用向量扩散小波提升几何图神经网络，对旋转平移有良好稳定性。
VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks
- 基于流形切空间数据设计新型向量扩散小波
- 在点云、风场和神经活动数据上表现优异
- 具备旋转平移对称性，适合几何结构数据建模
我们引入了向量扩散小波（VDWs），一种受向量扩散映射算法启发的新颖小波族，该算法用于分析位于黎曼流形切空间中的数据。我们证明这些小波可有效融入一类几何图神经网络，称为VDW-GNNs。实验表明，该网络在合成点云数据及真实世界数据（如风场与神经活动测量）上均表现良好。理论上，我们证明这些新小波具有类似传统扩散小波的优良框架性质；此外，还证明其对旋转和平移操作具有有用对称性。
原文摘要 · Abstract (English)
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 and neural activity measurements. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have useful symmetries with respect to rotations and translations.
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