Toward Understanding the Feature Learning Process of Self-supervised Contrastive Learning

How can neural networks trained by contrastive learning extract features from the unlabeled data? Why does contrastive learning usually need much stronger data augmentations than supervised learning to ensure good representations? These questions involve both the optimization and statistical aspects of deep learning, but can hardly be answered by the analysis of supervised learning, where the target functions are the highest pursuit. Indeed, in self-supervised learning, it is inevitable to relate to the optimization/generalization of neural networks to how they can encode the latent structures in the data, which we refer to as the feature learning process. In this work, we formally study how contrastive learning learns the feature representations for neural networks by analyzing its feature learning process. We consider the case where our data are comprised of two types of features: the more semantically aligned sparse features which we want to learn from, and the other dense features we want to avoid. Theoretically, we prove that contrastive learning using ReLU networks provably learns the desired sparse features if proper augmentations are adopted. We present an underlying principle called feature decoupling to explain the effects of augmentations, where we theoretically characterize how augmentations can reduce the correlations of dense features between positive samples while keeping the correlations of sparse features intact, thereby forcing the neural networks to learn from the self-supervision of sparse features. Empirically, we verified that the feature decoupling principle matches the underlying mechanism of contrastive learning in practice. V1 appeared on June 1, 2021. V2 polished writing and added citations, V3 corrected related works. We would like to thank Zeyuan Allen-Zhu for many helpful suggestions on the experiments, and thank Qi Lei, Jason D. Lee for clarifying results of their paper.