# FSX: Message Flow Sensitivity Enhanced Structural Explainer for Graph Neural Networks

arXiv: https://arxiv.org/abs/2601.14730 · HTML: https://mlsanity.com/paper/2601.14730/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 21 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [DIG: A Turnkey Library for Diving into Graph Deep Learning Research](https://mlsanity.com/paper/2103.12608/) (2021)
- [GraphSVX: Shapley Value Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.10482/) (2021)
- [FlowX: Towards Explainable Graph Neural Networks via Message Flows](https://mlsanity.com/paper/2206.12987/) (2022)
- [GOAt: Explaining Graph Neural Networks via Graph Output Attribution](https://mlsanity.com/paper/2401.14578/) (2024)
- [Faithful and Accurate Self-Attention Attribution for Message Passing Neural Networks via the Computation Tree Viewpoint](https://mlsanity.com/paper/2406.04612/) (2024)
- [Explainable Graph Neural Networks via Structural Externalities](https://mlsanity.com/paper/2507.17848/) (2025)

## Abstract (arXiv)

Despite the widespread success of Graph Neural Networks (GNNs), understanding the reasons behind their specific predictions remains challenging. Existing explainability methods face a trade-off that gradient-based approaches are computationally efficient but often ignore structural interactions, while game-theoretic techniques capture interactions at the cost of high computational overhead and potential deviation from the model's true reasoning path. To address this gap, we propose FSX (Message Flow Sensitivity Enhanced Structural Explainer), a novel hybrid framework that synergistically combines the internal message flows of the model with a cooperative game approach applied to the external graph data. FSX first identifies critical message flows via a novel flow-sensitivity analysis: during a single forward pass, it simulates localized node perturbations and measures the resulting changes in message flow intensities. These sensitivity-ranked flows are then projected onto the input graph to define compact, semantically meaningful subgraphs. Within each subgraph, a flow-aware cooperative game is conducted, where node contributions are evaluated fairly through a Shapley-like value that incorporates both node-feature importance and their roles in sustaining or destabilizing the identified critical flows. Extensive evaluation across multiple datasets and GNN architectures demonstrates that FSX achieves superior explanation fidelity with significantly reduced runtime, while providing unprecedented insights into the structural logic underlying model predictions--specifically, how important sub-structures exert influence by governing the stability of key internal computational pathways.