Sign and Basis Invariant Networks for Spectral Graph Representation Learning

TL;DR

This paper introduces SignNet and BasisNet, neural architectures that are invariant to eigenvector sign flips and basis changes, enhancing spectral graph representation learning with proven universality and superior empirical performance.

Contribution

The paper presents novel invariant neural networks for spectral graph analysis, with theoretical universality and improved expressiveness over existing spectral methods.

Findings

Networks outperform baselines on molecular graph regression

They are more expressive than existing spectral graph methods

Experiments demonstrate significant performance improvements

Abstract

We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet .