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Abstract
Multimodal learning has demonstrated strong potential for cancer survival prediction through the joint modeling of whole-slide images (WSIs) and genomic data. However, existing approaches struggle to capture deep interactions between genomic signals and multiscale pathological representations. Although hyperbolic geometry naturally accommodates hierarchical structures, most current hyperbolic multimodal methods still adopt proximity-driven contrastive paradigms and rely primarily on geodesic distance for similarity estimation. Such designs overemphasize cross-modal spatial proximity while neglecting intrinsic modality discrepancies, thereby weakening modality-specific structures and compromising hierarchical organization.
To overcome these limitations, we propose HyperGP, an angular-constrained hyperbolic learning framework for multimodal survival prediction. It explicitly models pathology as a patch–region–slide hierarchy and derives prognostic anchors from pathway-level genomics.
We introduce a geometry-aware hierarchical representation module to embed both modalities into a shared hyperbolic manifold and obtain risk-specific prototypes. These embeddings and prototypes are subsequently aligned by a designed unified multimodal angular contrastive learning module while preserving modality-specific structures. Finally, we propose an angular hyperbolic-guided survival prediction module for precise survival forecasting. Extensive experiments across multiple cancer cohorts demonstrate the superior performance of the proposed HyperGP, highlighting the effectiveness of angular constraints for hierarchical survival modeling in hyperbolic space. Code is available at: https://github.com/yang1987-star/hyperGP.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/4614_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{YanHao_AngularConstrained_MICCAI2026,
author = { Yang, Haotian AND Zhang, Qing AND Li, Qingli AND Wang, Yan},
title = { { Angular-Constrained Hyperbolic Learning for Hierarchical Multimodal Survival Prediction } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16887},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
In this paper, the authors propose an angular-constrained hyperbolic learning framework for multimodal survival prediction.
- 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.
Novel multimodal data integration model.
- 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.
See comments.
- 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.
(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?
1.For pathology feature extraction, the authors claim that “The patch features Fp are spatially partitioned into G groups, and the top-K patches in each group are maintained by calculating importance scores through an attention block.” First, in some regions, all patches may be normal or tumor tissue. This sampling strategy risks discarding critical information while retaining normal tissue content. Secondly, what exactly is the “attention block”? How is it obtained or trained? This needs clarification. 2.For genomic data, the design of L_proto requires further clarification. For example, a patient observed to survive until time c may still be alive at time c+1.However, Yet, in the current loss formulation, their similarity to p_{a,c+1} is penalized, which seems inconsistent. 3.What specific values are used for w1 and w2 in Eqn. 8? 4.What is the relationship between the patches shown in Fig. 3c and the attention maps in Fig. 3b? The correlation is not clearly explained. I believe this paper has merit, but the above points need to be addressed to improve clarity and technical rigor.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Reject
- [Post rebuttal] Please justify your final decision from above.
The responses to Q1 and Q3 are unsatisfactory and miss my points. Furthermore, using CAMELYON16 as an example is a poor choice, as it may limit the generalizability of the proposed methods. Therefore, I will decrease my score accordingly.
Review #2
- Please describe the contribution of the paper
The paper proposes HyperGP for multimodal survival prediction from WSIs and genomics. The method models WSIs in a patch-region-slide hierarchy, derives risk-specific genomic prototypes, embeds both modalities into a shared space, and aligns them with a unified multimodal angular contrastive learning objective. An angular hyperbolic-guided decoder is then used for survival prediction. Experiments show that HyperGP achieves the best overall performance among the compared 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 modeling of WSI in a hierarchical way using hyperbolic constraint is interesting and important.
2.The experimental results show promising results among the selected methods.
3.The paper is generally easy to understand and follow.
- 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 comparison methods seem a bit outdated. At least, direct baselines utilizing hyperbolic modeling are missing (MRePath IJCAI25, HyperPath MICCAI25, etc.) (and more general ones like MMP ICML24).
2.The novelty appears limited, and the paper mainly combines known components (Lorentz model, PIBD-style prototype, InfoNCE, etc.) under a new formulation rather than introducing a substantially new insight or principle.
