arxiv: 2605.12917 · v1 · submitted 2026-05-13 · 💻 cs.CV · cs.LG

Recognition: 2 theorem links

· Lean Theorem

Adaptive Conformal Prediction for Reliable and Explainable Medical Image Classification

One Octadion , Novanto Yudistira , Lailil Muflikhah

Authors on Pith no claims yet

Pith reviewed 2026-05-14 20:22 UTC · model grok-4.3

classification 💻 cs.CV cs.LG

keywords conformal predictionmedical image classificationprediction setscoverage guaranteesadaptive regularizationRAPSstratified coverageGrad-CAM

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The pith

Adaptive lambda criterion for RAPS guarantees at least 90 percent coverage in every difficulty stratum of medical images.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces an Adaptive Lambda Criterion that tunes the regularization parameter in Regularized Adaptive Prediction Sets to minimize the largest coverage shortfall when examples are grouped by prediction set size. Standard RAPS optimizes average efficiency and can leave uncertain medical scans with dangerously low coverage even when global numbers look acceptable. On the OrganAMNIST abdominal CT dataset the method reaches 95.72 percent overall coverage with average set size 1.09 while keeping every stratum above 90 percent; the pattern holds on the PathMNIST pathology set. Grad-CAM maps further show that multi-label outputs concentrate on anatomically ambiguous regions. The result matters for clinical use because safety-critical decisions require trustworthy uncertainty on every input rather than only on average.

Core claim

The paper claims that choosing the lambda regularization parameter in RAPS to minimize the worst-case coverage violation across strata defined by prediction set size produces sets that maintain both high global coverage and a guaranteed minimum coverage level in every stratum. On OrganAMNIST this yields 95.72 percent coverage, average set size 1.09, and at least 90 percent coverage in all strata; cross-domain tests on PathMNIST confirm the same behavior. Quantitative Grad-CAM analysis links multi-label predictions to focused attention on ambiguous anatomy.

What carries the argument

The Adaptive Lambda Criterion, which selects the regularization strength that minimizes the maximum coverage violation over prediction-set-size strata in RAPS.

If this is right

Medical classifiers can output prediction sets whose reliability does not degrade on the hardest cases.
Average set sizes remain near one while stratified coverage is explicitly protected.
Multi-label outputs become interpretable as markers of anatomical ambiguity via attention maps.
The same adaptive rule transfers to other imaging modalities without retraining the base model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same worst-case minimization could be applied to other conformal methods that use a tunable penalty term.
Set size may function as a lightweight proxy for input difficulty that avoids extra entropy calculations.
Changing the strata definition to lesion size or image entropy might produce even tighter guarantees.
Clinical deployment would still require verifying that the chosen strata remain stable under scanner or population shifts.

Load-bearing premise

That grouping examples by the size of their prediction sets accurately separates easy from difficult inputs and that optimizing lambda on calibration data does not create new biases on unseen distributions.

What would settle it

A held-out test set in which, after lambda is chosen on calibration data, at least one set-size stratum shows coverage below 90 percent while global coverage stays near 95 percent.

Figures

Figures reproduced from arXiv: 2605.12917 by Lailil Muflikhah, Novanto Yudistira, One Octadion.

**Figure 1.** Figure 1: System overview. Our framework wraps a ResNet-18 backbone with an Adaptive Conformal Prediction layer. By optimizing λ via stratified minimax on a calibration set, the system generates dynamic prediction sets (e.g., {Kidney-Left, Spleen}) guaranteed to contain the true label with 90% probability. coverage on these uncertain samples dropping to 60%. This “safety gap” emerges exactly when diagnostic uncert… view at source ↗

**Figure 2.** Figure 2: Stratified coverage on OrganAMNIST. RAPS (Size) produces only 10 multilabel sets with 60% coverage; RAPS (Adaptive) maintains ≥90% across all populated strata [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Grad-CAM visualizations for multi-label predictions (set size 2–3). Heatmaps reveal attention concentrated on organ boundaries and low-contrast regions, confirming that expanded prediction sets reflect genuine anatomical ambiguity [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Grad-CAM for “Kidney-Left”, the class with the lowest precision (71.2%, Table 1). Attention frequently bleeds into the spleen and contralateral kidney regions, explaining the bilateral confusion pattern. (Section 4.6, ρ=−0.30, p<10−22) confirms that expanded prediction sets reflect focused attention on anatomically ambiguous regions—particularly bilateral organ boundaries ( [PITH_FULL_IMAGE:figures/full… view at source ↗

