Why Barlow Twins Work: The Critical Role of Normalization and Its Link to Sample Contrastive Learning

Hans-Oliver Hansen, Marius Jahrens, Thomas Martinetz

Keywords: self-supervised Learning, pretaining, cross-correlation matrix, covariance matrix, diagonalization

TL;DR: We highlight the importance of normalization in the Barlow Twins framework for self-supervised learning, showing that it shifts the objective from feature contrastive learning to sample contrastive learning.

Abstract: Barlow Twins is a feature-contrastive self-supervised learning framework built on the principle of redundancy reduction. The idea is to train a network by maximizing the correlation between corresponding features and minimizing the correlation between non-corresponding features in distorted views of the same image, through this facilitating effective pretraining of a backbone network for a subsequent classification head. This is achieved by diagonalizing the cross-correlation matrix of the network’s representations and scaling it towards the identity matrix. We show that the cross-correlation matrix of distorted images is inherently symmetric, independent of the backbone network's weights, which leads to two key insights: (i) the cross-correlation matrix can always be diagonalized using a linear transformation (layer), and (ii) the core idea of maximizing correlations between corresponding features while minimizing them for non-corresponding features alone is insufficient for effective backbone network pretraining. Nevertheless, Barlow Twins provide highly effective pretraining. We show that this is due to the normalization of the cross-correlation matrix in the Barlow Twins cost function. This normalization leads to minima of the cost function which are equivalent to the minima of sample contrastive approaches to enforce invariance.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 10174