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

arXiv: https://arxiv.org/abs/2406.07100 · HTML: https://mlsanity.com/paper/2406.07100/

## 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 (most cited first, 22 of 22)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Stochastic subgradient method converges on tame functions](https://mlsanity.com/paper/1804.07795/) (2018)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology](https://mlsanity.com/paper/1907.05008/) (2019)
- [A Framework for Differential Calculus on Persistence Barcodes](https://mlsanity.com/paper/1910.00960/) (2019)
- [Gradient Sampling Methods for Nonsmooth Optimization](https://mlsanity.com/paper/1804.11003/) (2018)
- [Interactive Visualization of 2-D Persistence Modules](https://mlsanity.com/paper/1512.00180/) (2015)
- [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures](https://mlsanity.com/paper/2306.03801/) (2023)
- [A Kernel for Multi-Parameter Persistent Homology](https://mlsanity.com/paper/1809.10231/) (2018)
- [ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery](https://mlsanity.com/paper/2211.03808/) (2022)
- [GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning](https://mlsanity.com/paper/2304.04970/) (2023)
- [Generalized Persistence Diagrams for Persistence Modules over Posets](https://mlsanity.com/paper/1810.11517/) (2018)
- [Fast Computation of Zigzag Persistence](https://mlsanity.com/paper/2204.11080/) (2022)
- [Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications](https://mlsanity.com/paper/2111.15058/) (2021)
- [EMP: Effective Multidimensional Persistence for Graph Representation Learning](https://mlsanity.com/paper/2401.13713/) (2024)

## Built on by (most cited first, 5 of 5)

- [Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data](https://mlsanity.com/paper/2502.16049/) (2025)
- [TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration](https://mlsanity.com/paper/2510.05102/) (2025)
- [TopoPrune: Robust Data Pruning via Unified Latent Space Topology](https://mlsanity.com/paper/2602.02739/) (2026)
- [A Persistent Homology Design Space for 3D Point Cloud Deep Learning](https://mlsanity.com/paper/2604.04299/) (2026)
- [COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules](https://mlsanity.com/paper/2609.22012/) (2026)

## 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.