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Abstract
Accurate brain age prediction is essential for understanding neurodevelopmental trajectories and detecting abnormal aging patterns. Morphological features derived from cortical shape provide informative structural representations for brain age prediction. Recent deep learning approaches for surface analysis primarily rely on local aggregation mechanisms. Transformer- and Mamba-based architectures model long-range dependencies through patch partitioning combined with self-attention or selective scan. However, these strategies introduce high computational cost, uncertainty at patch boundaries, and sensitivity to surface rotations that necessitate anatomical registration or extensive data augmentation. To address these limitations, we propose SPHARM-Mamba, a spherical harmonics-based generic backbone for genus-zero surface data that eliminates patch partitioning and avoids surface registration. To this end, dense cortical signals are projected onto spherical harmonics to construct compact rotation-invariant descriptors naturally ordered from global to local scales. Mamba is then employed to model dependencies across harmonic degrees and capture multiscale interactions efficiently. Experiments on cortical age prediction demonstrate superior performance over existing geometric and patch-based models with substantially fewer parameters. The software is available at https://github.com/Shape-Lab/SPHARM-Mamba.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/3058_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/Shape-Lab/SPHARM-Mamba
Link to the Dataset(s)
IXI dataset: https://brain-development.org/ixi-dataset/
OASIS-1 dataset: https://sites.wustl.edu/oasisbrains/home/oasis-1/
OASIS-2 dataset: https://sites.wustl.edu/oasisbrains/home/oasis-2/
Human Connectome Project Young Adult dataset: https://www.humanconnectome.org/study/hcp-young-adult/overview
BibTex
@InProceedings{ChoJun_SPHARMMamba_MICCAI2026,
author = { Choi, Junho AND Joo, Mingyu AND Son, Jiwon AND Kim, Won Hwa AND Lyu, Ilwoo},
title = { { SPHARM-Mamba: Rotation-Invariant Multiscale Modeling for Brain Age Prediction } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16894},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper proposes the SPHARM-Mamba model to achieve accurate brain age prediction. On the one hand, it employs spherical harmonic-based convolutions to extract rotation-invariant, multi-degree representations that capture information from local to global levels. On the other hand, it leverages the Mamba model to model cross-degree dependencies among these representations. As a result, the proposed approach yields an accurate and efficient brain age prediction model.
- 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 is well-structured, and the proposed method is developed based on established model frameworks, making it easy to understand and follow. 2.The model achieves high prediction accuracy while maintaining rotation invariance. It also features a lightweight set of learnable parameters and is computationally and memory efficient.
- 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.
Although the proposed method is built upon established models, it appears to be a relatively straightforward combination of existing components, with limited novelty.
- 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
1.The main difference between the proposed method and that in Reference 15 appears to be the additional use of the Mamba model for modeling cross-degree dependencies, which leads to a reported 19.5% improvement in accuracy. However, I am curious about the additional parameter count and computational overhead introduced compared to the model in Reference 15.If such a substantial performance gain is achieved with only a modest increase in parameters and computation, it would further justify the use of Mamba in this work. 2.Most of the ablation studies in this paper are presented in a purely textual form. It would be more intuitive and clearer if they were organized in a more structured format, such as tables.
- 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 paper is comprehensive and well-presented. The proposed model achieves high accuracy and exhibits several valuable properties, although its novelty is limited. Overall, it remains a competent conference paper.
- 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 author provided a detailed explanation of the theoretical basis for the model’s design with his unique insights, which partially dispelled my preconceived notion that it lacked innovation.
Review #2
- Please describe the contribution of the paper
The paper proposes SPHARM-Mamba, a spherical harmonics-based framework for cortical surface analysis, targeting brain age prediction without relying on patch-based representations or anatomical registration. The method projects cortical signals onto the spherical harmonic domain and constructs compact rotation-invariant spectral descriptors, which provide a scale-aware representation naturally ordered from global to local structures. Building upon this representation, the authors introduce a Mamba-based sequence model to capture dependencies across harmonic degrees, aiming to model multiscale interactions efficiently. The overall framework integrates spectral-domain convolution for intra-degree feature learning and sequence modeling for cross-degree aggregation, and demonstrates improved empirical performance over existing geometric and patch-based baselines with fewer parameters.
