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Hyperbolic Contrastive Learning with Entailment for Spatial Transcriptomics
Daniela Vega, Paula Cárdenas, Hannah Ceballos, Leonardo Manrique, Pablo Arbelaéz
TL;DR
Spatial transcriptomics is costly and noise-sensitive, and existing methods often leave biological hierarchy implicit. HyCLoST combines hyperbolic contrastive learning with gene-to-image entailment; across 26 SpaRED datasets, it reports a 6% reduction in MSE and an 8% increase in PCC over prior methods.
Problem
Spatial transcriptomics is costly and susceptible to technical noise, while existing approaches often fail to model biological hierarchy explicitly.
Source: §1 · pp. 1–3Method
HyCLoST learns hyperbolic representations with contrastive learning and a gene-to-image entailment loss to model hierarchical and directional relationships.
Source: §1 · p. 3, §2.2 · p. 5Results
Across the 26 SpaRED datasets, HyCLoST reports a 6% reduction in MSE and an 8% increase in PCC over the second-best method.
Source: §3.2 · p. 6Takeaways & Limitations
The results indicate that refining representation geometry and semantics is a promising direction for spatial gene-expression prediction.
Source: §4 · p. 9
Abstract
from arXiv · showhide
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
1 Introduction
Spatial transcriptomics is costly and susceptible to technical noise, while existing approaches often fail to model biological hierarchy explicitly. HyCLoST uses hyperbolic contrastive learning and gene-to-image entailment, reporting improved prediction across 26 SpaRED datasets.
1 Introduction
- Spatial transcriptomics maps gene expression within tissue architecture, but its cost, specialized equipment, and susceptibility to noise and missing measurements limit scalability.These constraints also limit development of robust AI models.Source: §1 · pp. 1–2
- Existing methods include architecture- and representation-focused approaches, but many still rely on Euclidean embeddings and do not explicitly model biological hierarchy.The introduction notes that DELST uses hyperbolic entailment mainly as a regularizer while retaining Euclidean multimodal alignment.Source: §1 · pp. 2–3
- HyCLoST combines hyperbolic representations with a gene-to-image entailment loss to model hierarchical structure and directional relationships between gene expression and tissue morphology.The framework uses pretrained UNI2-h and Geneformer features and evaluates recent methods within the unified SpaRED benchmark.Source: §1 · p. 3
- HyCLoST reports an average 6% reduction in MSE and an 8% increase in PCC over prior methods across the 26 SpaRED datasets.The evaluation is conducted under a unified benchmark.Source: §1 · p. 3
2 Method
HyCLoST maps image-patch and gene-expression embeddings into a shared hyperbolic space, then trains them with symmetric contrastive and directional entailment objectives. At inference, it predicts gene expression by retrieving nearby training gene embeddings.
2 Method
- At inference, HyCLoST retrieves nearby training gene embeddings for each test patch and averages their expression vectors; embeddings are precomputed per dataset.The retrieval uses the Lorentzian inner product, and its KNN cost grows linearly with dataset size.Source: §2 · pp. 3–4
2.1 Data encoding and hyperbolic mapping
- UNI2-h and Geneformer encode patches and gene profiles; projected embeddings are mapped from the tangent space onto a learned-curvature Lorentz hyperboloid.The Lorentz model represents hyperbolic space on the upper sheet of a two-sheeted hyperboloid.Source: §2.1 · p. 4
2.2 Contrastive learning with hyperbolic representations
- A symmetric contrastive objective uses negative hyperbolic distance as similarity, treating paired patch–gene embeddings as positives and other pairs as negatives.The objective pulls matched embeddings closer and pushes mismatched pairs apart.Source: §2.2 · pp. 4–5
2.3 Gene-to-Image entailment
- The entailment loss models the asymmetric gene-to-image relationship by placing image embeddings within gene-induced cones and penalizing violations of that containment.The total training objective combines contrastive and entailment losses, weighted by μ.Source: §2.3 · p. 5
3 Results
HyCLoST is evaluated against nine methods across 26 SpaRED datasets, where it leads on average MSE and PCC. Qualitative comparisons and ablations examine prediction patterns, model components, and entailment direction.
3.1 Experimental Framework
- Across 26 SpaRED datasets spanning 14 human and 12 mouse datasets and nine tissue types, evaluation uses directly measured genes and nine baselines, with inference k=80.M2TGLGO and TRIPLEX include starred variants reflecting gene-coverage and constant-prediction evaluation constraints.Source: §3.1 · p. 6
3.2 Main Results
- HyCLoST ranks first in 10 of 26 datasets, while improvements over simpler models remain modest.The paper reports consistent improvements in both MSE and PCC across diverse tissues and acquisition settings.Source: §3.2 · p. 6
- 6% reduction in MSE and 8% increase in PCC over the second-best method across 26 SpaRED datasets.HyCLoST also achieves the best average rank (2.79) and significantly outperforms 10 of 11 baseline configurations.Source: §3.2 · p. 6, Table 1 · p. 7
3.3 Qualitative Results
- Across representative low-error and harder cases, HyCLoST preserves dynamic range and spatial patterns and better captures extreme expression values while competitors flatten predictions.All methods have higher errors in the harder examples.Source: §3.3 · p. 7
3.4 Ablation Experiments
- Table 2 reports 26-dataset ablation MSE: entailment improves accuracy; a small ViT raises MSE, Geneformer improves performance, and Euclidean geometry raises MSE.The Euclidean comparison keeps other components unchanged.Source: §3.4 · pp. 7–8, Table 2 · p. 8
- Gene-to-image entailment achieves lower MSE than image-to-gene in 21 of 26 datasets, with a consistent but moderate average gap.The authors interpret this direction as matching gene expression's role in constraining plausible tissue morphologies.Source: §3.4 · p. 8
4 Conclusions
HyCLoST predicts gene expression from histopathology images using hyperbolic geometry and gene-to-image entailment. Across 26 SpaRED datasets, it improves average MSE by 6% and PCC by 8% over prior methods.
4 Conclusions
- HyCLoST predicts gene expression from histopathology images using a joint hyperbolic space and gene-to-image entailment loss.The framework models hierarchical relationships and asymmetric dependence between gene expression and tissue appearance.Source: §4 · p. 9
- Across 26 SpaRED datasets, HyCLoST improves average MSE by 6% and PCC by 8% over prior methods.Source: §4 · p. 9
- The results point to refining representation-space geometry and semantics as a direction for modeling biological structure in spatial gene expression prediction.Source: §4 · p. 9