Learning from Frustration: Torsor CNNs on Graphs

• URL: http://arxiv.org/abs/2510.23288v1
• Date: Mon, 27 Oct 2025 12:59:45 GMT
• Title: Learning from Frustration: Torsor CNNs on Graphs
• Authors: Daiyuan Li, Shreya Arya, Robert Ghrist,
• Abstract summary: We introduce Torsor CNNs, a framework for learning on graphs with local symmetries encoded as edge potentials.<n>We demonstrate its applicability to multi-view 3D recognition, where relative camera poses naturally define the required edge potentials.
• Score: 0.4369550829556577
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Most equivariant neural networks rely on a single global symmetry, limiting their use in domains where symmetries are instead local. We introduce Torsor CNNs, a framework for learning on graphs with local symmetries encoded as edge potentials-- group-valued transformations between neighboring coordinate frames. We establish that this geometric construction is fundamentally equivalent to the classical group synchronization problem, yielding: (1) a Torsor Convolutional Layer that is provably equivariant to local changes in coordinate frames, and (2) the frustration loss--a standalone geometric regularizer that encourages locally equivariant representations when added to any NN's training objective. The Torsor CNN framework unifies and generalizes several architectures--including classical CNNs and Gauge CNNs on manifolds-- by operating on arbitrary graphs without requiring a global coordinate system or smooth manifold structure. We establish the mathematical foundations of this framework and demonstrate its applicability to multi-view 3D recognition, where relative camera poses naturally define the required edge potentials.

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