🍩 Database of Original & Non-Theoretical Uses of Topology

1. TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration (2025)

   Cheng Xin, Fan Xu, Xin Ding, Jie Gao, Jiaxin Ding

   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.

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   • graph learning
   • graph learning:graph neural networks
   • graph learning:graph neural networks:graph interpretability
   • machine learning
   • machine learning:explainable AI
   • machine learning:robust learning
   • graphs
   • graphs:graph classification datasets
   • graphs:molecular graphs
   • graphs:rationale subgraphs
   • graphs:synthetic graph datasets
   • Innovate
   • graph neural networks
   • persistent homology
   • persistent homology:persistent rationale filtration
   • topological discrepancy
   • topological regularization

2. D-Gril: End-to-End Topological Learning With 2-Parameter Persistence (2026)

   Soham Mukherjee, Shreyas N. Samaga, Cheng Xin, Steve Oudot, Tamal K. Dey

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   • cheminformatics
   • cheminformatics:bioactivity prediction
   • drug discovery
   • machine learning
   • machine learning:graph learning
   • machine learning:graph learning:graph neural networks
   • ChEMBL bioactivity data
   • graphs
   • graphs:molecular graphs
   • generalized rank invariant landscape
   • persistent homology
   • persistent homology:differentiable persistence
   • persistent homology:multiparameter
   • persistent homology:multiparameter:bifiltration
   • topological machine learning

3. Topological Graph Neural Networks (2021)

   Max Horn, Edward De Brouwer, Michael Moor, Yves Moreau, Bastian Rieck, Karsten Borgwardt

   Abstract

   Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures, such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive in terms of the Weisfeiler--Lehman test of isomorphism. Augmenting GNNs with our layer leads to beneficial predictive performance, both on synthetic data sets, which can be trivially classified by humans but not by ordinary GNNs, and on real-world data.

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   • Graph classification
   • Machine learning
   • Machine learning:Graph Neural Networks
   • structured graph data
   • Innovate
   • Persistence diagrams
   • Topological graph layer
   • Weisfeiler–Lehman Analysis