mlsanityData to 14 Oct 2026

D-GRIL: End-to-End Topological Learning with 2-parameter Persistence

arXiv 2406.07100 ↗First posted 11 Jun 2024cs.LG cs.AI math.ATcited by 5

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Abstract (arXiv)

End-to-end topological learning using 1-parameter persistence is well-known. We show that the framework can be enhanced using 2-parameter persistence by adopting a recently introduced 2-parameter persistence based vectorization technique called GRIL. We establish a theoretical foundation of differentiating GRIL producing D-GRIL. We show that D-GRIL can be used to learn a bifiltration function on standard benchmark graph datasets. Further, we exhibit that this framework can be applied in the context of bio-activity prediction in drug discovery.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 22 of its 48 references that are in the map. First posted on arXiv 11 Jun 2024.

Builds on

22 of 48 references.

References · 22

  1. 2016XGBoost: A Scalable Tree Boosting Systemcited by 5,166
  2. 2018How Powerful are Graph Neural Networks?cited by 4,393
  3. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 728
  4. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 236
  5. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 126
  6. 2018Stochastic subgradient method converges on tame functionscited by 124
  7. 2017Deep Learning with Topological Signaturescited by 114
  8. 2021Topological Graph Neural Networkscited by 87
  9. 2014A Stable Multi-Scale Kernel for Topological Machine Learningcited by 75
  10. 2019Graph Filtration Learningcited by 69
  11. 2019Understanding the Representation Power of Graph Neural Networks in Learning Graph Topologycited by 52
  12. 2019A Framework for Differential Calculus on Persistence Barcodescited by 29
10 more
  1. 2018Gradient Sampling Methods for Nonsmooth Optimizationcited by 23
  2. 2015Interactive Visualization of 2-D Persistence Modulescited by 19
  3. 2023Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measurescited by 15
  4. 2018A Kernel for Multi-Parameter Persistent Homologycited by 13
  5. 2022ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discoverycited by 13
  6. 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
  7. 2018Generalized Persistence Diagrams for Persistence Modules over Posetscited by 6
  8. 2022Fast Computation of Zigzag Persistencecited by 6
  9. 2021Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applicationscited by 4
  10. 2024EMP: Effective Multidimensional Persistence for Graph Representation Learningcited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Datacited by 1
  2. 2025TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtrationcited by 1
  3. 2026TopoPrune: Robust Data Pruning via Unified Latent Space Topologycited by 1
  4. 2026A Persistent Homology Design Space for 3D Point Cloud Deep Learningcited by 1
  5. 2026COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modulescited by 0