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D-GRIL: End-To-End Topological Learning with 2-Parameter Persistence

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

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LIPIcs.SoCG.2026.79.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Algebraic topology
  • Computing methodologies → Machine learning
Keywords
  • Topological Data Analysis
  • Persistent Homology
  • Multiparameter Persistence
  • Graph Learning
  • Graph Neural Networks

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Abstract

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 theory for gradient descent on Gril producing D-Gril. We show that D-Gril can be used to learn a bifiltration function on benchmark graph datasets. Further, we exhibit that this framework can be applied in the context of bio-activity prediction in drug discovery.

Cite As Get BibTex

Soham Mukherjee, Shreyas N. Samaga, Cheng Xin, Steve Oudot, and Tamal K. Dey. D-GRIL: End-To-End Topological Learning with 2-Parameter Persistence. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 79:1-79:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.79

Author Details

Soham Mukherjee
  • Department of Computer Science, Purdue University, West Lafayette, IN, USA
Shreyas N. Samaga
  • Department of Computer Science, Purdue University, West Lafayette, IN, USA
Cheng Xin
  • Department of Computer Science, Rutgers University, New Brunswick, NJ, USA
Steve Oudot
  • GeomeriX team, Inria Saclay and École polytechnique, Palaiseau, France
Tamal K. Dey
  • Department of Computer Science, Purdue University, West Lafayette, IN, USA

Funding

This work is partially supported by NSF grants CCF 2049010 and DMS 2301360.

Supplementary Materials

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