- 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 adopts a spherical harmonics-based representation of cortical surfaces, enabling feature extraction directly on the spherical domain. This design naturally preserves geometric structure and avoids distortions introduced by planar projections or patch partitioning, which is well-motivated for cortical surface analysis. 2.The proposed method demonstrates improved performance over several geometric and patch-based baselines while maintaining a relatively lightweight model. This suggests practical potential for brain age prediction tasks where both accuracy and efficiency are important.
- 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 proposed framework closely follows prior work such as SPHARM-Net [1], with relatively minor modifications and the addition of a Mamba-based sequence modeling block. However, the motivation for introducing Mamba is not sufficiently justified. In particular, treating harmonic degrees as a sequence may not naturally align with the structure of spherical harmonic representations, and it remains unclear whether sequence modeling is necessary for this task. Comparisons with simpler alternatives (e.g., MLP or attention-based aggregation) are missing, making it difficult to assess whether the proposed design is essential. 2.The proposed rotation-invariant spectral descriptors aggregate coefficients across orders ‘m’, reducing the representation to degree-wise energy statistics. While this ensures invariance, it discards directional information and significantly compresses the original spectral representation. As a result, the subsequent cross-degree modeling operates on limited and less expressive features, which may weaken the overall modeling capacity. 3.The paper does not provide adequate ablation studies to validate the effectiveness of its main components, including the Mamba module and the rotation-invariant descriptor design. Without such analysis, it is unclear whether the observed performance improvements stem from the proposed modeling strategy or from increased model capacity. This significantly weakens the empirical support for the claimed contributions. 4.The paper claims that multiscale dependencies across harmonic degrees are not modeled by spherical harmonic convolution. However, while spectral operations are performed independently per degree in the frequency domain, cross-degree interactions are implicitly introduced through the inverse spherical harmonic transform (ISHT) in the spatial domain. Therefore, the claim that such dependencies are “unexplored” appears overstated and requires stronger justification or empirical validation.
[1] SPHARM-Net: Spherical Harmonics-Based Convolution for Cortical Parcellation (TMI 2022)
- 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?
While the method demonstrates promising empirical performance, the paper does not convincingly validate its central contributions. The motivation for the Mamba-based design is not well justified, and the lack of ablation studies makes it difficult to attribute performance gains to the proposed components. As a result, the technical novelty and empirical support of the work remain insufficient.
- Reviewer confidence
Very confident (4)
- [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.
While the paper shows strong empirical performance, I remain unconvinced that its methodological contribution is sufficient for acceptance. The framework largely follows prior spherical harmonic convolution approaches such as SPHARM-Net, with the main addition being a Mamba module over degree-wise spectral descriptors. The rebuttal clarifies the motivation but does not fully justify why Mamba-based sequence modeling is necessary. The added MLP baseline is also not a clean ablation, since it changes the SHConv depth and bandwidth in addition to replacing the head, making it hard to isolate the contribution of Mamba. I also remain concerned about information loss from degree-wise energy aggregation and the somewhat overstated claim that prior SHConv methods do not model cross-degree interactions. The rebuttal partially addresses my concerns, but the novelty and controlled empirical validation remain insufficient for MICCAI.
Review #3
- Please describe the contribution of the paper
The main contribution of the paper is a surface-learning framework, SPHARM-Mamba, for brain age prediction that replaces patch-based cortical surface representations with rotation-invariant spherical harmonic descriptors and then uses Mamba to model dependencies across harmonic degrees in a natural coarse-to-fine order. More specifically, the method combines spherical harmonic convolution for rotation-equivariant feature extraction, degree-wise power aggregation for rotation invariance, and cross-degree Mamba modeling for multiscale integration, with the goal of avoiding patch partitioning and removing the need for anatomical registration while improving predictive accuracy and parameter efficiency.
