexplored. In this paper, we present an information-theoretic perspective on the VICReg objective. We begin by deriving information-theoretic quantities for deterministic networks as an alternative to unrealistic stochastic network assumptions. We then relate the optimization of the VICReg objective to mutual information optimization, highlighting underlying assumptions and facilitating a constructive comparison with other SSL algorithms and derive a generalization bound for VICReg, revealing its inherent advantages for downstream tasks. Building on these results, we introduce a family of SSL methods derived from information-theoretic principles that outperform existing SSL techniques.

Submission Number: 116