# TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration

arXiv: https://arxiv.org/abs/2510.05102 · HTML: https://mlsanity.com/paper/2510.05102/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 70 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (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)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Interpreting Graph Neural Networks for NLP With Differentiable Edge Masking](https://mlsanity.com/paper/2010.00577/) (2020)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Graph Information Bottleneck for Subgraph Recognition](https://mlsanity.com/paper/2010.05563/) (2020)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology](https://mlsanity.com/paper/1907.05008/) (2019)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [New Bounds for Matrix Multiplication: from Alpha to Omega](https://mlsanity.com/paper/2307.07970/) (2023)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [D-Separation for Causal Self-Explanation](https://mlsanity.com/paper/2309.13391/) (2023)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning](https://mlsanity.com/paper/2304.04970/) (2023)
- [Explaining Graph Neural Networks via Structure-aware Interaction Index](https://mlsanity.com/paper/2405.14352/) (2024)
- [Is the MMI Criterion Necessary for Interpretability? Degenerating Non-causal Features to Plain Noise for Self-Rationalization](https://mlsanity.com/paper/2410.06003/) (2024)
- [Rethinking Explaining Graph Neural Networks via Non-parametric Subgraph Matching](https://mlsanity.com/paper/2301.02780/) (2023)
- [PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Prediction](https://mlsanity.com/paper/2010.16027/) (2020)
- [Breaking Free from MMI: A New Frontier in Rationalization by Probing Input Utilization](https://mlsanity.com/paper/2503.06202/) (2025)
- [GEFL: Extended Filtration Learning for Graph Classification](https://mlsanity.com/paper/2406.02732/) (2024)

## Built on by (most cited first, 1 of 1)

- [From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features](https://mlsanity.com/paper/2606.11911/) (2026)

## Abstract (arXiv)

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, intrinsically 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 generation 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.