3.One of the central claim of this paper is that angular-constraint matching is better in geodesic-based matching. However, there is no direct comparison between these two matching strategies in the ablation studies. Because of this, it would be hard to tell the performance gain is from this or the hierarchical design.
- 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 weaknesses outweigh the strengths to me. Lacking of most recent baselines and novelty make this paper less attractive to the readers.
- 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 rebuttal has addressed most of my concerns. Based on other reviewers’ feedback, I think the paper has its merits, and would recommend accept.
Review #3
- Please describe the contribution of the paper
The authors propose the HyperGP framework, which integrates pathological multi-scale features and genomic pathway prototype representations within a shared Lorentz hyperbolic manifold. They develop a unified multi-modal angular contrastive learning approach that achieves hierarchical semantic alignment across scales and modalities through bidirectional angular constraints. Additionally, they introduce an angular hyperbolic-guided decoder that directly predicts survival risk on the hyperbolic manifold using angular distances.
- 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.
The novelty of this approach lies in its geometric perspective, which reframes multi-modal fusion for survival prediction as a hierarchical geometric alignment problem. It leverages the inherent suitability of hyperbolic space for representing hierarchical structures, thereby introducing an innovative concept. The technical pipeline is comprehensive, encompassing hierarchical representation construction, hyperbolic mapping, angular contrastive learning, and hyperbolic decoding, resulting in a systematic and logically coherent framework. The experimental results are robust: the method consistently outperforms existing uni-modal and multi-modal approaches across five TCGA cohorts, achieving a competitive overall C-index of 0.711.The analysis is thorough, including ablation studies, hyperparameter tuning, Kaplan–Meier survival curves, and attention visualizations, all of which substantiate the validity of the proposed method.
- 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.
The performance gains are unevenly distributed, with the most substantial improvement observed on the COADREAD dataset (0.845 vs. 0.786), while the advantages on other cohorts are comparatively limited. Therefore, the generalizability of the method should be evaluated more cautiously. The baseline comparisons are insufficient, as no strong baseline employing the same hierarchical supervision but using Euclidean representations is included, making it difficult to disentangle the respective contributions of hierarchical modeling and hyperbolic geometry. The ablation study is limited in scope: key modules are ablated on only two datasets, which fails to fully reveal the independent role of each component across all five cohorts. Moreover, the analysis of hyperparameter sensitivity is inadequate, with limited discussion regarding the rationale for selecting critical hyperparameters and their sensitivity, such as the hierarchical loss weight and the temperature coefficient in angular contrastive learning.
- 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?
The strengths of this work include a novel geometric modeling perspective, a comprehensive technical framework, state-of-the-art performance on multiple datasets, and robust experimental support. However, the weaknesses involve inconsistent performance gains across datasets, the absence of a critical baseline comparison, a limited scope in the ablation study, and insufficient depth in the hyperparameter analysis. The authors conclude that, while the work is innovative and promising, there remains room for improvement in experimental rigor and completeness of the argumentation, placing it near the acceptance threshold.
- 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.
The authors’ rebuttal directly addresses the key concerns raised in my original review, particularly regarding novelty, baseline comparisons, ablation studies, and hyperparameter sensitivity.
Author Feedback
We thank the reviewers and the AC for the careful comments. HyperGP aligns genomic risk prototypes with the WSI slide-region-patch hierarchy in Lorentz space using directed angular constraints. We address the main concerns below.
1) @R2 @R4: novelty Existing multimodal methods usually use Euclidean distance to pull matched cross-modal embeddings close. In contrast, HyperGP models directed hierarchy and inclusion relations among prototype-slide, slide-region, and region-patch representations. We therefore introduce Directed Angular Entailment, which uses angular constraints to describe semantic direction and entailment across different levels. This keeps the ability of hyperbolic space to unfold hierarchy along the radial direction, while aligning multi-level pathology representations and genomic risk prototypes in one directed hierarchy.
2) @R2: recent baselines 2.1) Under the same five-cohort setting, HyperGP obtains 0.711 mean C-index, compared with MRePath 0.679 and MMP 0.665.These comparisons support the effectiveness of directed angular relations. HyperPath is relevant but not a direct quantitative baseline because it models pathology-text hierarchy, whereas our task is genomics-pathology survival prediction. We will add the full table and citations in the final manuscript.
3) @R2 @R4: ablation 3.1) Angular: Replacing only the angular relation with geodesic matching drops mean C-index from 0.711 to 0.673. 3.1) Euclidean hierarchy control: Keeping the same hierarchical supervision/architecture but replacing Lorentz hyperbolic space with Euclidean space drops mean C-index from 0.711 to 0.689.Together with the angular-vs-geodesic result in 1.2, this separates the effect of hierarchy, hyperbolic geometry, and angular relation. 3.2) Hyperparameter sensitivity: For tau in {0.04, 0.08, 0.12}, mean C-index is 0.731/0.758/0.753, proving that setting tau to 0.08 yields the best C-index. For w_2 in {0.8, 1.0, 1.2} in L_{uni}, mean C-index is 0.729/0.758/0.733.The experiments prove that w_2=1.0 is best, and the model’s performance is not sensitivity to these hyperparameters.
4) @R4: generalization The gains differ because survival signal is disease-specific. HyperGP helps most when morphology and genomic risk are strongly coupled; when this coupling is weaker or tissue heterogeneity makes survival risk less separable, margins shrink. Still, HyperGP achieves the best five-cohort mean C-index and remains above the geodesic and Euclidean controls.
5) @R1: details 5.1) Patch selection is group-wise denoising, not tumor-only filtering. Each WSI is split into G=10 groups and keeps K=80% patches per group. Prior WSI studies such as TransMIL found that tumor regions occupy less than 10% of CAMELYON16 positive slides on average, suggesting most patches are weakly informative or distracting. 5.2) The attention block is the standard gated-attention MIL module used in pathology models such as CLAM, trained end-to-end with L_{surv}, L_{proto}, and L_{uni}. 5.3) For L_{proto}, each sample has one prototype label p_{a,c}. It is single-label representation regularization: the true-label prototype is positive and other prototypes are negatives for learning risk/censoring anchors. It does not make “alive at c” and “alive at c+1” mutually exclusive and does not model temporal monotonicity; censoring and time likelihood are handled by L_{surv}. 5.4) Eq. 8 uses w_1=0.1 for L_{proto} and w_2=1.0 for L_{uni}; Eq. 4/5 uses tau=0.08.5.5) Fig. 3B shows the model response map. Fig. 3C crops representative patches from the corresponding high-response and low-response regions; we will clarify this in the caption.
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.
This paper proposes an angular-constrained hyperbolic learning framework for multimodal survival prediction using pathology and genomic data. The reviewers generally recognize the geometric modeling perspective and the good empirical results, but raise several concerns such as missing recent baselines, limited analysis of the key design choices. And several methodological details also need clarification. The authors are encouraged to address these concerns in the rebuttal.
- 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 rebuttal addressed most of the reviewers’ comments. Some concerns remain about patch selection details and the generality of the supporting explanation which should be further clarified, but the overall post-rebuttal assessment remains positive.
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 paper proposes a coherent hyperbolic geometric framework for multimodal survival prediction, and the rebuttal addressed key concerns about recent baselines, angular versus geodesic matching, Euclidean hierarchy control, hyperparameter sensitivity, and methodological details. Although some concerns remain about patch-selection justification and uneven gains across cohorts, two reviewers support acceptance after rebuttal, and I consider the paper slightly above the acceptance threshold.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Reject
- Please justify your recommendation.
This paper proposes HyperGP, a hyperbolic multimodal survival prediction framework that aligns genomic prototypes with hierarchical pathology representations through directed angular constraints. Reviewers appreciated the strong empirical results and the additional analyses provided in the rebuttal. However, after considering the reviews and rebuttal, I remain concerned about the degree of methodological novelty. The proposed framework builds upon several existing ideas, including hyperbolic embedding, prototype learning, and contrastive alignment, and the incremental contribution beyond recent hyperbolic survival prediction methods remains unclear. In particular, closely related hyperbolic approaches such as HysurvPred are not compared or sufficiently discussed. While the proposed directed angular entailment is an interesting extension, I am not convinced that it constitutes a sufficiently substantial methodological advance to meet the bar for acceptance. Therefore, I do not recommend acceptance.