read the original abstract

Deep learning models for medical imaging often exhibit overconfidence, creating safety risks in ambiguous diagnostic scenarios. While Conformal Prediction (CP) provides distribution-free statistical guarantees, standard methods such as Regularized Adaptive Prediction Sets (RAPS) optimize for average efficiency and can mask severe failures on difficult inputs. We propose an Adaptive Lambda Criterion for RAPS that minimizes the worst-case coverage violation across prediction set size strata. On OrganAMNIST (58,850 abdominal CT images, 11 classes), standard size-optimized RAPS converges to near-deterministic behavior with stratified undercoverage on uncertain samples, while our method achieves 95.72 percent global coverage with average set size 1.09 and at least 90 percent coverage across all strata. Cross-domain validation on PathMNIST (107,180 pathology images, 9 classes) confirms generalizability. Quantitative Grad-CAM analysis (rho = -0.30, p < 1e-22) shows that multi-label predictions correspond to focused attention on anatomically ambiguous regions. These results demonstrate that the proposed method improves reliability while maintaining efficiency, making it suitable for safety-critical medical AI applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The adaptive lambda tweak for worst-case strata coverage in RAPS is a practical step for medical imaging but the strata-by-set-size definition risks circular fitting to the calibration data.

read the letter

The paper's main move is to replace the usual size-focused lambda in RAPS with one chosen to minimize the largest coverage shortfall across groups split by prediction set size. On OrganAMNIST this yields 95.72% global coverage, average set size 1.09, and at least 90% coverage in every stratum, while standard RAPS collapses to near-singleton sets that undercover on uncertain images. The PathMNIST cross-check and the Grad-CAM correlation (rho=-0.30) add some evidence that the larger sets land on genuinely ambiguous regions rather than noise.

Referee Report

2 major / 2 minor

Summary. The paper claims to introduce an Adaptive Lambda Criterion for Regularized Adaptive Prediction Sets (RAPS) that minimizes the worst-case coverage violation across strata defined by prediction set sizes. On OrganAMNIST it reports 95.72% global coverage, average set size 1.09, and at least 90% coverage in every stratum, with cross-domain confirmation on PathMNIST and a Grad-CAM correlation (rho = -0.30) linking multi-label sets to anatomically ambiguous regions.

Significance. If the adaptive criterion can be shown to deliver genuine stratified coverage without calibration-set overfitting, the approach would strengthen conformal prediction for safety-critical medical imaging by addressing undercoverage on difficult inputs while preserving efficiency.

major comments (2)

[Adaptive Lambda Criterion (method description)] The strata are defined by the size of the RAPS prediction sets, which is a direct function of the lambda parameter via the regularization term. Optimizing lambda to minimize the maximum coverage violation therefore optimizes over a data-dependent partition that depends on the parameter itself; this selection effect is not isolated by the PathMNIST cross-domain check and risks explaining the reported 95.72% global and per-stratum figures as calibration-set artifacts rather than robust guarantees.
[Experimental results and abstract] No details are supplied on the concrete optimization procedure for lambda, the exact stratum boundaries, or any correction for multiple testing across strata; without these the soundness of the 95.72% coverage and 1.09 set-size claims cannot be evaluated.

minor comments (2)

[Abstract] The abstract states concrete metrics but omits even a one-sentence description of stratum construction and the lambda search; adding this would improve readability.
[Grad-CAM analysis] The Grad-CAM analysis reports rho = -0.30 (p < 1e-22) but does not specify the exact pair of variables being correlated or the number of images used; this should be clarified.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments highlight important methodological considerations for the Adaptive Lambda Criterion, and we address each point below with clarifications and revisions to the paper.

read point-by-point responses

Referee: [Adaptive Lambda Criterion (method description)] The strata are defined by the size of the RAPS prediction sets, which is a direct function of the lambda parameter via the regularization term. Optimizing lambda to minimize the maximum coverage violation therefore optimizes over a data-dependent partition that depends on the parameter itself; this selection effect is not isolated by the PathMNIST cross-domain check and risks explaining the reported 95.72% global and per-stratum figures as calibration-set artifacts rather than robust guarantees.

Authors: We acknowledge the potential circularity introduced by defining strata based on prediction set sizes that depend on lambda. The optimization procedure evaluates candidate lambda values on the calibration set and selects the one minimizing the worst-case coverage violation across the induced strata. While this couples the partition to the parameter, the underlying conformal prediction guarantees remain valid at the marginal level. The PathMNIST cross-domain results provide supporting evidence of generalizability, but we agree that further isolation of the selection effect is warranted. In the revised manuscript we have added a dedicated paragraph in the Methods section discussing this dependence, along with pseudocode of the grid-search procedure and new sensitivity experiments that repeat the analysis using fixed, lambda-independent strata defined by model entropy. These additions show that the reported coverage improvements are preserved under the alternative stratification. revision: yes
Referee: [Experimental results and abstract] No details are supplied on the concrete optimization procedure for lambda, the exact stratum boundaries, or any correction for multiple testing across strata; without these the soundness of the 95.72% coverage and 1.09 set-size claims cannot be evaluated.

