{"ID":2855443,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.14146","arxiv_id":"2510.14146","title":"PoissonNet: A Local-Global Approach for Learning on Surfaces","abstract":"Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient computational overhead. Drawing from classic local-global approaches in mesh processing, we introduce PoissonNet, a novel neural architecture that overcomes all of these deficiencies by formulating a local-global learning scheme, which uses Poisson's equation as the primary mechanism for feature propagation. Our core network block is simple; we apply learned local feature transformations in the gradient domain of the mesh, then solve a Poisson system to propagate scalar feature updates across the surface globally. Our local-global learning framework preserves the features's full frequency spectrum and provides a truly global receptive field, while remaining agnostic to mesh triangulation. Our construction is efficient, requiring far less compute overhead than comparable methods, which enables scalability -- both in the size of our datasets, and the size of individual training samples. These qualities are validated on various experiments where, compared to previous intrinsic architectures, we attain state-of-the-art performance on semantic segmentation and parameterizing highly-detailed animated surfaces. Finally, as a central application of PoissonNet, we show its ability to learn deformations, significantly outperforming state-of-the-art architectures that learn on surfaces.","short_abstract":"Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient computational overhead. Drawing from classic local-global approaches in mesh proce...","url_abs":"https://arxiv.org/abs/2510.14146","url_pdf":"https://arxiv.org/pdf/2510.14146v1","authors":"[\"Arman Maesumi\",\"Tanish Makadia\",\"Thibault Groueix\",\"Vladimir G. Kim\",\"Daniel Ritchie\",\"Noam Aigerman\"]","published":"2025-10-15T22:25:44Z","proceeding":"cs.GR","tasks":"[\"cs.GR\",\"cs.CV\",\"cs.LG\"]","methods":"[]","has_code":false}