An Information-Theoretic Perspective on Variance-Invariance-Covariance Regularization

In this paper, we provide an information-theoretic perspective on Variance-Invariance-Covariance Regularization (VICReg) for self-supervised learning. To do so, we first demonstrate how information-theoretic quantities can be obtained for deterministic networks as an alternative to the commonly used unrealistic stochastic networks assumption. Next, we relate the VICReg objective to mutual information maximization and use it to highlight the underlying assumptions of the objective. Based on this relationship, we derive a generalization bound for VICReg, providing generalization guarantees for downstream supervised learning tasks and present new self-supervised learning methods, derived from a mutual information maximization objective, that outperform existing methods in terms of performance. This work provides a new information-theoretic perspective on self-supervised learning and Variance-Invariance-Covariance Regularization in particular and guides the way for improved transfer learning via information-theoretic self-supervised learning objectives.