An Information Theory Perspective on Variance-Invariance-Covariance Regularization

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.

Ravid Shwartz Ziv

AI Researcher

AI researcher at Meta MSL with a background in information theory and computational neuroscience, working on world models, memory, and compression. Former Assistant Professor and Faculty Fellow at NYU. My industry experience spans Wand AI, Intel, Google AI, and Wikipedia.