# Globally Interpretable Graph Learning via Distribution Matching

arXiv: https://arxiv.org/abs/2306.10447 · HTML: https://mlsanity.com/paper/2306.10447/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 18 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [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)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Explainability Techniques for Graph Convolutional Networks](https://mlsanity.com/paper/1905.13686/) (2019)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [ROLAND: Graph Learning Framework for Dynamic Graphs](https://mlsanity.com/paper/2208.07239/) (2022)
- [Condensing Graphs via One-Step Gradient Matching](https://mlsanity.com/paper/2206.07746/) (2022)
- [Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data](https://mlsanity.com/paper/2306.02664/) (2023)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [Spectral Augmentation for Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2210.00643/) (2022)
- [Unbiased Graph Embedding with Biased Graph Observations](https://mlsanity.com/paper/2110.13957/) (2021)
- [Graph Structural Attack by Perturbing Spectral Distance](https://mlsanity.com/paper/2111.00684/) (2021)
- [FusionRetro: Molecule Representation Fusion via In-Context Learning for Retrosynthetic Planning](https://mlsanity.com/paper/2209.15315/) (2022)
- [Graph Embedding with Hierarchical Attentive Membership](https://mlsanity.com/paper/2111.00604/) (2021)

## Built on by (most cited first, 3 of 3)

- [A Review of Graph Neural Networks in Epidemic Modeling](https://mlsanity.com/paper/2403.19852/) (2024)
- [Towards Faithful Class-level Self-explainability in Graph Neural Networks by Subgraph Dependencies](https://mlsanity.com/paper/2508.11513/) (2025)
- [Explaining Synergistic Effects in Social Recommendations](https://mlsanity.com/paper/2601.18151/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have emerged as a powerful model to capture critical graph patterns. Instead of treating them as black boxes in an end-to-end fashion, attempts are arising to explain the model behavior. Existing works mainly focus on local interpretation to reveal the discriminative pattern for each individual instance, which however cannot directly reflect the high-level model behavior across instances. To gain global insights, we aim to answer an important question that is not yet well studied: how to provide a global interpretation for the graph learning procedure? We formulate this problem as globally interpretable graph learning, which targets on distilling high-level and human-intelligible patterns that dominate the learning procedure, such that training on this pattern can recover a similar model. As a start, we propose a novel model fidelity metric, tailored for evaluating the fidelity of the resulting model trained on interpretations. Our preliminary analysis shows that interpretative patterns generated by existing global methods fail to recover the model training procedure. Thus, we further propose our solution, Graph Distribution Matching (GDM), which synthesizes interpretive graphs by matching the distribution of the original and interpretive graphs in the GNN's feature space as its training proceeds, thus capturing the most informative patterns the model learns during training. Extensive experiments on graph classification datasets demonstrate multiple advantages of the proposed method, including high model fidelity, predictive accuracy and time efficiency, as well as the ability to reveal class-relevant structure.