Neural Point-Forms
The paper titled 'Neural Point-Forms' introduces a new family of learnable geometric features for point clouds. These features, called neural point-forms (NPFs), utilize Laplacian-based techniques to compare differential forms on point clouds. The authors demonstrate that NPFs provide a competitive and interpretable representation, particularly in scenarios where labels depend on sampling density and manifold-like structures.
- ▪Neural point-forms (NPFs) are introduced as a new family of learnable geometric features for point clouds.
- ▪The approach uses Laplacian-based techniques from Diffusion Geometry to compare differential forms on point clouds.
- ▪NPFs yield a compact, efficient, and permutation-invariant neural layer that outputs a learned form-comparison matrix.
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Computer Science > Machine Learning arXiv:2605.15524 (cs) [Submitted on 15 May 2026] Title:Neural Point-Forms Authors:Bruno Trentini, Jacob Hume, Vincenzo Antonio Isoldi, Philipp Misof, Ekaterina S. Ivshina, Kelly Maggs View a PDF of the paper titled Neural Point-Forms, by Bruno Trentini and 5 other authors View PDF HTML (experimental) Abstract:Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature space. Yet much of this geometry is not captured directly by coordinates, pairwise distances, or learned graph neighborhoods alone. In the smooth setting, differential forms are devices to encode higher order tangency information.
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