RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

arXiv:2505.13289v4 Announce Type: replace-cross 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 $g\in G$ 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.