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

Abstract

End-to-end topological learning with 1-parameter persistence has become an important way to incorporate topological information into machine learning models. This paper extends that direction to 2-parameter persistence by building on the GRIL vectorization. We analyze differentiability properties of GRIL, establish a gradient-based learning framework for bifiltration functions, and develop D-GRIL as a differentiable topological layer. The resulting framework is evaluated on graph learning benchmarks and bio-activity prediction tasks, showing how 2-parameter topological features can be learned directly in a machine learning pipeline.

Key Contributions

• Differentiable 2-parameter topology: Develops a differentiable learning layer based on the GRIL vectorization.
• Bifiltration learning: Learns a bifiltration function instead of relying on hand-designed filter functions.
• Theory for optimization: Analyzes the structure needed for gradient-based learning with GRIL.
• Applications: Applies the framework to graph learning and bio-activity prediction.

Citation

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), LIPIcs 367, 79:1-79:17, 2026.

BibTeX Citation

@inproceedings{mukherjee2026dgril,
  title={D-GRIL: End-To-End Topological Learning with 2-Parameter Persistence},
  author={Soham Mukherjee and Shreyas N. Samaga and Cheng Xin and Steve Oudot and Tamal K. Dey},
  booktitle={42nd International Symposium on Computational Geometry (SoCG 2026)},
  series={Leibniz International Proceedings in Informatics (LIPIcs)},
  volume={367},
  pages={79:1--79:17},
  year={2026},
  doi={10.4230/LIPIcs.SoCG.2026.79}
}

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