Homomorphic Self-Supervised Learning

This paper was accepted at the workshop "Self-Supervised Learning - Theory and Practice" at NeurIPS 2022.

Many state of the art self-supervised learning approaches fundamentally rely on transformations applied to the input in order to selectively extract task-relevant information. Recently, the field of equivariant deep learning has developed to introduce structure into the feature space of deep neural networks, specifically with respect to such input transformations. In this work, we observe both theoretically and empirically, that through the lens of equivariant representations, many existing self-supervised learning algorithms can be both unified and generalized. Specifically, we introduce a general framework we call Structured Self-Supervised Learning (S-SSL), and theoretically show how it may subsume the concept of input-augmentations provided a sufficiently structured representation. We validate this theory experimentally for simple augmentations, demonstrate how the framework fails when representational structure is removed, and further empirically explore how the parameters of this framework relate to those traditional augmentation-based self-supervised learning. We conclude with a discussion of the potential benefits of this framework as a new perspective on self-supervised learning.