# GrassNet: State Space Model Meets Graph Neural Network

arXiv: https://arxiv.org/abs/2408.08583 · HTML: https://mlsanity.com/paper/2408.08583/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 16 Aug 2024.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [QA-GNN: Reasoning with Language Models and Knowledge Graphs for Question Answering](https://mlsanity.com/paper/2104.06378/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [Vivim: a Video Vision Mamba for Medical Video Segmentation](https://mlsanity.com/paper/2401.14168/) (2024)
- [What Can We Learn from State Space Models for Machine Learning on Graphs?](https://mlsanity.com/paper/2406.05815/) (2024)

## Built on by (most cited first, 2 of 2)

- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [Exploring Graph Mamba: A Comprehensive Survey on State-Space Models for Graph Learning](https://mlsanity.com/paper/2412.18322/) (2024)

## Abstract (arXiv)

Designing spectral convolutional networks is a formidable task in graph learning. In traditional spectral graph neural networks (GNNs), polynomial-based methods are commonly used to design filters via the Laplacian matrix. In practical applications, however, these polynomial methods encounter inherent limitations, which primarily arise from the the low-order truncation of polynomial filters and the lack of overall modeling of the graph spectrum. This leads to poor performance of existing spectral approaches on real-world graph data, especially when the spectrum is highly concentrated or contains many numerically identical values, as they tend to apply the exact same modulation to signals with the same frequencies. To overcome these issues, in this paper, we propose Graph State Space Network (GrassNet), a novel graph neural network with theoretical support that provides a simple yet effective scheme for designing and learning arbitrary graph spectral filters. In particular, our GrassNet introduces structured state space models (SSMs) to model the correlations of graph signals at different frequencies and derives a unique rectification for each frequency in the graph spectrum. To the best of our knowledge, our work is the first to employ SSMs for the design of GNN spectral filters, and it theoretically offers greater expressive power compared with polynomial filters. Extensive experiments on nine public benchmarks reveal that GrassNet achieves superior performance in real-world graph modeling tasks.