## Towards the Generalization of Contrastive Self-Supervised Learning

### Weiran Huang*, Mingyang Yi*, Xuyang Zhao*

Published in arXiv:2111.00743, 2021

### Abstract

Recently, self-supervised learning has attracted great attention, since it only requires unlabeled data for training. Contrastive learning is one popular method for self-supervised learning and has achieved promising empirical performance. However, the theoretical understanding of its generalization ability is still limited. To this end, we define a kind of $(\sigma,\delta)$-measure to mathematically quantify the data augmentation, and then provide an upper bound of the downstream classification error based on the measure. We show that the generalization ability of contrastive self-supervised learning depends on three key factors: alignment of positive samples, divergence of class centers, and concentration of augmented data. The first two factors can be optimized by contrastive algorithms, while the third one is priorly determined by pre-defined data augmentation. With the above theoretical findings, we further study two canonical contrastive losses, InfoNCE and cross-correlation loss, and prove that both of them are indeed able to satisfy the first two factors. Moreover, we empirically verify the third factor by conducting various experiments on the real-world dataset, and show that our theoretical inferences on the relationship between the data augmentation and the generalization of contrastive self-supervised learning agree with the empirical observations.