Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective

Steve Azzolin, Sagar Malhotra, Andrea Passerini, Stefano Teso
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:2045-2080, 2025.

Abstract

Self-Explainable Graph Neural Networks (SE-GNNs) are popular explainable-by-design GNNs, but their explanations’ properties and limitations are not well understood. Our first contribution fills this gap by formalizing the explanations extracted by some popular SE-GNNs, referred to as Minimal Explanations (MEs), and comparing them to established notions of explanations, namely Prime Implicant (PI) and faithful explanations. Our analysis reveals that MEs match PI explanations for a restricted but significant family of tasks. In general, however, they can be less informative than PI explanations and are surprisingly misaligned with widely accepted notions of faithfulness. Although faithful and PI explanations are informative, they are intractable to find and we show that they can be prohibitively large. Given these observations, a natural choice is to augment SE-GNNs with alternative modalities of explanations taking care of SE-GNNs’ limitations. To this end, we propose Dual-Channel GNNs that integrate a white-box rule extractor and a standard SE-GNN, adaptively combining both channels. Our experiments show that even a simple instantiation of Dual-Channel GNNs can recover succinct rules and perform on par or better than widely used SE-GNNs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-azzolin25a, title = {Beyond Topological Self-Explainable {GNN}s: A Formal Explainability Perspective}, author = {Azzolin, Steve and Malhotra, Sagar and Passerini, Andrea and Teso, Stefano}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {2045--2080}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/azzolin25a/azzolin25a.pdf}, url = {https://proceedings.mlr.press/v267/azzolin25a.html}, abstract = {Self-Explainable Graph Neural Networks (SE-GNNs) are popular explainable-by-design GNNs, but their explanations’ properties and limitations are not well understood. Our first contribution fills this gap by formalizing the explanations extracted by some popular SE-GNNs, referred to as Minimal Explanations (MEs), and comparing them to established notions of explanations, namely Prime Implicant (PI) and faithful explanations. Our analysis reveals that MEs match PI explanations for a restricted but significant family of tasks. In general, however, they can be less informative than PI explanations and are surprisingly misaligned with widely accepted notions of faithfulness. Although faithful and PI explanations are informative, they are intractable to find and we show that they can be prohibitively large. Given these observations, a natural choice is to augment SE-GNNs with alternative modalities of explanations taking care of SE-GNNs’ limitations. To this end, we propose Dual-Channel GNNs that integrate a white-box rule extractor and a standard SE-GNN, adaptively combining both channels. Our experiments show that even a simple instantiation of Dual-Channel GNNs can recover succinct rules and perform on par or better than widely used SE-GNNs.} }
Endnote
%0 Conference Paper %T Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective %A Steve Azzolin %A Sagar Malhotra %A Andrea Passerini %A Stefano Teso %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-azzolin25a %I PMLR %P 2045--2080 %U https://proceedings.mlr.press/v267/azzolin25a.html %V 267 %X Self-Explainable Graph Neural Networks (SE-GNNs) are popular explainable-by-design GNNs, but their explanations’ properties and limitations are not well understood. Our first contribution fills this gap by formalizing the explanations extracted by some popular SE-GNNs, referred to as Minimal Explanations (MEs), and comparing them to established notions of explanations, namely Prime Implicant (PI) and faithful explanations. Our analysis reveals that MEs match PI explanations for a restricted but significant family of tasks. In general, however, they can be less informative than PI explanations and are surprisingly misaligned with widely accepted notions of faithfulness. Although faithful and PI explanations are informative, they are intractable to find and we show that they can be prohibitively large. Given these observations, a natural choice is to augment SE-GNNs with alternative modalities of explanations taking care of SE-GNNs’ limitations. To this end, we propose Dual-Channel GNNs that integrate a white-box rule extractor and a standard SE-GNN, adaptively combining both channels. Our experiments show that even a simple instantiation of Dual-Channel GNNs can recover succinct rules and perform on par or better than widely used SE-GNNs.
APA
Azzolin, S., Malhotra, S., Passerini, A. & Teso, S.. (2025). Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:2045-2080 Available from https://proceedings.mlr.press/v267/azzolin25a.html.

Related Material