mlsanityData to 7 Oct 2026

Enhancing Graph Representation Learning with Localized Topological Features

arXiv 2501.09178 ↗First posted 15 Jan 2025cs.LG cs.SIcited by 6

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Abstract (arXiv)

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 61 of its 96 references that are in the map. First posted on arXiv 15 Jan 2025.

Builds on

61 of 96 references.

References · 61

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38 more
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50 most cited of 61 All 61 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025Positional Encoding meets Persistent Homology on Graphscited by 1
  2. 2025Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domainscited by 0
  3. 2025CoPHo: Classifier-guided Conditional Topology Generation with Persistent Homologycited by 0
  4. 2026Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cellscited by 0
  5. 2026Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspectivecited by 0
  6. 2026Signed Graph Pre-Training and Prompt Learningcited by 0