# Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space

arXiv: https://arxiv.org/abs/2501.15461 · HTML: https://mlsanity.com/paper/2501.15461/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Video, motion and generative Mamba models, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 45 of its 59 references that are in the map.
- First posted on arXiv 26 Jan 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 30 of 45)

- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [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)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [PlainMamba: Improving Non-Hierarchical Mamba in Visual Recognition](https://mlsanity.com/paper/2403.17695/) (2024)
- [Nested Graph Neural Networks](https://mlsanity.com/paper/2110.13197/) (2021)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [Self-supervised Graph-level Representation Learning with Local and Global Structure](https://mlsanity.com/paper/2106.04113/) (2021)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [ZigMa: A DiT-style Zigzag Mamba Diffusion Model](https://mlsanity.com/paper/2403.13802/) (2024)
- [GIT-Mol: A Multi-modal Large Language Model for Molecular Science with Graph, Image, and Text](https://mlsanity.com/paper/2308.06911/) (2023)
- [Hard Sample Aware Network for Contrastive Deep Graph Clustering](https://mlsanity.com/paper/2212.08665/) (2022)
- [Simple Contrastive Graph Clustering](https://mlsanity.com/paper/2205.07865/) (2022)
- [Demystifying Oversmoothing in Attention-Based Graph Neural Networks](https://mlsanity.com/paper/2305.16102/) (2023)
- [Node Dependent Local Smoothing for Scalable Graph Learning](https://mlsanity.com/paper/2110.14377/) (2021)

## Built on by (most cited first, 4 of 4)

- [Homophily Enhanced Graph Domain Adaptation](https://mlsanity.com/paper/2505.20089/) (2025)
- [Dual Mamba for Node-Specific Representation Learning: Tackling Over-Smoothing with Selective State Space Modeling](https://mlsanity.com/paper/2511.06756/) (2025)
- [A Spectral Theory of Normalized Corrected GNN Propagation](https://mlsanity.com/paper/2606.23572/) (2026)
- [End-to-End Cell Detection via Instance-aware Graph Modeling](https://mlsanity.com/paper/2609.15354/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown great success in various graph-based learning tasks. However, it often faces the issue of over-smoothing as the model depth increases, which causes all node representations to converge to a single value and become indistinguishable. This issue stems from the inherent limitations of GNNs, which struggle to distinguish the importance of information from different neighborhoods. In this paper, we introduce MbaGCN, a novel graph convolutional architecture that draws inspiration from the Mamba paradigm-originally designed for sequence modeling. MbaGCN presents a new backbone for GNNs, consisting of three key components: the Message Aggregation Layer, the Selective State Space Transition Layer, and the Node State Prediction Layer. These components work in tandem to adaptively aggregate neighborhood information, providing greater flexibility and scalability for deep GNN models. While MbaGCN may not consistently outperform all existing methods on each dataset, it provides a foundational framework that demonstrates the effective integration of the Mamba paradigm into graph representation learning. Through extensive experiments on benchmark datasets, we demonstrate that MbaGCN paves the way for future advancements in graph neural network research.