RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

Abstract: Real-world data often exhibits unknown or approximate symmetries, yet existing equivariant networks must commit to a fixed transformation group prior to training, e.g., continuous $SO(2)$ rotations. This mismatch degrades performance when the actual data symmetries differ from those in the transformation group. We introduce RECON, a framework to discover each input's intrinsic symmetry distribution from unlabeled data. RECON leverages class-pose decompositions and applies a data-driven normalization to align arbitrary reference frames into a common natural pose, yielding directly comparable and interpretable symmetry descriptors. We demonstrate effective symmetry discovery on 2D image benchmarks and -- for the first time -- extend it to 3D transformation groups, paving the way towards more flexible equivariant modeling.