Structuring Representation Geometry with Rotationally Equivariant Contrastive Learning

TL;DR

This paper introduces CARE, a contrastive learning method that enforces rotational equivariance in the embedding space, improving downstream task performance and capturing meaningful data variations.

Contribution

It presents a novel equivariance objective for contrastive learning that aligns input augmentations with rotations in the embedding space, supported by theoretical proof.

Findings

Improved downstream task performance.

Embedding space sensitivity to data variations.

Non-trivial representations without invariance.

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: Contrastive Augmentation-induced Rotational Equivariance, 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. Code is available at https://github.com/Sharut/CARE.