TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration

Cheng Xin, Fan Xu, Xin Ding, Jie Gao, Jiaxin Ding
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:68847-68869, 2025.

Abstract

Graph Neural Networks (GNNs) have shown remarkable success across various scientific fields, yet their adoption in critical decision-making is often hindered by a lack of interpretability. Recently, intrinsic interpretable GNNs have been studied to provide insights into model predictions by identifying rationale substructures in graphs. However, existing methods face challenges when the underlying rationale subgraphs are complex and varied. In this work, we propose TopInG: Topologically Interpretable Graph Learning, a novel topological framework that leverages persistent homology to identify persistent rationale subgraphs. TopInG employs a rationale filtration learning approach to model an autoregressive generating process of rationale subgraphs, and introduces a self-adjusted topological constraint, termed topological discrepancy, to enforce a persistent topological distinction between rationale subgraphs and irrelevant counterparts. We provide theoretical guarantees that our loss function is uniquely optimized by the ground truth under specific conditions. Extensive experiments demonstrate TopInG’s effectiveness in tackling key challenges, such as handling variform rationale subgraphs, balancing predictive performance with interpretability, and mitigating spurious correlations. Results show that our approach improves upon state-of-the-art methods on both predictive accuracy and interpretation quality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-xin25b, title = {{T}op{I}n{G}: Topologically Interpretable Graph Learning via Persistent Rationale Filtration}, author = {Xin, Cheng and Xu, Fan and Ding, Xin and Gao, Jie and Ding, Jiaxin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {68847--68869}, 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/xin25b/xin25b.pdf}, url = {https://proceedings.mlr.press/v267/xin25b.html}, abstract = {Graph Neural Networks (GNNs) have shown remarkable success across various scientific fields, yet their adoption in critical decision-making is often hindered by a lack of interpretability. Recently, intrinsic interpretable GNNs have been studied to provide insights into model predictions by identifying rationale substructures in graphs. However, existing methods face challenges when the underlying rationale subgraphs are complex and varied. In this work, we propose TopInG: Topologically Interpretable Graph Learning, a novel topological framework that leverages persistent homology to identify persistent rationale subgraphs. TopInG employs a rationale filtration learning approach to model an autoregressive generating process of rationale subgraphs, and introduces a self-adjusted topological constraint, termed topological discrepancy, to enforce a persistent topological distinction between rationale subgraphs and irrelevant counterparts. We provide theoretical guarantees that our loss function is uniquely optimized by the ground truth under specific conditions. Extensive experiments demonstrate TopInG’s effectiveness in tackling key challenges, such as handling variform rationale subgraphs, balancing predictive performance with interpretability, and mitigating spurious correlations. Results show that our approach improves upon state-of-the-art methods on both predictive accuracy and interpretation quality.} }
Endnote
%0 Conference Paper %T TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration %A Cheng Xin %A Fan Xu %A Xin Ding %A Jie Gao %A Jiaxin Ding %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-xin25b %I PMLR %P 68847--68869 %U https://proceedings.mlr.press/v267/xin25b.html %V 267 %X Graph Neural Networks (GNNs) have shown remarkable success across various scientific fields, yet their adoption in critical decision-making is often hindered by a lack of interpretability. Recently, intrinsic interpretable GNNs have been studied to provide insights into model predictions by identifying rationale substructures in graphs. However, existing methods face challenges when the underlying rationale subgraphs are complex and varied. In this work, we propose TopInG: Topologically Interpretable Graph Learning, a novel topological framework that leverages persistent homology to identify persistent rationale subgraphs. TopInG employs a rationale filtration learning approach to model an autoregressive generating process of rationale subgraphs, and introduces a self-adjusted topological constraint, termed topological discrepancy, to enforce a persistent topological distinction between rationale subgraphs and irrelevant counterparts. We provide theoretical guarantees that our loss function is uniquely optimized by the ground truth under specific conditions. Extensive experiments demonstrate TopInG’s effectiveness in tackling key challenges, such as handling variform rationale subgraphs, balancing predictive performance with interpretability, and mitigating spurious correlations. Results show that our approach improves upon state-of-the-art methods on both predictive accuracy and interpretation quality.
APA
Xin, C., Xu, F., Ding, X., Gao, J. & Ding, J.. (2025). TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:68847-68869 Available from https://proceedings.mlr.press/v267/xin25b.html.

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