This academic article discusses the limitations of Graph Neural Networks (GNNs) in discerning higher-order interactions in complex systems. A novel approach is proposed, which uses the mathematical theory of simplicial complexes (SCs) to model these interactions. The authors introduce a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. The article also presents a new Higher-order Graph Convolutional Network (HiGCN) based on FP Laplacians. This network is capable of identifying intrinsic features across varying topological scales. The authors assert that their method achieves state-of-the-art performance on a range of graph tasks and offers a scalable and flexible solution to explore higher-order interactions in graphs.
Publication date: 25 Sep 2023
Project Page: Not provided
Paper: https://arxiv.org/pdf/2309.12971
