# LanczosNet: Multi-Scale Deep Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1901.01484 · HTML: https://mlsanity.com/paper/1901.01484/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2019.

## Built on by (most cited first, 30 of 73)

- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Large-Scale Chemical Language Representations Capture Molecular Structure and Properties](https://mlsanity.com/paper/2106.09553/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [LaneRCNN: Distributed Representations for Graph-Centric Motion Forecasting](https://mlsanity.com/paper/2101.06653/) (2021)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Graph-MLP: Node Classification without Message Passing in Graph](https://mlsanity.com/paper/2106.04051/) (2021)
- [Local Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2109.03856/) (2021)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [Towards Understanding the Generalization of Graph Neural Networks](https://mlsanity.com/paper/2305.08048/) (2023)
- [p-Laplacian Based Graph Neural Networks](https://mlsanity.com/paper/2111.07337/) (2021)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networks](https://mlsanity.com/paper/2212.10822/) (2022)
- [Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks](https://mlsanity.com/paper/2201.08932/) (2022)
- [PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems](https://mlsanity.com/paper/2410.01337/) (2024)
- [Spatio-Spectral Graph Neural Networks](https://mlsanity.com/paper/2405.19121/) (2024)
- [Beyond Message Passing: Neural Graph Pattern Machine](https://mlsanity.com/paper/2501.18739/) (2025)
- [Graph Attention Networks with Positional Embeddings](https://mlsanity.com/paper/2105.04037/) (2021)
- [FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preference](https://mlsanity.com/paper/2410.20105/) (2024)
- [Towards Graph Self-Supervised Learning with Contrastive Adjusted Zooming](https://mlsanity.com/paper/2111.10698/) (2021)
- [Skeleton-based Action Recognition via Temporal-Channel Aggregation](https://mlsanity.com/paper/2205.15936/) (2022)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [From Local to Global: Spectral-Inspired Graph Neural Networks](https://mlsanity.com/paper/2209.12054/) (2022)
- [Non-convolutional Graph Neural Networks](https://mlsanity.com/paper/2408.00165/) (2024)
- [Why Propagate Alone? Parallel Use of Labels and Features on Graphs](https://mlsanity.com/paper/2110.07190/) (2021)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)

## Abstract (arXiv)

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: urlhttps://github.com/lrjconan/LanczosNetwork.