Sheaf Neural Networks and biomedical applications

TL;DR

This work introduces Sheaf Neural Networks (SNNs) as a generalization of Graph Neural Networks by equipping graphs with a sheaf structure and a corresponding sheaf Laplacian diffusion operator $\mathcal{L}_{\mathcal{F}} = \delta^\top \delta$. It applies SNNs to a biomedical graph derived from osteosarcoma XANES spectra and shows that the SNN variant with learned, general sheaves (SheafGeneral) outperforms standard GNNs such as GCN, GAT, and GraphSAGE in binary tissue classification. The results demonstrate improved expressive power and generalization for node classification on biomedical graphs, validating the approach and suggesting future work on clustering and multi-graph analyses. The study highlights the potential of sheaf-based representations to capture richer inter-node relationships beyond conventional adjacency-based diffusion.

Abstract

The purpose of this paper is to elucidate the theory and mathematical modelling behind the sheaf neural network (SNN) algorithm and then show how SNN can effectively answer to biomedical questions in a concrete case study and outperform the most popular graph neural networks (GNNs) as graph convolutional networks (GCNs), graph attention networks (GAT) and GraphSage.

Figures (2)

• Figure 1: Irreducible open sets for the Alexandrov topology on graphs
• Figure 2: Training and evaluation workflow for each cross-validation iteration.

Theorems & Definitions (2)

• Definition 2.1
• Example 2.2