# Hyperbolic Contrastive Learning with Entailment for Spatial Transcriptomics

arXiv: https://arxiv.org/abs/2609.16207 · HTML: https://mlsanity.com/paper/2609.16207/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Spatially Resolved Gene Expression Prediction from H&E Histology Images via Bi-modal Contrastive Learning](https://mlsanity.com/paper/2306.01859/) (2023)
- [Accurate Spatial Gene Expression Prediction by integrating Multi-resolution features](https://mlsanity.com/paper/2403.07592/) (2024)
- [Exemplar Guided Deep Neural Network for Spatial Transcriptomics Analysis of Gene Expression Prediction](https://mlsanity.com/paper/2210.16721/) (2022)
- [MERGE: Multi-faceted Hierarchical Graph-based GNN for Gene Expression Prediction from Whole Slide Histopathology Images](https://mlsanity.com/paper/2412.02601/) (2024)
- [SEPAL: Spatial Gene Expression Prediction from Local Graphs](https://mlsanity.com/paper/2309.01036/) (2023)
- [Spatially Gene Expression Prediction using Dual-Scale Contrastive Learning](https://mlsanity.com/paper/2506.23827/) (2025)
- [Latent Gene Diffusion for Spatial Transcriptomics Completion](https://mlsanity.com/paper/2509.01864/) (2025)

## Abstract (arXiv)

Spatial Transcriptomics (ST) has transformed biomedical research by enabling the spatial mapping of gene expression across tissue sections. However, high operational costs, specialized equipment requirements, and sensitivity to experimental noise limit the accessibility and scalability of ST. Recent computer vision approaches aim to overcome these limitations by predicting spatial gene expression directly from histopathology images. While effective, current approaches often suffer from gene expression over-smoothing and overly uniform predictions across tissue regions, suggesting that further progress depends on learning representations that reflect the hierarchical and asymmetric structure of gene regulation and tissue morphology. To address these issues, we propose Hyperbolic Contrastive Learning with Entailment for Spatial Transcriptomics (HyCLoST), a hyperbolic contrastive learning model that captures the intrinsic hierarchical relationships within ST data. By leveraging hyperbolic geometry and a gene-to-image entailment loss, HyCLoST learns structured, biologically grounded representations that improve gene expression prediction accuracy, achieving a 6% reduction in MSE and an 8% increase in PCC across 26 ST datasets, over previous methods. Our source code is publicly available at https://github.com/BCV-Uniandes/HyCLoST