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

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y,g y), where g is 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.