# FlowX: Towards Explainable Graph Neural Networks via Message Flows

arXiv: https://arxiv.org/abs/2206.12987 · HTML: https://mlsanity.com/paper/2206.12987/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 71 references that are in the map.
- First posted on arXiv 26 Jun 2022.

## Builds on (most cited first, 30 of 50)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)

## Built on by (most cited first, 21 of 21)

- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [GNNShap: Scalable and Accurate GNN Explanation using Shapley Values](https://mlsanity.com/paper/2401.04829/) (2024)
- [Masked Graph Autoencoder with Non-discrete Bandwidths](https://mlsanity.com/paper/2402.03814/) (2024)
- [Graph Structure and Feature Extrapolation for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.08076/) (2023)
- [L2XGNN: Learning to Explain Graph Neural Networks](https://mlsanity.com/paper/2209.14402/) (2022)
- [Generating Human Understandable Explanations for Node Embeddings](https://mlsanity.com/paper/2406.07642/) (2024)
- [Message-passing selection: Towards interpretable GNNs for graph classification](https://mlsanity.com/paper/2306.02081/) (2023)
- [SliceGX: Layer-wise GNN Explanation with Model-slicing](https://mlsanity.com/paper/2506.17977/) (2025)
- [Explainable Graph Neural Networks via Structural Externalities](https://mlsanity.com/paper/2507.17848/) (2025)
- [Fragment-Wise Interpretability in Graph Neural Networks via Molecule Decomposition and Contribution Analysis](https://mlsanity.com/paper/2508.15015/) (2025)
- [GRExplainer: A Universal Explanation Method for Temporal Graph Neural Networks](https://mlsanity.com/paper/2512.22772/) (2025)
- [Cooperative Causal GraphSAGE](https://mlsanity.com/paper/2505.14748/) (2025)
- [DistShap: Scalable GNN Explanations with Distributed Shapley Values](https://mlsanity.com/paper/2506.22668/) (2025)
- [Model Metamers Reveal Invariances in Graph Neural Networks](https://mlsanity.com/paper/2510.17378/) (2025)
- [FSX: Message Flow Sensitivity Enhanced Structural Explainer for Graph Neural Networks](https://mlsanity.com/paper/2601.14730/) (2026)
- [Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability](https://mlsanity.com/paper/2604.21175/) (2026)
- [Graph Navier Stokes Networks](https://mlsanity.com/paper/2605.21247/) (2026)
- [Towards the Explainability of Temporal Graph Networks via Memory Backtracking and Topological Attribution](https://mlsanity.com/paper/2607.07716/) (2026)
- [A Polynomial Architecture-Attribution Co-Design Framework for Exact Aumann-Shapley Attribution in GNNs](https://mlsanity.com/paper/2607.21094/) (2026)
- [Self-Explainable Multi-Label Graph Neural Network for Correlated Evidence Attribution](https://mlsanity.com/paper/2608.27574/) (2026)
- [Beyond Trained Models: Compiling GNNs for a Sound Explainer Benchmark](https://mlsanity.com/paper/2610.03526/) (2026)

## Abstract (arXiv)

We investigate the explainability of graph neural networks (GNNs) as a step toward elucidating their working mechanisms. While most current methods focus on explaining graph nodes, edges, or features, we argue that, as the inherent functional mechanism of GNNs, message flows are more natural for performing explainability. To this end, we propose a novel method here, known as FlowX, to explain GNNs by identifying important message flows. To quantify the importance of flows, we propose to follow the philosophy of Shapley values from cooperative game theory. To tackle the complexity of computing all coalitions' marginal contributions, we propose a flow sampling scheme to compute Shapley value approximations as initial assessments of further training. We then propose an information-controlled learning algorithm to train flow scores toward diverse explanation targets: necessary or sufficient explanations. Experimental studies on both synthetic and real-world datasets demonstrate that our proposed FlowX and its variants lead to improved explainability of GNNs. The code is available at https://github.com/divelab/DIG.