Sign and Basis Invariant Networks for Spectral Graph Representation Learning
This work addresses the challenge of handling symmetries in spectral graph representation learning for applications such as molecular modeling and mesh processing, representing an incremental improvement over prior methods.
The authors tackled the problem of learning from graph eigenvectors by introducing SignNet and BasisNet, which are invariant to sign flips and basis symmetries, and demonstrated that these networks outperform existing baselines in tasks like molecular graph regression and learning neural fields on triangle meshes, with significant performance gains.
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 .