  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.
