{"ID":2849610,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.23288","arxiv_id":"2510.23288","title":"Learning from Frustration: Torsor CNNs on Graphs","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.","short_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 est...","url_abs":"https://arxiv.org/abs/2510.23288","url_pdf":"https://arxiv.org/pdf/2510.23288v1","authors":"[\"Daiyuan Li\",\"Shreya Arya\",\"Robert Ghrist\"]","published":"2025-10-27T12:59:45Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.AT\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}