Pointspectrum: Equivariance Meets Laplacian Filtering for Graph Representation Learning

Graph Representation Learning (GRL) has revolutionized learning on graphs, by combining the graph’s structural information with node/edge attributes. While Graph Neural Networks (GNNs) have been used in state-of-the-art GRL architectures, they suffer from over smoothing when many GNN layers need to be stacked. In a different approach, spectral methods based on graph filtering have emerged addressing over smoothing; however, up to now, they employ traditional neural networks that cannot efficiently exploit the structure of graph data. Motivated by this, we propose PointSpectrum, a spectral method that incorporates a set equivariant network to account for graph structure. PointSpectrum enhances the efficiency and expressiveness of spectral methods, while it outperforms or competes with state-of-the-art GRL methods. Overall, PointSpectrum addresses over smoothing through graph filtering and captures a graph’s structure through set equivariance. Our findings are promising for this architectural shift for (spectral) GRL methods.