Incidence Networks for Geometric Deep Learning

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors, analyze their structure, and present the family of equivariant networks that operate on them. We show that any incidence tensor decomposes into invariant subsets. This decomposition, in turn, leads to a decomposition of the corresponding equivariant layer that allows efficient and intuitive pooling-and-broadcasting implementation, for both dense and sparse tensors. We demonstrate the effectiveness of this family of networks by reporting state-of-the-art on graph learning tasks for many targets in the QM9 dataset.