Title: RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization
Primary area: learning on graphs and other geometries & topologies
Keywords: symmetry discovery, canonicalization, equivariance

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 \textsc{recon}, a class-pose agnostic \emph{canonical orientation normalization} that corrects arbitrary canonicals via a simple right-multiplication, yielding \emph{natural}, data-aligned canonicalizations. This enables (i) unsupervised discovery of instance-specific symmetry distributions, (ii) detection of out-of-distribution poses, and (iii) test-time canonicalization, granting group invariance to pre-trained models without retraining and irrespective of model architecture, improving downstream performance. We demonstrate results on 2D image benchmarks and --for the first time-- extend symmetry discovery to 3D groups.

TL;DR: An architecture-agnostic framework to align arbitrary canonical representations in class–pose methods with the data symmetries, enabling symmetry discovery and downstream practical applications