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Schmidt, T. ; Schneider, S. ; Bethge, M.*

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

In: (39th Conference on Neural Information Processing Systems, NeurIPS 2025, 02-07 December 2025, San Diego). 2025. 79850-79890 (Advances in Neural Information Processing Systems ; 38)
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. 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.
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Publikationstyp Artikel: Konferenzbeitrag
ISSN (print) / ISBN 1049-5258
Konferenztitel 39th Conference on Neural Information Processing Systems, NeurIPS 2025
Konferzenzdatum 02-07 December 2025
Konferenzort San Diego
Quellenangaben Band: 38, Heft: , Seiten: 79850-79890 Artikelnummer: , Supplement: ,
Institut(e) Institute of Computational Biology (ICB)