Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks

Understand

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems.

• However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited.
• To overcome these limitations, we propose Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs).
• To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs.