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Abstract
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.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/3824_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/BCV-Uniandes/HyCLoST
Link to the Dataset(s)
Spared Dataset: https://drive.google.com/drive/mobile/folders/15W_rZlt5PhUlslM-u5_jw9etjkGRXb-N?usp=sharing
BibTex
@InProceedings{VegDan_Hyperbolic_MICCAI2026,
author = { Vega, Daniela AND Cárdenas, Paula AND Ceballos, Hannah AND Manrique, Leonardo AND Arbeláez, Pablo},
title = { { Hyperbolic Contrastive Learning with Entailment for Spatial Transcriptomics } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16891},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper proposes a hyperbolic contrastive learning framework for predicting spatial gene expression from histopathology images. It maps image patches and gene expression embeddings into a shared hyperbolic space and introduces a gene-to-image entailment loss to model asymmetric biological relationships. The method is evaluated on the SpaRED benchmark across 26 datasets and demonstrates improved prediction performance over existing methods.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The paper proposes a hyperbolic contrastive learning framework that maps histopathology patches and gene expression embeddings into a shared hyperbolic space, aiming to capture the intrinsic hierarchical relationships in spatial transcriptomics data. 2.The proposed gene-to-image entailment loss captures the asymmetric relationship between gene expression and tissue morphology, going beyond conventional symmetric contrastive alignment. 3.The experimental evaluation is conducted on 26 datasets under the SpaRED benchmark, with consistent improvements in both MSE and PCC, and is supported by ablation studies validating the roles of hyperbolic geometry and entailment objectives.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.The claim that hyperbolic space better captures hierarchical structure is not fully substantiated, as the hierarchical relationships in gene expression or tissue organization are not explicitly analyzed or validated. 2.The method ultimately relies on a retrieval-based prediction scheme (top-k nearest gene embeddings), which limits its ability to model the underlying gene expression generation process. 3.The experimental comparison includes several methods that are relatively dated, which may limit how well the results reflect performance against more recent approaches. 4.The framework builds on pretrained foundation models (UNI2-h and Geneformer), but the contribution of the proposed hyperbolic contrastive learning is not clearly isolated from that of the underlying pretrained representations. 5.While the method improves MSE and PCC, the performance gains are relatively limited, and the biological relevance of the learned representations is not further validated through additional analysis or interpretation.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The authors claimed to release the source code and/or dataset upon acceptance of the submission.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper presents a well-motivated framework that leverages hyperbolic geometry and a gene-to-image entailment objective to model hierarchical and asymmetric relationships in spatial transcriptomics data. The method is technically sound, and the experimental evaluation is relatively comprehensive, showing consistent improvements across multiple datasets under a standardized benchmark. However, several concerns limit the overall impact. The justification for adopting hyperbolic representations is not fully substantiated, and the biological claims are not supported by additional analysis. The method also relies on a retrieval-based prediction scheme and pretrained foundation models, making it unclear how much of the performance gain is attributable to the proposed design. In addition, the empirical improvements, while consistent, remain relatively modest, and the experimental comparisons may not fully reflect the most recent advances. Overall, the paper offers a reasonable and well-executed contribution with some interesting ideas, but the current evidence is not entirely sufficient to firmly establish its significance.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #2
- Please describe the contribution of the paper
1) introduce a novel hyperbolic contrastive learning framework for multimodal Spatial Transcriptomics alignment that leverages hierarchical geometry to improve multimodal alignment and prediction accuracy.
2) Propose a new gene-to-image entailment loss that captures the directional and asymmetric relationships between gene expression profiles and tissue morphology.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1）Introduce a novel gene-to-image entailment loss that addresses the conceptual shortcomings of previous contrastive learning methods, which treat the image-gene relationship as purely symmetric. 2) The transition to hyperbolic space is fundamentally motivated by the hierarchical structures inherent in gene regulation. This provides a significantly stronger inductive bias for modeling biological data compared to standard Euclidean distance metrics.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1).The directional ablation is not fully convincing. Although “gene entails image” performs better than “image entails gene” (0.899 vs. 0.919 MSE), the gap is small, and the paper does not report per-dataset results or statistical testing for this comparison. It is therefore unclear whether this reflects a robust effect across all 26 datasets or only a marginal average gain. 2) The retrieval-based inference is insufficiently analyzed. Prediction relies on k-nearest-neighbor retrieval in the learned hyperbolic space, but the paper does not discuss how this strategy generalizes when test samples are underrepresented in the training set, such as rare morphologies or distribution-shifted cases.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The authors claimed to release the source code and/or dataset upon acceptance of the submission.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
It proposes a technically solid method and validates it fairly extensively on 26 SpaRED datasets. The evaluation is reasonably comprehensive, and the reported performance gains, ablation studies, and statistical analyses make the work sufficiently convincing at the benchmark level.
However, I do not view the method as a major methodological breakthrough; rather, it appears to be a well-motivated integration of existing ideas. Its novelty is relatively limited, and the analysis of the retrieval-based inference mechanism is insufficient.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The authors have provided a detailed response to the reviewers’ comments, clarifying the motivation for hyperbolic geometry, the directionality from genes to images, and the improvements in efficiency and performance of their method. The contributions of the paper—namely the hyperbolic contrastive learning framework and the directional gene-to-image loss—clearly demonstrate the novelty and applicability of the approach.
However, some issues remain. The effect of the directional ablation is relatively modest, and the generalization ability of retrieval-based reasoning under rare morphologies or distribution shifts has not been evaluated. It is recommended that the final version include ablation results for each dataset and discuss the potential limitations of the retrieval strategy.
Review #3
- Please describe the contribution of the paper
This paper introduces HyCLoST, a method for predicting spatial gene expression from H&E patches by learning a joint hyperbolic representation of image and gene features. The main idea is to move beyond standard Euclidean alignment and instead model the hierarchical structure of the problem in hyperbolic space. On top of the contrastive objective, the paper adds a gene-to-image entailment loss, which is meant to reflect the asymmetric relationship between molecular profiles and tissue morphology. The method is evaluated on the unified SpaRED benchmark over 26 datasets, where it shows improved average MSE and PCC compared with previous approaches.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
(1)The motivation for using hyperbolic space is sensible in this setting, since the authors argue that gene regulation and tissue morphology are organized in a hierarchical way. This makes the method feel more principled than many purely architectural refinements. (2)The proposed gene-to-image entailment loss is a nice addition. The paper does not simply assume that image and gene embeddings should be matched symmetrically; instead, it encodes the idea that gene expression constrains morphology. I think this is one of the more interesting parts of the paper, and the directionality experiment in the ablation section helps support that this choice is meaningful rather than arbitrary. (3)The results are reported on 26 SpaRED datasets, which gives a broader picture than papers evaluated on only a few datasets. The comparison set is also reasonably strong and includes several recent methods. HyCLoST achieves the best average MSE and PCC, and the statistical testing further strengthens the empirical claim. (4)The visual comparisons suggest that the method is better at preserving spatial variation and dynamic range, while some competing methods tend to produce flatter predictions. Since over-smoothing is one of the issues raised early in the paper, it is good to see qualitative evidence that the proposed method addresses that point.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
(1)At inference time, predictions are obtained by averaging the gene expression vectors of the top-k nearest training gene embeddings. This is simple and effective, but it may raise questions about sensitivity to k, memory/computation at scale, and whether a more direct decoding strategy could further improve generalization. The paper specifies k=80, but deeper analysis of robustness to this choice would strengthen the work. (2)The model relies on foundation encoders (UNI2-h and Geneformer) and hyperbolic operations. Although embeddings are precomputed to reduce computation, the paper provides limited discussion of training/inference efficiency, resource requirements, and whether the method is practical in lower-resource settings.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The authors claimed to release the source code and/or dataset upon acceptance of the submission.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper presents a technically novel and well-motivated method, supported by broad and credible experimental validation. In particular, the combination of hyperbolic contrastive learning and a directional gene-to-image entailment loss is conceptually meaningful for this task and is not merely an architectural variation of existing methods. The empirical results on 26 public SpaRED datasets show that the method consistently outperforms a strong set of baselines in both MSE and PCC, and the ablation studies provide evidence that the gains come from the core proposed ideas rather than incidental implementation choices.My score is 5 (Accept) rather than 6 because, although the work is strong, the practical performance gains are still moderate rather than transformative, and some aspects such as computational cost, retrieval sensitivity, and deeper biological interpretation could be better developed. Still, the paper is clearly above the acceptance threshold and makes a meaningful methodological contribution to spatial transcriptomics prediction from histology.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
Thank you, I will keep the score unchanged.
Author Feedback
We thank the reviewers for recognizing HyCLoST’s contributions: hyperbolic contrastive learning for spatial transcriptomics (ST) alignment, directional gene-to-image entailment, and broad SpaRED evaluation with statistical testing, ablations, and qualitative evidence. We respond by issue.
Hyperbolic motivation and isolation from foundation encoders (R1, Meta). HyCLoST treats hyperbolic geometry as an inductive bias for the multi-scale organization, linking tissue morphology to underlying regulatory programs [8]. We do not claim to discover a new biological hierarchy; rather, we test this inductive bias through controlled comparisons. Tab 2 provides this test under matched conditions: replacing hyperbolic with Euclidean while keeping identical UNI2-h/Geneformer increases MSE from 0.899 to 1.043, isolating the geometric contribution from the foundation encoders. Leveraging strong pretrained representations is complementary to our approach, as improvements in foundation models can directly benefit our framework. We will clarify this motivation and biological scope.
Directional entailment (R2). Gene-to-image entailment encodes a biological asymmetry: gene expression is the underlying causal state and image morphology its observable manifestation, so morphology should be “entailed by” expression rather than the reverse. Tab. 2 (Row 5 vs Row 7) compares gene-to-image vs image-to-gene under identical settings on all datasets; gene-to-image yields lower average MSE (0.899 vs 0.919), consistent with the biological asymmetry argued in Sec. 2.3.The mean gap is moderate, but the effect is consistent across datasets. Inspecting the per-dataset results underlying Tab. 2, gene-to-image obtains lower MSE in 21/26 datasets and higher PCC in 23/26.We will discuss these results in the final version.
Retrieval robustness, k-sensitivity and scalability (all reviewers). Sec. 2 specifies non-parametric inference: each test patch is projected and predicted by averaging its top-k nearest training gene embeddings under the Lorentzian inner product (k=80, Sec. 3.1). The design is motivated by SpaRED’s heterogeneity across tissues and species: a single parametric decoder must compress these heterogeneous output distributions, whereas retrieval adapts locally to the nearest learned morphologies. At scale, embeddings are precomputed once per dataset, so KNN cost grows linearly with dataset size and remains negligible relative to encoding. We acknowledge finer k-sensitivity and alternative decoder studies as valuable future work, but per the rebuttal guidelines, we do not introduce new experiments here.
Efficiency and practicality (R4). UNI2-h/Geneformer embeddings are precomputed once; training and inference then run on a lightweight projection head. HyCLoST trains on a single GPU in ~2h on small datasets and ~1 day on the largest; inference takes 1–2 min per dataset, making the method practical for lower-resource settings.
Magnitude of gains (R1). Tab. 1 reports robustness measures beyond the mean. HyCLoST attains the best average rank (2.792) under the Friedman test. Across 9 baseline methods, HyCLoST is best on 10/26 datasets and significantly outperforms 10/11 configurations under paired Wilcoxon tests with Holm–Bonferroni correction. Given SpaRED’s heterogeneity across 9 tissue types and 2 species, these complementary statistics indicate consistent, not marginal, gains.
Comparison with dated methods (R1). 7 of our 9 baselines are from 2023 or later, including MERGE [7] and M2TGLGO [20] (both 2025). We attempted to include NH2ST (Qu et al., 2025) and HAGE (Dang et al., 2025), but key implementation details were unavailable, preventing a fair, reproducible comparison. However, we will include these methods in the related work section.
In the camera-ready, we will (i) clarify the geometric motivation and biological scope, (ii) discuss per-dataset directional results, and (iii) note the additional 2025 methods.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
On the positive side, the reviewers found it generally sound in terms of the technical details and the quality of the evaluation. They particularly liked how the work introduces the usage of hyperbolic contrastive learning and a directional gene-to-image entailment loss. The biggest issue that the reviewers found with this paper is that the justification behind the hyperbolic/hierarchical assumption is not well supported by both biological and empirical evidence. There is also a concern about the proposed retrieval-based inference strategy with respect to robustness, sensitivity to k, scalability and generalization, particularly in rare/shifting test scenarios. They also raised concerns about the claimed contribution versus what could be attributed to strong foundation pretrained encoders in use here. Overall, while the performance is consistent, the improvements are not significant. They would also like to see better support in the form of more biological interpretation/statistics and stronger comparison with prior/recent works. The author is recommended to provide responses to all of the raised points with particular attention to: the modeling assumptions, the justification of components of the proposed method, robustness beyond just averaging over the benchmarks.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
After rebuttal, the available post-rebuttal opinions are clearly positive: R2 accepts after the authors clarified the hyperbolic motivation, directionality, efficiency, and performance, R4 also maintains Accept and states that the authors have addressed the concerns sufficiently. R1 did not submit their final rating, but after review, I think that most of the concerns could be fine.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The proposed combination of hyperbolic contrastive learning and directional gene-to-image entailment is novel, technically sound, and well motivated. The paper is supported by a comprehensive evaluation across 26 SpaRED datasets, demonstrating consistent improvements over strong baselines. The rebuttal satisfactorily addressed the main concerns regarding the motivation for hyperbolic geometry, the contribution beyond foundation encoders, and the role of the entailment objective. While some limitations of the retrieval-based inference strategy remain, they do not outweigh the paper’s methodological contributions and strong empirical validation.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper proposes HyCLoST, a hyperbolic contrastive learning framework with a directional gene-to-image entailment objective for spatial transcriptomics prediction. Reviewers appreciated the motivation, the novel use of hyperbolic geometry and entailment learning, as well as the comprehensive evaluation on 26 SpaRED datasets. I agree with Reviewers #2 and #4 that the method is technically sound and well validated. The rebuttal satisfactorily clarified the contribution of hyperbolic geometry beyond the foundation encoders and provided additional evidence supporting the directional design. While some limitations of the retrieval-based inference remain, they do not undermine the main contribution. Overall, I find the work novel, well evaluated, and worthy of acceptance.