@inproceedings{
zhang2024schur,
title={Schur Nets: exploiting local structure for equivariance in higher order graph neural networks},
author={QINGQI ZHANG and Ruize Xu and Risi Kondor},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=HRnSVflpgt}
}
Several recent works have shown that extending the message passing paradigm to subgraphs communicating with other subgraphs, especially via higher order messages, can boost the expressivity of graph neural networks. In such architectures, to faithfully account for local structure such as cycles, the local operations must be equivariant to the automorphism group of the local environment. 
However, enumerating the automorphism groups of all subgraphs of interest and finding appropriate equivariant operations for each one of them separately is generally not feasible. In this paper we propose a solution to this problem based on spectral graph theory that bypasses 
having to determine the automorphism group entirely and constructs a basis for equivariant operations directly from the graph Laplacian. 
We show that empirically this approach can boost the performance of GNNs.
Schur Nets: exploiting local structure for equivariance in higher order graph neural networks
QINGQI ZHANG Ruize Xu Risi Kondor