RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

• URL: http://arxiv.org/abs/2505.13289v1
• Date: Mon, 19 May 2025 16:10:23 GMT
• Title: RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization
• Authors: Alonso Urbano, David W. Romero, Max Zimmer, Sebastian Pokutta,
• Abstract summary: We introduce RECON, a framework to discover each input's intrinsic symmetry distribution from unlabeled data.<n>We demonstrate effective symmetry discovery on 2D image benchmarks and -- for the first time -- extend it to 3D transformation groups.
• Score: 29.869911304798553
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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