TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration

TL;DR

TopInG introduces TopInG, a topological framework for intrinsically interpretable GNNs that identifies persistent rationale subgraphs through a learnable edge filtration guided by persistent homology. By enforcing a topological discrepancy between rationale and non-rationale components via a tractable lower bound and a two-Gaussian prior, it provides theoretical guarantees that the ground-truth rationale uniquely optimizes the loss under certain conditions. The approach yields stable explanations across variform rationales and improves interpretability while maintaining competitive predictive accuracy, demonstrated on eight benchmark datasets with diverse motif structures. This topological perspective enables more trustworthy AI in scientific domains by capturing stable, scale-spanning topological features that underlie predictions. The framework highlights a path toward robust, interpretable graph learning that can resist spurious correlations and variations in subgraph structure.

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, 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.

Figures (14)

• Figure 1: An overview of TopInG. A GNN parameterized by $f_\phi$ is used to learn a filtration, from which we sample the subgraphs $G_X$ and $G_{\epsilon}$. These subgraphs yield topological features through their respective filtrations ${\mathcal{F}}$. Meanwhile, the combined subgraph $G_X \sqcup G_{\epsilon}$ is processed by the same GNN (sharing parameters with $f_\phi$) to produce a graph feature. Finally, the topological features ${\mathcal{T}}$ (which capture global structural information) are combined with the graph feature to form the final graph representation for classification tasks.
• Figure 2: The top row is a learned graph filtration on an example graph through our method. Red and yellow points correspond to ground truth rationale subgraph $G_X^*$ and noisy subgraph $G_\epsilon^*$ respectively. Each snapshot is a subgraph of $G$ on edges with filtration values greater than a decreasing threshold value indicated on top of each snapshot. Below each subgraph, the number in small box is the size of cycle basis for the current subgraph, which equals to the dimension of the cycle space, also known as the 1st betti number. The bottom part shows the 1st persistent homology. Each horizontal bar corresponds to a topological feature (basic cycle).
• Figure 3: In BA-HouseOrGrid-nRnd dataset, as nRnd increases, the complexity of rationale subgraphs increases. Existing SOTA methods struggles on such datasets, while TopInG's performance is much better and stable.
• Figure 4: A sensitivity study on BA-HouseAndGrid shows results with the topological constraint coefficient varied from [0.001, 0.005, 0.01, 0.05] and the coefficient of prior regularization term from [0.005, 0.05, 0.5].
• Figure 5: Learned interpretable subgraphs by GSAT, GMT-Lin and TopInG on BA-HouseAndGrid. Figures in each row belong to the same class. Nodes colored red are ground-truth explanations.

Theorems & Definitions (9)

• Remark 2.1
• Remark 3.1
• Definition 3.2: Topological Discrepancy
• Proposition 3.3
• Theorem 3.4
• Remark 3.5
• Remark 3.6
• Definition 2.1: Bottleneck Distance
• proof