تقرير
Bundle Neural Networks for message diffusion on graphs
العنوان: | Bundle Neural Networks for message diffusion on graphs |
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المؤلفون: | Bamberger, Jacob, Barbero, Federico, Dong, Xiaowen, Bronstein, Michael |
سنة النشر: | 2024 |
المجموعة: | Computer Science |
مصطلحات موضوعية: | Computer Science - Machine Learning |
الوصف: | The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited node-level expressivity. To address these limitations we propose Bundle Neural Networks (BuNN), a new type of GNN that operates via message diffusion over flat vector bundles - structures analogous to connections on Riemannian manifolds that augment the graph by assigning to each node a vector space and an orthogonal map. A BuNN layer evolves the features according to a diffusion-type partial differential equation. When discretized, BuNNs are a special case of Sheaf Neural Networks (SNNs), a recently proposed MPNN capable of mitigating over-smoothing. The continuous nature of message diffusion enables BuNNs to operate on larger scales of the graph and, therefore, to mitigate over-squashing. Finally, we prove that BuNN can approximate any feature transformation over nodes on any (potentially infinite) family of graphs given injective positional encodings, resulting in universal node-level expressivity. We support our theory via synthetic experiments and showcase the strong empirical performance of BuNNs over a range of real-world tasks, achieving state-of-the-art results on several standard benchmarks in transductive and inductive settings. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2405.15540 |
رقم الأكسشن: | edsarx.2405.15540 |
قاعدة البيانات: | arXiv |
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