RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

2025-05-19

AI Summary

Real-world data often exhibit unknown or approximate symmetries, yet existing equivariant networks require prespecified transformation groups (e.g., SO(2)), leading to misalignment between the imposed group structure and the data’s intrinsic symmetries—thereby degrading generalization. To address this, we propose the first sample-level symmetry discovery framework for unlabeled data: it employs class-pose disentangled modeling and data-driven explicit canonical orientation normalization to automatically align inputs to a natural reference frame, enabling interpretable and comparable symmetry distribution estimation. Our method is the first to extend such symmetry discovery to the 3D rotation group SO(3) and the rigid-body motion group SE(3), eliminating reliance on predefined groups in equivariant learning. Extensive evaluation on 2D and 3D benchmarks demonstrates substantial improvements in model flexibility and generalization. This work establishes a new paradigm—shifting equivariant learning from “group-prior-driven” design to “data-driven symmetry perception.”

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Visual Reasoning & Symbolic Representations
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Discover intrinsic symmetry distribution from unlabeled data
• Align arbitrary reference frames into common natural pose
• Extend symmetry discovery to 3D transformation groups

Innovation

• Discovers intrinsic symmetry distribution from unlabeled data
• Uses class-pose decompositions for data-driven normalization
• Aligns arbitrary reference frames into common natural pose