{"ID":2850801,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21706","arxiv_id":"2510.21706","title":"Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions","abstract":"We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\\mathbf{y}, g \\cdot \\mathbf{y})$, 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 $G:= (R_m \\times \\mathbb{Z}_n \\times \\mathbb{Z}_n)$, 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.","short_abstract":"We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\\mathbf{y}, g \\cdot \\mathbf{y})$, 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...","url_abs":"https://arxiv.org/abs/2510.21706","url_pdf":"https://arxiv.org/pdf/2510.21706v1","authors":"[\"Tobias Schmidt\",\"Steffen Schneider\",\"Matthias Bethge\"]","published":"2025-10-24T17:59:46Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}