CIN++: Enhancing Topological Message Passing

TL;DR

CIN++ improves graph neural networks by incorporating comprehensive topological message passing, enabling better modeling of complex, higher-order, and long-range interactions in graph-structured data.

Contribution

This work introduces CIN++, a novel enhancement to Cellular Isomorphism Networks that incorporates lower messages for more expressive topological representations.

Findings

Achieves state-of-the-art results on large-scale chemistry benchmarks.

Effectively models long-range interactions in complex systems.

Enhances the expressive power of topological message passing.

Abstract

Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, they face significant limitations in expressive power, struggling with long-range interactions and lacking a principled approach to modeling higher-order structures and group interactions. Cellular Isomorphism Networks (CINs) recently addressed most of these challenges with a message passing scheme based on cell complexes. Despite their advantages, CINs make use only of boundary and upper messages which do not consider a direct interaction between the rings present in the underlying complex. Accounting for these interactions might be crucial for learning representations of many real-world complex phenomena such as the dynamics of supramolecular assemblies, neural activity within the brain, and gene regulation processes. In this work, we propose CIN++, an enhancement of the topological message passing scheme introduced in CINs. Our message passing scheme accounts for the aforementioned limitations by letting the cells to receive also lower messages within each layer. By providing a more comprehensive representation of higher-order and long-range interactions, our enhanced topological message passing scheme achieves state-of-the-art results on large-scale and long-range chemistry benchmarks.