# Large-Scale Spectral Graph Neural Networks via Laplacian Sparsification: Technical Report

arXiv: https://arxiv.org/abs/2501.04570 · HTML: https://mlsanity.com/paper/2501.04570/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 59 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 30 of 43)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Exploring the Potential of Large Language Models (LLMs) in Learning on Graphs](https://mlsanity.com/paper/2307.03393/) (2023)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1911.07323/) (2019)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)

## Built on by (most cited first, 5 of 5)

- [SPECTRA: Spectral Domain-Aware Graph Generation for Imbalanced Molecular Property Regression](https://mlsanity.com/paper/2511.04838/) (2025)
- [Rethinking Link Prediction for Directed Graphs](https://mlsanity.com/paper/2502.05724/) (2025)
- [Spectral Graph Sparsification Preserves Representation Geometry in Graph Neural Networks](https://mlsanity.com/paper/2605.01136/) (2026)
- [Spectral Flow Certificates for Depth-Aware Long-Range Propagation in Graph Neural Networks](https://mlsanity.com/paper/2607.21607/) (2026)
- [Scaffold: Support Graph Theory Based Sparsification for Graph Neural Networks](https://mlsanity.com/paper/2609.31466/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks involving both homophilous and heterophilous graph structures. However, The scalability of spectral GNNs on large graphs is limited because they learn the polynomial coefficients through multiple forward propagation executions during forward propagation. Existing works have attempted to scale up spectral GNNs by eliminating the linear layers on the input node features, a change that can disrupt end-to-end training, potentially impact performance, and become impractical with high-dimensional input features. To address the above challenges, we propose "Spectral Graph Neural Networks with Laplacian Sparsification (SGNN-LS)", a novel graph spectral sparsification method to approximate the propagation patterns of spectral GNNs. We prove that our proposed method generates Laplacian sparsifiers that can approximate both fixed and learnable polynomial filters with theoretical guarantees. Our method allows the application of linear layers on the input node features, enabling end-to-end training as well as the handling of raw text features. We conduct an extensive experimental analysis on datasets spanning various graph scales and properties to demonstrate the superior efficiency and effectiveness of our method. The results show that our method yields superior results in comparison with the corresponding approximated base models, especially on dataset Ogbn-papers100M(111M nodes, 1.6B edges) and MAG-scholar-C (2.8M features).