🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.000875s)

  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.

    Community Resources

  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

    Community Resources

  3. Differentiable Euler Characteristic Transforms for Shape Classification (2023)

    Ernst Röell, Bastian Rieck
    Abstract The _Euler Characteristic Transform_ (ECT) is a powerful invariant, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method, the _Differentiable Euler Characteristic Transform_ (DECT) is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly simple statistic provides the same topological expressivity as more complex topological deep learning layers.

  5. Simplicial Representation Learning With Neural \$K\$-Forms (2023)

    Kelly Maggs, Celia Hacker, Bastian Rieck
    Abstract Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as the need for graph rewiring, ambiguity in interpreting data, and over-smoothing. In this paper, we take a different approach, focusing on leveraging geometric information from simplicial complexes embedded in \$\mathbb\R\\textasciicircumn\$ using node coordinates. We use differential \$k\$-forms in \$\mathbb\R\\textasciicircumn\$ to create representations of simplices, offering interpretability and geometric consistency without message passing. This approach also enables us to apply differential geometry tools and achieve universal approximation. Our method is efficient, versatile, and applicable to various input complexes, including graphs, simplicial complexes, and cell complexes. It outperforms existing message passing neural networks in harnessing information from geometrical graphs with node features serving as coordinates.