RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization
This addresses the challenge of handling unknown symmetries in data for machine learning applications, offering a novel approach to enhance model invariance and performance, though it builds incrementally on class-pose decomposition concepts.
The paper tackles the problem of unknown, instance-specific symmetries in real-world data by introducing RECON, a method for canonical orientation normalization that corrects arbitrary canonical representations via right-multiplication, enabling unsupervised symmetry discovery, out-of-distribution pose detection, and test-time canonicalization. It demonstrates results on 2D image benchmarks and extends symmetry discovery to 3D groups for the first time, improving downstream performance without retraining.
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 $\textit{canonical orientation normalization}$ that corrects arbitrary canonicals via a simple right-multiplication, yielding $\textit{natural}$, 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.