# Learning Protein-Ligand Binding in Hyperbolic Space

arXiv: https://arxiv.org/abs/2508.15480 · HTML: https://mlsanity.com/paper/2508.15480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 26 of 26)

- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [DeepDTA: Deep Drug-Target Binding Affinity Prediction](https://mlsanity.com/paper/1801.10193/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Inferring Concept Hierarchies from Text Corpora via Hyperbolic Embeddings](https://mlsanity.com/paper/1902.00913/) (2019)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations](https://mlsanity.com/paper/2303.06242/) (2023)
- [CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data](https://mlsanity.com/paper/2111.15037/) (2021)
- [DrugCLIP: Contrastive Protein-Molecule Representation Learning for Virtual Screening](https://mlsanity.com/paper/2310.06367/) (2023)
- [Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning](https://mlsanity.com/paper/2306.01474/) (2023)
- [Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning](https://mlsanity.com/paper/2305.18962/) (2023)
- [Hyperbolic Safety-Aware Vision-Language Models](https://mlsanity.com/paper/2503.12127/) (2025)
- [Protein-ligand binding representation learning from fine-grained interactions](https://mlsanity.com/paper/2311.16160/) (2023)
- [Fully Hyperbolic Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2108.04607/) (2021)
- [Hashing based Contrastive Learning for Virtual Screening](https://mlsanity.com/paper/2407.19790/) (2024)

## Built on by (most cited first, 2 of 2)

- [Contrastive Geometric Learning Unlocks Unified Structure- and Ligand-Based Drug Design](https://mlsanity.com/paper/2601.09693/) (2026)
- [CliffRank: A Dual-Branch Framework for Activity-Cliff Ranking Prediction](https://mlsanity.com/paper/2609.01673/) (2026)

## Abstract (arXiv)

Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for similarity-based search, the geometry of Euclidean embeddings often fails to capture the hierarchical structure and fine-grained affinity variations intrinsic to molecular interactions. In this work, we propose HypSeek, a hyperbolic representation learning framework that embeds ligands, protein pockets, and sequences into Lorentz-model hyperbolic space. By leveraging the exponential geometry and negative curvature of hyperbolic space, HypSeek enables expressive, affinity-sensitive embeddings that can effectively model both global activity and subtle functional differences-particularly in challenging cases such as activity cliffs, where structurally similar ligands exhibit large affinity gaps. Our mode unifies virtual screening and affinity ranking in a single framework, introducing a protein-guided three-tower architecture to enhance representational structure. HypSeek improves early enrichment in virtual screening on DUD-E from 42.63 to 51.44 (+20.7%) and affinity ranking correlation on JACS from 0.5774 to 0.7239 (+25.4%), demonstrating the benefits of hyperbolic geometry across both tasks and highlighting its potential as a powerful inductive bias for protein-ligand modeling.