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

2024-06-11

arXiv.org

AI Summary

This work addresses the limited representational capacity of single-parameter persistent homology in graph representation learning. We propose D-GRIL, the first differentiable vectorization method for two-parameter persistent homology, and introduce 2-parameter persistent homology into end-to-end topological learning for the first time. D-GRIL features a differentiable GRIL layer that jointly learns two filtration functions over graph structures while guaranteeing theoretical differentiability via rigorous gradient computation. The method integrates seamlessly with graph neural networks and supports fully end-to-end training. Extensive experiments on standard graph benchmarks validate its effectiveness. Notably, on molecular bioactivity prediction tasks, D-GRIL significantly enhances the discriminative power of topological representations—establishing a novel, more expressive paradigm for topological modeling in drug discovery.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Applications

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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 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.

Problem

• Enhance topological learning with 2-parameter persistence
• Differentiate GRIL to produce D-GRIL
• Apply D-GRIL in bio-activity prediction

Innovation

• 2-parameter persistence technique
• D-GRIL for bifiltration learning
• Bio-activity prediction application