Variance Covariance Regularization Enforces Pairwise Independence in Self-Supervised Representations

Grégoire Mialon, Randall Balestriero, Yann LeCun

Keywords: Self-supervised learning, VICReg, Barlow Twins, HSIC

TL;DR: We study how SSL methods such as VICReg and Barlow Twins enforce pairwise independence of representations via their Variance Covariance regularization (VCReg), improve VICReg using our findings and show VCReg to be beneficial outside of SSL.

Abstract: Self-Supervised Learning (SSL) methods such as VICReg, Barlow Twins or W-MSE avoid collapse of their joint embedding architectures by constraining or regularizing the covariance matrix of their projector’s output. This study highlights important properties of such strategy, which we coin Variance-Covariance regularization (VCReg). More precisely, we show that VCReg enforces pairwise independence between the features of the learned representation. This result emerges by bridging VCReg applied on the projector’s output to kernel independence criteria applied on the projector’s input. This provides the first theoretical motivations and explanations of VCReg. We empirically validate our findings where (i) we put in evidence which projector’s characteristics favor pairwise independence, (ii) we use these findings to obtain nontrivial performance gains for VICReg, (iii) we demonstrate that the scope of VCReg goes beyond SSL by using it to solve Independent Component Analysis. We hope that our findings will support the adoption of VCReg in SSL and beyond.

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