# Global Explainability of GNNs via Logic Combination of Learned Concepts

arXiv: https://arxiv.org/abs/2210.07147 · HTML: https://mlsanity.com/paper/2210.07147/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [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)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Deep Learning for Case-Based Reasoning through Prototypes: A Neural Network that Explains Its Predictions](https://mlsanity.com/paper/1710.04806/) (2017)
- [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)
- [Generative Causal Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.06643/) (2021)
- [ProtGNN: Towards Self-Explaining Graph Neural Networks](https://mlsanity.com/paper/2112.00911/) (2021)
- [Evaluating Explainability for Graph Neural Networks](https://mlsanity.com/paper/2208.09339/) (2022)
- [Beyond Sparsity: Tree Regularization of Deep Models for Interpretability](https://mlsanity.com/paper/1711.06178/) (2017)
- [Entropy-based Logic Explanations of Neural Networks](https://mlsanity.com/paper/2106.06804/) (2021)
- [GLocalX -- From Local to Global Explanations of Black Box AI Models](https://mlsanity.com/paper/2101.07685/) (2021)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [GCExplainer: Human-in-the-Loop Concept-based Explanations for Graph Neural Networks](https://mlsanity.com/paper/2107.11889/) (2021)
- [OrphicX: A Causality-Inspired Latent Variable Model for Interpreting Graph Neural Networks](https://mlsanity.com/paper/2203.15209/) (2022)
- [Encoding Concepts in Graph Neural Networks](https://mlsanity.com/paper/2207.13586/) (2022)
- [Algorithmic Concept-based Explainable Reasoning](https://mlsanity.com/paper/2107.07493/) (2021)

## Built on by (most cited first, 30 of 65)

- [Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunities](https://mlsanity.com/paper/2302.01018/) (2023)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [The expressive power of pooling in Graph Neural Networks](https://mlsanity.com/paper/2304.01575/) (2023)
- [A Survey on Explainability of Graph Neural Networks](https://mlsanity.com/paper/2306.01958/) (2023)
- [Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks](https://mlsanity.com/paper/2310.01820/) (2023)
- [Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs](https://mlsanity.com/paper/2406.15156/) (2024)
- [GNNX-BENCH: Unravelling the Utility of Perturbation-based GNN Explainers through In-depth Benchmarking](https://mlsanity.com/paper/2310.01794/) (2023)
- [Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective](https://mlsanity.com/paper/2502.02719/) (2025)
- [GOAt: Explaining Graph Neural Networks via Graph Output Attribution](https://mlsanity.com/paper/2401.14578/) (2024)
- [A Logic for Reasoning About Aggregate-Combine Graph Neural Networks](https://mlsanity.com/paper/2405.00205/) (2024)
- [Factorized Explainer for Graph Neural Networks](https://mlsanity.com/paper/2312.05596/) (2023)
- [MAGE: Model-Level Graph Neural Networks Explanations via Motif-based Graph Generation](https://mlsanity.com/paper/2405.12519/) (2024)
- [Logical Distillation of Graph Neural Networks](https://mlsanity.com/paper/2406.07126/) (2024)
- [A Self-Explainable Heterogeneous GNN for Relational Deep Learning](https://mlsanity.com/paper/2412.00521/) (2024)
- [State of the Art and Potentialities of Graph-level Learning](https://mlsanity.com/paper/2301.05860/) (2023)
- [From Nodes to Narratives: Explaining Graph Neural Networks with LLMs and Graph Context](https://mlsanity.com/paper/2508.07117/) (2025)
- [How Faithful are Self-Explainable GNNs?](https://mlsanity.com/paper/2308.15096/) (2023)
- [Faithful and Accurate Self-Attention Attribution for Message Passing Neural Networks via the Computation Tree Viewpoint](https://mlsanity.com/paper/2406.04612/) (2024)
- [GNN Explanations that do not Explain and How to find Them](https://mlsanity.com/paper/2601.20815/) (2026)
- [Interpretable Graph Networks Formulate Universal Algebra Conjectures](https://mlsanity.com/paper/2307.11688/) (2023)
- [Generative Explanations for Graph Neural Network: Methods and Evaluations](https://mlsanity.com/paper/2311.05764/) (2023)
- [Improving deep learning with prior knowledge and cognitive models: A survey on enhancing explainability, adversarial robustness and zero-shot learning](https://mlsanity.com/paper/2403.07078/) (2024)
- [Utilizing Description Logics for Global Explanations of Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2405.12654/) (2024)
- [Towards Few-shot Self-explaining Graph Neural Networks](https://mlsanity.com/paper/2408.07340/) (2024)
- [B-XAIC Dataset: Benchmarking Explainable AI for Graph Neural Networks Using Chemical Data](https://mlsanity.com/paper/2505.22252/) (2025)
- [Globally Interpretable Graph Learning via Distribution Matching](https://mlsanity.com/paper/2306.10447/) (2023)
- [xAI-Drop: Don't Use What You Cannot Explain](https://mlsanity.com/paper/2407.20067/) (2024)
- [Unstructured and structured data: Can we have the best of both worlds with large language models?](https://mlsanity.com/paper/2304.13010/) (2023)
- [On the Robustness of Post-hoc GNN Explainers to Label Noise](https://mlsanity.com/paper/2309.01706/) (2023)

## Abstract (arXiv)

While instance-level explanation of GNN is a well-studied problem with plenty of approaches being developed, providing a global explanation for the behaviour of a GNN is much less explored, despite its potential in interpretability and debugging. Existing solutions either simply list local explanations for a given class, or generate a synthetic prototypical graph with maximal score for a given class, completely missing any combinatorial aspect that the GNN could have learned. In this work, we propose GLGExplainer (Global Logic-based GNN Explainer), the first Global Explainer capable of generating explanations as arbitrary Boolean combinations of learned graphical concepts. GLGExplainer is a fully differentiable architecture that takes local explanations as inputs and combines them into a logic formula over graphical concepts, represented as clusters of local explanations. Contrary to existing solutions, GLGExplainer provides accurate and human-interpretable global explanations that are perfectly aligned with ground-truth explanations (on synthetic data) or match existing domain knowledge (on real-world data). Extracted formulas are faithful to the model predictions, to the point of providing insights into some occasionally incorrect rules learned by the model, making GLGExplainer a promising diagnostic tool for learned GNNs.