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[2510.01022] VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks
Summary
The paper introduces Vector Diffusion Wavelets (VDWs) for geometric graph neural networks (VDW-GNNs), demonstrating their effectiveness on synthetic and real-world data.
Why It Matters
This research is significant as it presents a novel approach to enhance geometric graph neural networks using vector diffusion wavelets, potentially improving data analysis in various applications, including neural activity and environmental data.
Key Takeaways
- VDWs are a new family of wavelets inspired by vector diffusion maps.
- VDW-GNNs show effectiveness on both synthetic and real-world datasets.
- Theoretical proofs confirm desirable properties of the new wavelets.
- VDWs maintain symmetries with respect to rotations and translations.
- This approach could advance the field of geometric deep learning.
Computer Science > Machine Learning arXiv:2510.01022 (cs) [Submitted on 1 Oct 2025 (v1), last revised 12 Feb 2026 (this version, v2)] Title:VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks Authors:David R. Johnson, Alexander Sietsema, Rishabh Anand, Deanna Needell, Smita Krishnaswamy, Michael Perlmutter View a PDF of the paper titled VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks, by David R. Johnson and 5 other authors View PDF HTML (experimental) Abstract:We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind-field measurements and neural activity data. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have desirable symmetries with respect to rotations and translations. Comments: Subjects: Machine Learning (cs.LG); Signal Processing (eess.SP); Machine Learning (stat.ML) MSC classes: 68T07 ACM classes: I.5.1; I.2.6 Cite as: arXiv:2510.01022 [cs.LG] (or arXiv:2510.01022v2 [cs.LG] f...
