mlsanityData to 7 Oct 2026

Topological Neural Networks go Persistent, Equivariant, and Continuous

arXiv 2406.03164 ↗First posted 5 Jun 2024cs.LGcited by 15

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Abstract (arXiv)

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 49 of its 69 references that are in the map. First posted on arXiv 5 Jun 2024.

Builds on

49 of 69 references.

References · 49

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
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37 more
  1. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  2. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  3. 2020Directional Message Passing for Molecular Graphscited by 556
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  11. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  12. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217
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  16. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
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  22. 2021Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-designcited by 82
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  32. 2023Going beyond persistent homology using persistent homologycited by 21
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  36. 2022Modular Flows: Differential Molecular Generationcited by 11
  37. 2023Trainability, Expressivity and Interpretability in Gated Neural ODEscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 8; 2026: 6.

15 papers.

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  1. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  2. 2025LEAP: Local ECT-Based Learnable Positional Encodings for Graphscited by 2
  3. 2025On topological descriptors for graph productscited by 2
  4. 2026The Logical Expressiveness of Topological Neural Networkscited by 2
  5. 2025Positional Encoding meets Persistent Homology on Graphscited by 1
  6. 2025Graph Persistence goes Spectralcited by 1
  7. 2025Heat Kernel Goes Topologicalcited by 1
  8. 2025T3former: Temporal Graph Classification with Topological Machine Learningcited by 1
  9. 2026TopoFormer: Topology Meets Attention for Graph Learningcited by 1
  10. 2025Topological Feature Compression for Molecular Graph Neural Networkscited by 0
  11. 2025Persistent Topological Structures and Cohomological Flows as a Mathematical Framework for Brain-Inspired Representation Learningcited by 0
  12. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0
3 more
  1. 2026From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Featurescited by 0
  2. 2026Differentiable Lifting for Topological Neural Networkscited by 0
  3. 2026Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operatorscited by 0