  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}.
