# Distill n' Explain: explaining graph neural networks using simple surrogates

arXiv: https://arxiv.org/abs/2303.10139 · HTML: https://mlsanity.com/paper/2303.10139/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 61 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 30 of 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (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)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (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)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (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)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [PLOP: Learning without Forgetting for Continual Semantic Segmentation](https://mlsanity.com/paper/2011.11390/) (2020)
- [Dataset Distillation using Neural Feature Regression](https://mlsanity.com/paper/2206.00719/) (2022)
- [Ensemble Distribution Distillation](https://mlsanity.com/paper/1905.00076/) (2019)
- [Cross-Layer Distillation with Semantic Calibration](https://mlsanity.com/paper/2012.03236/) (2020)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)

## Built on by (most cited first, 18 of 18)

- [A Survey on Explainability of Graph Neural Networks](https://mlsanity.com/paper/2306.01958/) (2023)
- [Explaining Graph Neural Networks via Structure-aware Interaction Index](https://mlsanity.com/paper/2405.14352/) (2024)
- [Graph Neural Network Causal Explanation via Neural Causal Models](https://mlsanity.com/paper/2407.09378/) (2024)
- [Recent Advances in Malware Detection: Graph Learning and Explainability](https://mlsanity.com/paper/2502.10556/) (2025)
- [EiG-Search: Generating Edge-Induced Subgraphs for GNN Explanation in Linear Time](https://mlsanity.com/paper/2405.01762/) (2024)
- [Faithful and Accurate Self-Attention Attribution for Message Passing Neural Networks via the Computation Tree Viewpoint](https://mlsanity.com/paper/2406.04612/) (2024)
- [Quantifying Explanation Quality in Graph Neural Networks using Out-of-Distribution Generalization](https://mlsanity.com/paper/2602.07708/) (2026)
- [Game-theoretic Counterfactual Explanation for Graph Neural Networks](https://mlsanity.com/paper/2402.06030/) (2024)
- [GnnXemplar: Exemplars to Explanations -- Natural Language Rules for Global GNN Interpretability](https://mlsanity.com/paper/2509.18376/) (2025)
- [On the Feasibility of Fidelity^- for Graph Pruning](https://mlsanity.com/paper/2406.11504/) (2024)
- [Interpretability of Graph Neural Networks to Assess Effects of Global Change Drivers on Ecological Networks](https://mlsanity.com/paper/2503.15107/) (2025)
- [Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation](https://mlsanity.com/paper/2602.07834/) (2026)
- [GNNAnatomy: Rethinking Model-Level Explanations for Graph Neural Networks](https://mlsanity.com/paper/2406.04548/) (2024)
- [DistShap: Scalable GNN Explanations with Distributed Shapley Values](https://mlsanity.com/paper/2506.22668/) (2025)
- [ARM-Explainer -- Explaining and improving graph neural network predictions for the maximum clique problem using node features and association rule mining](https://mlsanity.com/paper/2511.22866/) (2025)
- [CIExplainer++: Generating Causal and Interpretable Explanations for Graph Neural Networks](https://mlsanity.com/paper/2606.20747/) (2026)
- [Towards Faithful Graph Explanations with Synergistic Edge Effects via Granular Balls](https://mlsanity.com/paper/2607.21381/) (2026)
- [From Abductive Explanations to Global Logical Rules for Node Classification in SGCs](https://mlsanity.com/paper/2608.17103/) (2026)

## Abstract (arXiv)

Explaining node predictions in graph neural networks (GNNs) often boils down to finding graph substructures that preserve predictions. Finding these structures usually implies back-propagating through the GNN, bonding the complexity (e.g., number of layers) of the GNN to the cost of explaining it. This naturally begs the question: Can we break this bond by explaining a simpler surrogate GNN? To answer the question, we propose Distill n' Explain (DnX). First, DnX learns a surrogate GNN via knowledge distillation. Then, DnX extracts node or edge-level explanations by solving a simple convex program. We also propose FastDnX, a faster version of DnX that leverages the linear decomposition of our surrogate model. Experiments show that DnX and FastDnX often outperform state-of-the-art GNN explainers while being orders of magnitude faster. Additionally, we support our empirical findings with theoretical results linking the quality of the surrogate model (i.e., distillation error) to the faithfulness of explanations.