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Abstract
Image segmentation is a fundamental task in both image analysis and medical applications. State-of-the-art methods predominantly rely on encoder-decoder architectures with a U-shaped design, commonly referred to as U-Net. Recent advancements integrating transformers and MLPs improve performance but still face key limitations, such as poor interpretability, difficulty handling intrinsic noise, and constrained expressiveness due to discrete layer structures, often lacking a solid theoretical foundation.In this work, we introduce Implicit U-KAN 2.0, a novel U-Net variant that adopts a two-phase encoder-decoder structure. In the SONO phase, we use a second-order neural ordinary differential equation (NODEs), called the SONO block, for a more efficient, expressive, and theoretically grounded modeling approach. In the SONO-MultiKAN phase, we integrate the second-order NODEs and MultiKAN layer as the core computational block to enhance interpretability and representation power. Our contributions are threefold. First, U-KAN 2.0 is an implicit deep neural network incorporating MultiKAN and second order NODEs, improving interpretability and performance while reducing computational costs. Second, we provide a theoretical analysis demonstrating that the approximation ability of the MultiKAN block is independent of the input dimension. Third, we conduct extensive experiments on a variety of 2D and a single 3D dataset, demonstrating that our model consistently outperforms existing segmentation networks.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/2894_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{CheChu_Implicit_MICCAI2025,
author = { Cheng, Chun-Wun AND Zhao, Yining AND Cheng, Yanqi AND Montoya-Zegarra, Javier A. AND Schönlieb, Carola-Bibiane AND Aviles-Rivero, Angelica I.},
title = { { Implicit U-KAN2.0: Dynamic, Efficient and Interpretable Medical Image Segmentation } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15970},
month = {September},
page = {304 -- 314}
}
Reviews
Review #1
- Please describe the contribution of the paper
The main contribution of this paper is the development of Implicit U-KAN2.0, a novel U-Net variant for medical image segmentation that integrates second-order neural ordinary differential equations (SONO blocks) with MultiKAN layers to achieve dynamic, interpretable, and memory-efficient learning.
- 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 presents a novel and theoretically grounded segmentation framework by combining second-order neural ODEs (SONO blocks) with MultiKAN layers, enabling continuous feature evolution with improved interpretability and stability. It claims to achieves constant memory cost, is fully GPU-compatible, and demonstrates strong performance across multiple 2D and 3D medical imaging datasets. The method shows superior robustness to noise and offers significant improvements in segmentation accuracy and boundary precision over state-of-the-art models.
- 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.
While the integration of SONO and MultiKAN is well-executed, the paper builds on existing frameworks like U-KAN [12], NODEs [3], and MultiKAN [16], limiting the novelty of individual components. The clinical applicability is not explored beyond standard benchmark datasets, and no real-world deployment or user validation is presented. Additionally, some implementation details (e.g., training stability, runtime efficiency in 3D) are underexplored, and the mathematical exposition could benefit from clearer formal proofs.
- 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 submission does not provide sufficient information for reproducibility.
- 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/2025/en/REVIEWER-GUIDELINES.html
Please be aware of some minor typos. A couple rounds of proof reading could enhance the quality of the paper. Also in the ablation study you want to analyze the contribution of the different components in your architecture, rather than the performance under different noise levels (adversarial). Also please revise Figure 1, the blocks names are already named in the main plot, so maybe no need to be named in the legend sections. Instead you can represent the SODE conv and the ODE block.
- 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 — could be 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 proposes a technically sound and well-structured segmentation model by combining SONO blocks with MultiKAN layers, achieving strong results on benchmark datasets. However, the core components are based on previously established methods, with limited architectural novelty. Additionally, the paper lacks real-world clinical validation, ablation on runtime/memory efficiency in 3D, and clarity in theoretical derivations. While promising, the work would benefit from deeper empirical and clinical insights to justify acceptance.
- 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 rebuttal effectively addressed key concerns, clarifying the novelty of combining second-order ODEs with MultiKAN layers and the architectural shift from discrete to continuous-time modeling. The authors provided additional insight into efficiency in 3D, interpretability by design, and methodological distinctions from related works. Given the sound theoretical foundation, strong experimental results across diverse datasets, and the thoughtful integration of dynamic and interpretable components, I recommend acceptance.
Review #2
- Please describe the contribution of the paper
The paper presents Implicit U-KAN2.0, an architecture for medical image segmentation that improves on conventional U-Net-style encoder-decoder structures by introducing: a) A Second-Order Neural ODE (SONO) block, used to model continuous feature evolution with constant memory cost and enhanced numerical stability. b) A SONO-MultiKAN block, which integrates second-order dynamics with MultiKAN, a tokenized block inspired by Kolmogorov–Arnold networks (KANs), to improve interpretability and representational capacity. The model is validated on multiple 2D (Kvasir-SEG, ISIC, Breast Ultrasound) and a 3D (MSD Spleen) dataset. It outperforms a broad set of baselines including U-Net, TransUNet, Mamba-like models, and U-KAN, achieving state-of-the-art performance in both accuracy and noise resilience.
- 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.
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It is novel to integrate continuous dynamics with interpretable networks. Combining second-order NODEs with MultiKAN creates a unique and compelling hybrid of interpretability and implicit modeling. Also, the use of the Kolmogorov–Arnold theorem to support MultiKAN’s expressiveness is well-presented and distinguishes this from empirical-only studies.
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The method demonstrates superior results in Dice, HD95, and F1 across multiple datasets and domains (2D and 3D) with extensive experiments.