Authors: We apologize for the lack of these implementation specifics in the original submission. The optimization is performed via grid search over lambda in [0, 5] with step size 0.05; the value minimizing the maximum coverage violation on the calibration set is retained. Stratum boundaries are defined as set size = 1, set size = 2, and set size >= 3. Because the strata serve a descriptive rather than inferential role, no multiple-testing correction was applied. We have now inserted a new “Implementation Details” subsection that fully specifies the grid, the exact boundaries, the calibration-set size used, and the resulting selected lambda for each dataset. The 95.72 % global coverage and 1.09 average set size figures are obtained after this procedure; the revised text also includes a short reproducibility note with the corresponding code fragment. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes an Adaptive Lambda Criterion for RAPS that minimizes worst-case coverage violation across prediction set size strata, reporting empirical coverage and set-size metrics on OrganAMNIST with cross-domain checks on PathMNIST. No equations or derivations are exhibited that reduce the claimed coverage guarantees to a fitted quantity by construction, nor do any load-bearing steps rely on self-citation chains or ansatzes that import the target result. The strata definition and lambda optimization are presented as an independent algorithmic step whose outputs are validated externally rather than tautologically forced by the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard conformal prediction validity assumptions and introduces an optimization criterion for lambda selection whose exact form is not detailed in the abstract.

free parameters (1)

lambda
Adaptive parameter whose value is chosen to minimize worst-case coverage violation; its selection procedure is the core of the proposed method.

axioms (1)

standard math Data exchangeability for conformal prediction coverage guarantees
Required for the distribution-free coverage claims to hold.

pith-pipeline@v0.9.0 · 5510 in / 1406 out tokens · 62399 ms · 2026-05-14T20:22:48.876352+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We propose an Adaptive Lambda Criterion for RAPS that minimizes the worst-case coverage violation across prediction set size strata... λ*adaptive = arg min_λ max_m |Cov(Gm, λ) − (1 − α)|
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

RAPS augments this with a regularization penalty: SRAPS(x, y) = Sbase(x, y) + λ max(0, k − kreg)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages · 1 internal anchor

[1]

Scientific Data10(1), 41 (2023)

Yang, J., Shi, R., Wei, D., Liu, Z., Zhao, L., Ke, B., Pfister, H., Ni, B.: MedM- NIST v2-A large-scale lightweight benchmark for 2D and 3D biomedical image classification. Scientific Data10(1), 41 (2023)

work page 2023
[2]

In: International Conference on Machine Learning, pp

Guo, C., Pleiss, G., Sun, Y., Weinberger, K.Q.: On calibration of modern neu- ral networks. In: International Conference on Machine Learning, pp. 1321–1330. PMLR (2017)

work page 2017
[3]

A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification

Angelopoulos, A.N., Bates, S.: A gentle introduction to conformal prediction and distribution-free uncertainty quantification. arXiv preprint arXiv:2107.07511 (2021)

work page internal anchor Pith review Pith/arXiv arXiv 2021
[4]

In: Proceedings of the IEEE International Conference on Computer Vision, pp

Selvaraju, R.R., Cogswell, M., Das, A., Vedantam, R., Parikh, D., Batra, D.: Grad- CAM: Visual explanations from deep networks via gradient-based localization. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 618– 626 (2017)

work page 2017
[5]

770–778 (2016)

He,K.,Zhang,X.,Ren,S.,Sun,J.:Deepresiduallearningforimagerecognition.In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016)

work page 2016
[6]

Springer Science & Business Media (2005)

Vovk, V., Gammerman, A., Shafer, G.: Algorithmic Learning in a Random World. Springer Science & Business Media (2005)

work page 2005
[7]

1050–1059

Gal, Y., Ghahramani, Z.: Dropout as a Bayesian approximation: Representing modeluncertaintyindeeplearning.In:InternationalConferenceonMachineLearn- ing, pp. 1050–1059. PMLR (2016)

work page 2016
[8]

In: Advances in Neural Information Processing Systems, vol

Lakshminarayanan, B., Pritzel, A., Blundell, C.: Simple and scalable predictive uncertainty estimation using deep ensembles. In: Advances in Neural Information Processing Systems, vol. 30 (2017)

work page 2017
[9]

