LanczosNet: Multi-Scale Deep Graph Convolutional Networks

TL;DR

LanczosNet introduces a multi-scale deep graph convolutional network leveraging the Lanczos algorithm for efficient low-rank Laplacian approximation, enabling learnable spectral filters and state-of-the-art performance on graph tasks.

Contribution

It presents LanczosNet, a novel graph neural network using the Lanczos algorithm for scalable multi-scale spectral filtering and node embedding learning.

Findings

Achieves state-of-the-art results on citation networks.

Effectively captures multi-scale graph information.

Demonstrates strong performance on quantum chemistry dataset.

Abstract

We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only efficiently exploit multi-scale information via fast approximated computation of matrix power but also design learnable spectral filters. Being fully differentiable, LanczosNet facilitates both graph kernel learning as well as learning node embeddings. We show the connection between our LanczosNet and graph based manifold learning methods, especially the diffusion maps. We benchmark our model against several recent deep graph networks on citation networks and QM8 quantum chemistry dataset. Experimental results show that our model achieves the state-of-the-art performance in most tasks. Code is released at: \url{https://github.com/lrjconan/LanczosNetwork}.