Incidence Networks for Geometric Deep Learning

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Authors

Marjan Albooyeh, Daniele Bertolini, Siamak Ravanbakhsh

Abstract

<p>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. 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.</p>