# GREAD: Graph Neural Reaction-Diffusion Networks

arXiv: https://arxiv.org/abs/2211.14208 · HTML: https://mlsanity.com/paper/2211.14208/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 74 references that are in the map.
- First posted on arXiv 25 Nov 2022.

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

- [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)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [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)
- [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)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [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)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)

## Built on by (most cited first, 30 of 54)

- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [An Attentive Inductive Bias for Sequential Recommendation beyond the Self-Attention](https://mlsanity.com/paper/2312.10325/) (2023)
- [On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems](https://mlsanity.com/paper/2405.01009/) (2024)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND](https://mlsanity.com/paper/2404.17099/) (2024)
- [Graph Neural Rough Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2303.10909/) (2023)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyond](https://mlsanity.com/paper/2309.02769/) (2023)
- [Graph Convolutions Enrich the Self-Attention in Transformers!](https://mlsanity.com/paper/2312.04234/) (2023)
- [Temporal Graph ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2404.19508/) (2024)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [Can TabPFN Compete with GNNs for Node Classification via Graph Tabularization?](https://mlsanity.com/paper/2512.08798/) (2025)
- [Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priors](https://mlsanity.com/paper/2604.19028/) (2026)
- [Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study](https://mlsanity.com/paper/2401.04331/) (2024)
- [On The Temporal Domain of Differential Equation Inspired Graph Neural Networks](https://mlsanity.com/paper/2401.11074/) (2024)
- [Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theory](https://mlsanity.com/paper/2402.15326/) (2024)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings](https://mlsanity.com/paper/2308.01084/) (2023)
- [SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification](https://mlsanity.com/paper/2408.16698/) (2024)
- [DeepSN: A Sheaf Neural Framework for Influence Maximization](https://mlsanity.com/paper/2412.12416/) (2024)
- [RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2312.16563/) (2023)
- [When Graph Neural Networks Meet Dynamic Mode Decomposition](https://mlsanity.com/paper/2410.05593/) (2024)
- [Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning](https://mlsanity.com/paper/2506.20324/) (2025)
- [Stuart-Landau Oscillatory Graph Neural Network](https://mlsanity.com/paper/2511.08094/) (2025)
- [Are Graph Transformers Necessary? Efficient Long-Range Message Passing with Fractal Nodes in MPNNs](https://mlsanity.com/paper/2511.13010/) (2025)
- [Improving Signed Propagation for Graph Neural Networks in Multi-Class Environments](https://mlsanity.com/paper/2301.08918/) (2023)
- [Graph Neural Aggregation-diffusion with Metastability](https://mlsanity.com/paper/2403.20221/) (2024)
- [Quadratic Binary Optimization with Graph Neural Networks](https://mlsanity.com/paper/2404.04874/) (2024)
- [Faster Local Solvers for Graph Diffusion Equations](https://mlsanity.com/paper/2410.21634/) (2024)
- [Resolving Oversmoothing with Opinion Dissensus](https://mlsanity.com/paper/2501.19089/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for designing the core processing layer of GNNs, and therefore they are inevitably vulnerable to the notorious oversmoothing problem. Recently, a couple of papers paid attention to reaction equations in conjunctions with diffusion equations. However, they all consider limited forms of reaction equations. To this end, we present a reaction-diffusion equation-based GNN method that considers all popular types of reaction equations in addition to one special reaction equation designed by us. To our knowledge, our paper is one of the most comprehensive studies on reaction-diffusion equation-based GNNs. In our experiments with 9 datasets and 28 baselines, our method, called GREAD, outperforms them in a majority of cases. Further synthetic data experiments show that it mitigates the oversmoothing problem and works well for various homophily rates.