- 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 paper is well motivated by a clear limitation of existing cortical surface models, namely the dependence of patch-based Transformer/Mamba methods on patch partitioning, explicit ordering, and anatomical registration. The proposed method is conceptually elegant because it turns spherical harmonic degrees into a naturally ordered multiscale sequence, which is a more principled input to Mamba than artificial patch ordering. The rotation-invariant design is a strong technical strength, since the model explicitly builds invariant descriptors from spherical harmonic coefficients instead of relying on registration or heavy augmentation. The empirical results are strong, with the method outperforming all reported baselines under original, random-rotation, and registered settings while using far fewer parameters than the strongest patch-based baseline. The experimental section is reasonably convincing because it includes ablations on cross-degree modeling, degree ordering, spatial resolution, and harmonic truncation, rather than reporting only final benchmark numbers. The paper’s robustness claim is supported by a meaningful experimental setup, since performance is explicitly evaluated under random SO(3) rotations and compared against both geometric and patch-based baselines.
- 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 methodological novelty is somewhat limited at the component level, because the core building blocks are largely inherited from prior spherical harmonic convolution work, prior rotation-invariant spherical harmonic descriptors, and standard Mamba sequence modeling, so the main novelty lies more in the integration than in a fundamentally new formulation. The claim that this is a generic backbone for genus-zero surface analysis is stronger than what is actually demonstrated, since the experiments only evaluate a single downstream task, namely brain age prediction. The paper combines four datasets into one pooled cohort, but does not provide a leave-one-dataset-out or cross-cohort generalization experiment, so it is difficult to judge how much the performance reflects true biological generalization versus dataset-specific patterns. The experimental protocol is not fully clear about whether fold splitting is performed strictly at the subject level after treating each hemisphere as an independent sample, which is important because any leakage across hemispheres of the same subject could inflate performance. Although the paper argues that rotation invariance is a key advantage, it would be even more convincing to include a more direct ablation isolating the contribution of the invariant descriptor itself, rather than only comparing the full method under different alignment conditions.
- 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?
I recommend Weak Accept because the paper is technically coherent, well motivated, and supported by strong empirical results, especially under rotation perturbations, although the novelty is more integrative than fundamentally new and the generic-backbone claim is broader than the current experimental scope.
- Reviewer confidence
Somewhat confident (2)
- [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
Author Feedback
We thank all reviewers for their feedback and recognition of our well-motivated spherical harmonics-based approach that preserves geometric structure and addresses limitations of patch-based modeling (R2,R3), achieves strong rotation-invariant prediction with few parameters (R1,R2,R3), and elegantly formulates naturally ordered harmonic degrees as multiscale inputs to Mamba instead of artificial patch ordering (R3).
Technical Novelty (R1-W1,R2-W1,R3-W1): Existing attention/Mamba-based cortical surface models rely on artificially ordered patch tokens, which may introduce patch-boundary artifacts, require registration for patch correspondence, and often rely on rotational data augmentation. As noted in the introduction, these limitations motivate a geometrically grounded representation that naturally supports ordered tokens without arbitrary patch partitioning. In the spherical harmonic domain, degree-wise rotation-invariant SH energy inherently follows a coarse-to-fine spectral hierarchy [18]. Thus, we reinterpret this hierarchy as a multiscale sequence with an intrinsic harmonic-degree ordering as also acknowledged by R3.Therefore, the novelty is not simply combining SHConv and Mamba, but the use of compact rotation-invariant SH descriptors as naturally ordered spectral tokens for sequence modeling such as Mamba. This is the first non-patch-based spectral-sequence model for cortical surface age prediction, achieving strong performance with few parameters.
