An Information-Theoretic Perspective on Variance-Invariance-Covariance Regularization
arxiv(2023)
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.
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