Expressive Sign Equivariant Networks for Spectral Geometric Learning

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 spotlightEveryoneRevisionsBibTeX
Keywords: Eigenvectors, spectral, geometry, universal approximation, graph, equivariance, invariance
TL;DR: We prove that a novel type of equivariance to eigenvector symmetries is useful in several applications, and develop provably expressive networks with this equivariance.
Abstract: Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector. However, we show that sign invariance is theoretically limited for tasks such as building orthogonally equivariant models and learning node positional encodings for link prediction in graphs. In this work, we demonstrate the benefits of sign equivariance for these tasks. To obtain these benefits, we develop novel sign equivariant neural network architectures. Our models are based on a new analytic characterization of sign equivariant polynomials and thus inherit provable expressiveness properties. Controlled synthetic experiments show that our networks can achieve the theoretically predicted benefits of sign equivariant models.
Supplementary Material: zip
Submission Number: 7752
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