Motivation for Sequence Modeling and Mamba (R2-W1): We clarify that treating harmonic degrees as a sequence is not arbitrary. [18] states that the SH energy representation is “inherently multiresolutional”, which supports our view that the degree axis provides a natural coarse-to-fine spectral hierarchy, not an artificial ordering. Moreover, [18] notes that energy descriptors encode different harmonic degrees independently. Our method is motivated by this limitation and addresses it through explicit cross-degree modeling along the intrinsic multiscale degree axis. We adopt Mamba instead of an attention-based sequence model because its hidden-state mechanism provides a sequential inductive bias; it can accumulate low-degree global context and selectively propagate it to high-degree components for task-relevant fine-scale modeling. Our reverse-order ablation supports this, as reversing the degree sequence reduced performance by 15.7%.
Information Loss (R2-W2): We agree with R2 that degree-wise energy aggregation introduces information loss. However, following [18], this is an intentional trade-off for rotation invariance, compactness, and robustness. Although full order SH coefficients retain more directional information, it would also make the representation rotation-dependent, making model performance highly sensitive to data orientation and alignment. In this work, to mitigate expressiveness loss, we avoid applying invariant aggregation solely to the input SH coefficients. We instead use SHConv to learn richer spectral features, which are then aggregated into invariant descriptors.
Ablation study with MLP (R1-C1/R2-W1/R2-W3): We replaced SPHARM-Mamba with an MLP head, which yields a model equivalent to [15]. This MLP baseline uses 3 SHConv layers with bandwidth 120 whereas our approach uses only 2 SHConv layers with bandwidth 80.Despite having more parameters (0.998M vs. 0.856M) and requiring over 2x longer training time due to the larger harmonic basis size (121^2 vs 81^2), the MLP baseline still performs worse. This supports the effectiveness of Mamba-based cross-degree modeling rather than larger model capacity.
Cross-Degree Modeling in ISHT (R2-W4): In SHConv, convolution is performed independently per degree, while ISHT is only a fixed basis transform. Although ISHT may aggregate spectral components, this aggregation is non-learnable and thus does not provide task-dependent cross-degree modeling. Our ablation further supports the benefit of explicit modeling.
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.
The primary consensus is that the proposed SPHARM-Mamba model demonstrates strong empirical performance for rotation-invariant brain age prediction, is technically coherent, and is well-motivated by limitations in patch-based methods. However, the most critical weakness raised by all reviewers is the limited methodological novelty, particularly the straightforward integration of existing components. A stronger justification and ablation of the Mamba module compared to simpler aggregators and would be necessary for a better support on claims mad e in the paper.
- 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 authors successfully addressed the primary concerns regarding architectural choices by providing a direct comparison against the baseline multi-layer perceptron. The empirical validation and theoretical clarifications regarding cross-degree modeling satisfied the majority of the reviewers.
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.
This paper proposes SPHARM-Mamba for cortical brain age regression, using rotation-invariant spherical-harmonic spectral descriptors ordered from global to local scales with a Mamba sequence model for cross-degree dependencies, without registration or patch partitioning. The reviewers agree that the approach is well motivated, conceptually elegant, and supported by strong empirical results, including robustness under SO(3) rotations and high parameter efficiency relative to the strongest baseline. The shared reservation is that the novelty is integrative, combining established spherical-harmonic convolution and rotation-invariant descriptors with standard Mamba modeling. The rebuttal made a reasonable case that the contribution lies in using compact rotation-invariant harmonic descriptors as intrinsically ordered spectral tokens rather than an arbitrary combination, and clarified the motivation for the coarse-to-fine sequential modeling. For the camera-ready version, the authors are encouraged to temper the claim that prior harmonic-convolution methods leave cross-degree dependencies unmodeled and to qualify the generic-backbone framing to the single brain-age task evaluated.
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 proposes a Mamba-based approach using SPHARMs for a rotation-invariant framework for brain age prediction. The reviewers noted a limited novelty (mostly reusing existing methods needing more motivation) and limited clinical impact. The rebuttal has addressed some novelty and but validtion issues remains, notably on ablation studies and reliance on baseline choices that were not specifically dedicated to brain age prediction. Consensus remains around borderline reject and borderline acceptance. For all these reasons, and with respect to the other submissions, the recommendation is towards Rejection.