Expressive Sign Equivariant Networks for Spectral Geometric Learning

TL;DR

This paper introduces sign equivariant neural networks that respect eigenvector sign structures, improving tasks like orthogonal models and node encoding in graphs, with provable expressiveness and demonstrated benefits.

Contribution

The work develops novel sign equivariant neural architectures based on analytic characterization, addressing limitations of sign invariance in spectral geometric learning.

Findings

Sign equivariance enhances orthogonal and node encoding tasks.

Proposed models have provable expressiveness properties.

Synthetic experiments confirm theoretical benefits.

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. Code is available at https://github.com/cptq/Sign-Equivariant-Nets.