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- 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.
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The explanation of the model components, especially the SONO-MultiKAN phase and tokenization steps, is dense and hard to parse for readers unfamiliar with NODEs or KANs. A clearer schematic or pseudo-code would improve reproducibility.
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While the paper references USODE and U-KAN, it does not compare with or ablate against other NODE-based methods (e.g., Neural ODE [1] or FFJORD [2]).
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Given that one of the key claims is improved interpretability, qualitative results (e.g., saliency maps, feature attributions) should be provided to demonstrate this advantage.
[1] Chen, Ricky TQ, et al. “Neural ordinary differential equations.” Advances in neural information processing systems 31 (2018). [2] Grathwohl, Will, et al. “FFJORD: Free-Form Continuous Dynamics for Scalable Reversible Generative Models.” International Conference on Learning Representations. 2018.
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- 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 submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.
- 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/2025/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 — could be accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The proposed method is a thoughtful combination of implicit neural modeling and interpretable architectures, backed by sound theoretical underpinnings and strong experimental validation. It performs particularly well across 2D and 3D segmentation tasks and demonstrates robustness to noise. However, the presentation suffers from clarity issues, and some key claims (interpretability, theoretical expressiveness) would benefit from more concrete analysis.
- 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.
Authors has explained my confusion and also promise to add clarity in the final version.
Review #3
- Please describe the contribution of the paper
MEHTODS: developing the KANs and its application. EXPRIMENT: solid in 2d and 3ddegmntations. The evidences are strong. OPENSOURCE CODES: helpful for further works
- 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 work is solid in exploring ways to effectively apply KANs into the deep learning Framework. The work is prior with potential in methodology and engineering.
- 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.
As a conference paper, no significant flaws concerned.
- 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 submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- 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/2025/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.
(6) Strong Accept — must be accepted due to excellence
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
This manuscript is with high quality.
- 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 have responded all my concerns.
Author Feedback
[Reviewer #1] :: We sincerely thank the reviewer for the encouraging and positive feedback. We appreciate your recognition of our methodological contributions, and strong experimental results.
[Reviewer #2] :: [Novelty] While our work is inspired by other principles, our Implicit U-KAN2.0 is a novel architecture built on continuous-time and tokenised representations: 1) U-KAN2.0 vs. U-KAN: U-Net and U-KAN are discrete architectures with layer-wise transformations, whereas U-KAN2.0 is based on second-order neural ODEs (SONO), modelling the latent trajectory as a continuous-time dynamical system. This shift enables constant memory cost and improved numerical stability, diverging fundamentally from the discrete encoder-decoder structure of U-KAN. 2) SONO vs. NODEs: Unlike first-order NODEs, our SONO introduces an additional initial condition (initial velocity), leading to richer dynamics and better convergence behaviour. This is not a trivial extension—it changes the underlying differential formulation and solution space. 3) MultiKAN Block: We propose a novel integration in which the SONO block performs continuous downsampling, followed by the application of a new MultiKAN module. Our version introduces multiplicative operators in the MultiKAN layers, increasing expressivity and enabling interactions between learned features in a way not previously explored in KANs or U-KAN.
Q2. [Clinical Evaluation] In this work, we follow standard protocol by evaluating on widely-used clinical benchmark datasets (Kvasir-SEG, ISIC, Breast Ultrasound, MSD Spleen), which reflect real-world variability in anatomy, pathology, and acquisition artefacts. These datasets allow for standardised and reproducible comparison against existing methods. We agree that clinical validation is a good step, but it involves controlled data acquisition, outcome assessment, and user studies—constituting a full study beyond the scope of this paper. This is why we have categorised our submission under MIC as the primary area. We view clinical validation as important future work.
Q3. [On 3D Performance]. Our model is designed for efficiency and stability. In 3D, it achieves 15.6M parameters vs. 11.1M for U-KAN3D, but only 1.7 GFLOPs vs. 22.6 GFLOPs, yielding ~13× lower GFLOPs with better accuracy. This is due to the SONO encoder reducing redundant operations and the MultiKAN block enabling compact, expressive representations. Training was stable across all experiments without special tricks.
Q4. [Theory & Typos] We are not certain which part of the mathematical derivations was unclear. Many of the co-authors are from math background, and we believe all notations are clear. We appreciate the comment and will ensure careful proofreading of the theoretical part, typos for the camera-ready version for improved clarity, and the other optional comments.
[Reviewer #3] Q1. Thanks! The SONO-MultiKAN block proposed continuous latent dynamics with a tokenized representation based on flattened 2D patches projected into an embedding space. These embeddings are then processed by a MultiKAN module with interleaved multiplicative layers to capture higher-order, non-linear feature interactions. We will make sure to add clarity on this.
Q2. We chose to compare vs USODE, which directly extends NODEs and has shown superior performance in segmentation contexts. Since our method outperforms USODE across multiple datasets, this indirectly supports that we exceed standard NODE baselines. FFJORD, while related to continuous modelling, is designed for generative tasks and does not extend naturally to segmentation pipelines, making direct comparison infeasible.
Q3. We refer to interpretability by design, not post hoc explainability. The MultiKAN block provides structural transparency through tokenized basis functions with explicit mathematical roles, unlike saliency maps, which offer approximate explanations for black-box models. We will clarify this distinction in the final version.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.
N/A
- 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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
N/A
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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
The authors have addressed most of the comments. Paper can be accepted
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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
N/A