  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 linear maps, for which we prove
an efficient pooling-and-broadcasting implementation.
