LanczosNet: Multi-Scale Deep Graph Convolutional Networks
Renjie Liao1,2,3, Zhizhen Zhao4, Raquel Urtasun1,2,3, Richard S. Zemel1,3,5 University of Toronto1, Uber ATG Toronto2, Vector Institute3, University of Illinois at Urbana-Champaign4, Canadian Institute for Advanced Research5 {rjliao, urtasun,
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: https://github.com/lrjconan/LanczosNetwork.
中文速览
图神经网络在处理图结构数据时，存在两大痛点：难以高效利用多尺度信息，以及谱域滤波器不可学习、表达能力有限。论文提出了 Lanczos 网络（LanczosNet），借助数值线性代数中的 Lanczos 算法对图拉普拉斯矩阵做低秩近似，用所得的三对角分解同时解决上述两个问题——利用对角矩阵的幂运算快速获取多尺度扩散信息，同时用 MLP 参数化 Ritz 值上的谱滤波器，使滤波函数完全可学习；进一步提出可自适应学习图核与节点嵌入的 AdaLanczosNet 变体，通过对整个 Lanczos 算法反向传播实现端到端训练。在引文网络分类和 QM8 量子化学回归等基准任务上，LanczosNet 在大多数任务中达到了当时最优性能，表明将经典数值方法与深度图网络结合是提升图表示学习能力的有效途径。
原文 arXiv:1901.01484;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1901.01484v2