Learning Structured Representations with Equivariant Contrastive Learning

Sharut Gupta, Joshua Robinson, Derek Lim, Soledad Villar, Stefanie Jegelka

Keywords: Self supervised learning, Equivariance, Contrastive learning

TL;DR: We add additional geometric structure to the embedding space of contrastive learning by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space.

Abstract: Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an _equivariance_ objective and theoretically prove that its minima forces augmentations on input space to correspond to _rotations_ on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: **C**ontrastive **A**ugmentation-induced **R**otational **E**quivariance, leads to improved performance on downstream tasks and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve.

Type Of Submission: Extended Abstract (4 pages, non-archival)

Submission Number: 64