Towards Stable, Globally Expressive Graph Representations with Laplacian Eigenvectors

ArXi:2410.09737v2 Announce Type: replace A popular way to improve the expressive power of graph neural networks (GNNs) is to use Laplacian eigenvectors as additional node features, since they can serve both as structural identifiers and global coordinates of nodes. Properly handling the orthogonal group symmetry among eigenvectors is crucial for the stability and generalizability of Laplacian eigenvector augmented GNNs. Previous studies have shown that using a naive $O(p)$-group invariant encoder for each $p$-dimensional eigenspace often leads to expressivity loss and numerical instability.