# Logical Distillation of Graph Neural Networks

arXiv: https://arxiv.org/abs/2406.07126 · HTML: https://mlsanity.com/paper/2406.07126/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [The Logic of Graph Neural Networks](https://mlsanity.com/paper/2104.14624/) (2021)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [Beyond Sparsity: Tree Regularization of Deep Models for Interpretability](https://mlsanity.com/paper/1711.06178/) (2017)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [GLocalX -- From Local to Global Explanations of Black Box AI Models](https://mlsanity.com/paper/2101.07685/) (2021)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [The Descriptive Complexity of Graph Neural Networks](https://mlsanity.com/paper/2303.04613/) (2023)
- [Enhancing Decision Tree based Interpretation of Deep Neural Networks through L1-Orthogonal Regularization](https://mlsanity.com/paper/1904.05394/) (2019)

## Built on by (most cited first, 7 of 7)

- [Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective](https://mlsanity.com/paper/2502.02719/) (2025)
- [GNN Explanations that do not Explain and How to find Them](https://mlsanity.com/paper/2601.20815/) (2026)
- [Sound Logical Explanations for Mean Aggregation Graph Neural Networks](https://mlsanity.com/paper/2511.11593/) (2025)
- [WILTing Trees: Interpreting the Distance Between MPNN Embeddings](https://mlsanity.com/paper/2505.24642/) (2025)
- [Discrete Diffusion-Based Model-Level Explanation of Heterogeneous GNNs with Node Features](https://mlsanity.com/paper/2508.08458/) (2025)
- [Overcoming Shortcut Learning in Graph Neural Networks through Active Explanation Guidance](https://mlsanity.com/paper/2608.14121/) (2026)
- [Beyond Trained Models: Compiling GNNs for a Sound Explainer Benchmark](https://mlsanity.com/paper/2610.03526/) (2026)

## Abstract (arXiv)

We present a logic based interpretable model for learning on graphs and an algorithm to distill this model from a Graph Neural Network (GNN). Recent results have shown connections between the expressivity of GNNs and the two-variable fragment of first-order logic with counting quantifiers (C2). We introduce a decision-tree based model which leverages an extension of C2 to distill interpretable logical classifiers from GNNs. We test our approach on multiple GNN architectures. The distilled models are interpretable, succinct, and attain similar accuracy to the underlying GNN. Furthermore, when the ground truth is expressible in C2, our approach outperforms the GNN.