DeepAI AI Chat
Log In Sign Up

Weisfeiler and Lehman Go Cellular: CW Networks

by   Cristian Bodnar, et al.

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models are severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph “lifting” transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and, in certain cases, not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higher-order signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.


page 1

page 2

page 3

page 4


CIN++: Enhancing Topological Message Passing

Graph Neural Networks (GNNs) have demonstrated remarkable success in lea...

From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networ...

Simplicial Attention Networks

Graph representation learning methods have mostly been limited to the mo...

Neural Message Passing on High Order Paths

Graph neural network have achieved impressive results in predicting mole...

Provably expressive temporal graph networks

Temporal graph networks (TGNs) have gained prominence as models for embe...

Topological Graph Signal Compression

Recently emerged Topological Deep Learning (TDL) methods aim to extend c...

Cell Complex Neural Networks

Cell complexes are topological spaces constructed from simple blocks cal...

Code Repositories


Message Passing on Simplicial and Cell Complexes

view repo