RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

2025/05/19 by Alonso Urbano, David W. Romero, Urbano, Alonso +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · #Computational Drug Discovery Methods #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.2505.13289

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Real world data often exhibits unknown, instance-specific symmetries that rarely exactly match a transformation group G fixed a priori. Class-pose decompositions aim to create disentangled representations by factoring inputs into invariant features and a pose g∈ G defined relative to a training-dependent, arbitrary canonical representation. We introduce RECON, a class-pose agnostic canonical orientation normalization that corrects arbitrary canonicals via a simple right translation, yielding natural, data-aligned canonicalizations. This enables (i) unsupervised discovery of instance-specific pose distributions, (ii) detection of out-of-distribution poses and (iii) a plug-and-play test-time canonicalization layer. This layer can be attached on top of any pre-trained model to infuse group invariance, improving its performance without retraining. We validate on images and molecular ensembles, demonstrating accurate symmetry discovery, and matching or outperforming other canonicalizations in downstream classification.

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Related

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• A Generative Model of Symmetry Transformations