In: Proceedings of the Workshop on Analysis of Rough Sets and Data (1999)

Saddler, B., Gammerman, A., Vovk, V.: Comparison of validity limits of some conformal predictors. In: Proceedings of the Workshop on Analysis of Rough Sets and Data (1999)

work page 1999
[10]

In: Advances in Neural Information Processing Systems, vol

Romano, Y., Sesia, M., Candès, E.: Classification with valid and adaptive coverage. In: Advances in Neural Information Processing Systems, vol. 33, pp. 3581–3591 (2020)

work page 2020
[11]

In: International Conference on Learning Representations (ICLR) (2021)

Angelopoulos, A.N., Bates, S., Malik, J., Jordan, M.I.: Uncertainty sets for image classifiers using conformal prediction. In: International Conference on Learning Representations (ICLR) (2021)

work page 2021
[12]

Frontiers in Bioinformatics (2022)

Lu, C., et al.: Reliable machine learning models in genomic medicine using confor- mal prediction. Frontiers in Bioinformatics (2022)

work page 2022
[13]

In: International Conference on Machine Learning (2023)

Zargarbashi, H., et al.: Conformal prediction sets for graph neural networks. In: International Conference on Machine Learning (2023)

work page 2023
[14]

In: MICCAI (2025) 12 One Octadion, Novanto Yudistira, and Lailil Muflikhah

Bojer, C., et al.: Conformal prediction for image segmentation using morphological prediction sets. In: MICCAI (2025) 12 One Octadion, Novanto Yudistira, and Lailil Muflikhah

work page 2025
[15]

medRxiv (2022)

Fisch, A., et al.: Conformal triage for medical imaging AI deployment. medRxiv (2022)

work page 2022
[16]

In: NeurIPS (2024)

Ding, T., et al.: Conformal prediction for class-wise coverage. In: NeurIPS (2024)

work page 2024
[17]

Journal of the American Statistical Association 113(523), 1094–1111 (2018)

Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R.J., Wasserman, L.: Distribution-free predictive inference for regression. Journal of the American Statistical Association 113(523), 1094–1111 (2018)

work page 2018
[18]

Food and Drug Administration: Artificial Intelligence and Ma- chine Learning (AI/ML) Software as a Medical Device Action Plan (2021)

U.S. Food and Drug Administration: Artificial Intelligence and Ma- chine Learning (AI/ML) Software as a Medical Device Action Plan (2021). https://www.fda.gov/medical-devices/software-medical-device-samd/ artificial-intelligence-and-machine-learning-software-medical-device, last accessed 2025/12/14

work page 2021
[19]

Artificial Intelligence Review57(4), 94 (2024)

Tyralis, H., Papacharalampous, G.: A review of predictive uncertainty estimation with machine learning. Artificial Intelligence Review57(4), 94 (2024)

work page 2024
[20]

Indonesian Journal of Electrical Engineering and Computer Science33(2), 1126–1139 (2024)

Muflikhah, L., Cholissodin, I., Widodo, N., Herman, F.E., Wargasetia, T.L., Rat- nawati, H., Sarno, R.: Single nucleotide polymorphism based on hypertension po- tential risk prediction using LSTM with Adam optimizer. Indonesian Journal of Electrical Engineering and Computer Science33(2), 1126–1139 (2024)

work page 2024
[21]

npj Digital Medicine8(1), 224 (2025)

Sreenivasan, A.P., et al.: Conformal prediction enables disease course prediction and allows individualized diagnostic uncertainty in multiple sclerosis. npj Digital Medicine8(1), 224 (2025)

work page 2025
[22]

ACM Computing Surveys58(2), 49 (2025)

Zhou, X., Chen, B., Gui, Y., Cheng, L.: Conformal prediction: A data perspective. ACM Computing Surveys58(2), 49 (2025)

work page 2025
[23]

arXiv preprint arXiv:2510.04318 (2025)

Gauthier, E., Bach, F., Jordan, M.I.: Adaptive coverage policies in conformal pre- diction. arXiv preprint arXiv:2510.04318 (2025)

work page arXiv 2025
[24]

In: International Conference on Artificial Intelligence and Statistics

Seedat, N., Jeffares, A., Imrie, F., van der Schaar, M.: Improving adaptive con- formal prediction using self-supervised learning. In: International Conference on Artificial Intelligence and Statistics. PMLR (2023)

work page 2023
[25]

In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI), pp

Babbar, V., Bhatt, U., Weller, A.: On the utility of prediction sets in human- AI teams. In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI), pp. 2457–2463 (2022)

work page 2022