RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

TL;DR

RECON introduces a method for data-aligned canonical orientation normalization that enables unsupervised symmetry discovery and improves model invariance without retraining.

Contribution

It provides a class-pose agnostic normalization technique that enhances symmetry detection and invariance in pre-trained models across various data types.

Findings

Accurately discovers instance-specific symmetries.

Outperforms existing canonicalization methods in classification tasks.

Works as a plug-and-play layer on pre-trained models.

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.