# Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks

arXiv: https://arxiv.org/abs/2506.07624 · HTML: https://mlsanity.com/paper/2506.07624/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 81 of its 95 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 30 of 81)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [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)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)

## Built on by (most cited first, 12 of 12)

- [A Mechanistic Analysis of Looped Reasoning Language Models](https://mlsanity.com/paper/2604.11791/) (2026)
- [Can You Hear Me Now? A Benchmark for Long-Range Graph Propagation](https://mlsanity.com/paper/2512.17762/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [gLSTM: Mitigating Over-Squashing by Increasing Storage Capacity](https://mlsanity.com/paper/2510.08450/) (2025)
- [GraphCliff: Short-Long Range Gating for Modeling Critical Activity Changes Caused by Subtle Molecular Differences](https://mlsanity.com/paper/2511.03170/) (2025)
- [Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs](https://mlsanity.com/paper/2602.10031/) (2026)
- [Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNs](https://mlsanity.com/paper/2602.18141/) (2026)
- [L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations](https://mlsanity.com/paper/2602.18837/) (2026)
- [Generalization Bounds for Spectral GNNs via Fourier Domain Analysis](https://mlsanity.com/paper/2604.00918/) (2026)
- [S3GNN: Efficient Global Mixing and Local Message Passing for Long-Range Graph Learning](https://mlsanity.com/paper/2605.23467/) (2026)
- [TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks](https://mlsanity.com/paper/2609.32940/) (2026)
- [Reachability is not enough: Diagnosing long-range behavior in GNNs](https://mlsanity.com/paper/2609.33674/) (2026)

## Abstract (arXiv)

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromises the computational efficiency that characterized early spatial message-passing architectures, and typically disregards the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNet model allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring. Across several benchmarks, Stable-ChebNet achieves near state-of-the-art performance.