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Equivariance by Contrast: Identifiable Equivariant Embeddings From Unlabeled Finite Group Actions

MCML Authors

Tobias Schmidt

→ Group Steffen Schneider
Dynamical Inference

Steffen Schneider

Dr.

Associate

Dynamical Inference

Abstract

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y,g·y), where gis drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps—without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group G := (Rm ×Zn ×Zn), combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group O(n) and the general linear group GL(n). We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

inproceedings SSB25