Sheaf Neural Networks with Connection Laplacians

06/17/2022
by   Federico Barbero, et al.
109

A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have useful theoretical properties that help tackle issues arising from heterophily and over-smoothing. One complication intrinsic to these models is finding a good sheaf for the task to be solved. Previous works proposed two diametrically opposed approaches: manually constructing the sheaf based on domain knowledge and learning the sheaf end-to-end using gradient-based methods. However, domain knowledge is often insufficient, while learning a sheaf could lead to overfitting and significant computational overhead. In this work, we propose a novel way of computing sheaves drawing inspiration from Riemannian geometry: we leverage the manifold assumption to compute manifold-and-graph-aware orthogonal maps, which optimally align the tangent spaces of neighbouring data points. We show that this approach achieves promising results with less computational overhead when compared to previous SNN models. Overall, this work provides an interesting connection between algebraic topology and differential geometry, and we hope that it will spark future research in this direction.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/17/2021

A singular Riemannian geometry approach to Deep Neural Networks II. Reconstruction of 1-D equivalence classes

In a previous work, we proposed a geometric framework to study a deep ne...
research
09/28/2020

Graph Neural Networks with Heterophily

Graph Neural Networks (GNNs) have proven to be useful for many different...
research
08/25/2022

Domain-informed graph neural networks: a quantum chemistry case study

We explore different strategies to integrate prior domain knowledge into...
research
11/26/2022

Latent Graph Inference using Product Manifolds

Graph Neural Networks usually rely on the assumption that the graph topo...
research
07/31/2023

MRA-GNN: Minutiae Relation-Aware Model over Graph Neural Network for Fingerprint Embedding

Deep learning has achieved remarkable results in fingerprint embedding, ...
research
12/18/2022

Influence-Based Mini-Batching for Graph Neural Networks

Using graph neural networks for large graphs is challenging since there ...

Please sign up or login with your details

Forgot password? Click here to reset