Regression Constraint for an Explainable Cervical Cancer Classifier

Antoine Pirovano; Leandro G. Almeida; Said Ladjal

REVIEW 3 major objections 5 minor 13 references

Regression Constraint for an Explainable Cervical Cancer Classifier

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Adding an ordinal regression constraint to a cervical-cell classifier's loss function raises severity accuracy from 70.1% to 74.5% while keeping the model's class probabilities, and attribution maps show the model focuses on the nucleus.

desk verdict A sensible ordinal-loss tweak with a plausible accuracy bump on Herlev, but the reported gain rests on a single split and the paper's own binary accuracy numbers disagree. read the letter →

arxiv 1908.02650 v2 pith:SHFWM3HY submitted 2019-08-07 eess.IV cs.CVcs.LG

Antoine Pirovano , Leandro G. Almeida , Said Ladjal This is my paper · ORCID

classification eess.IVcs.CVcs.LG

keywords cervicalcancerscreeningHerlevdatasetordinalregressionlossfunctiondesignintegratedgradientsexplainableAIcytomorphologicalfeaturesdeeplearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that a simple change to the training loss—adding an MSE penalty that encourages the softmax output to behave like a severity score on a 1-to-5 ordinal scale—improves a deep CNN's ability to grade cervical cell abnormalities. The authors argue this works because it explicitly encodes the ordinal structure of the WHO severity classification, which a plain cross-entropy loss ignores. They show that on the Herlev dataset this regression constraint lifts five-class severity accuracy from 70.1% to 74.5% and binary normal/abnormal accuracy from 90.8% to 94%, while also improving the model's focus on the nucleus as shown by integrated-gradient attributions. The practical payoff is a classifier that is both more accurate and more aligned with how cytotechnicians actually read slides.

What carries the argument

The central mechanism is the combined loss function $$L(x) = CE(p; y_x) + \left(y_x - \sum_{i=0}^{4} (i+1)\,p_i\right)^2,$$ where $p_i$ are the softmax class probabilities for a five-class severity label, $y_x$ is the ground-truth class index (1 to 5), and $CE$ is the cross-entropy loss. The second term is a regression constraint that turns the softmax distribution into an expected severity score and penalizes predictions that are far from the true ordinal class, effectively weighting misclassifications by their clinical distance. This simple addition is what carries the accuracy gain.

What would settle it

A concrete check would be to compute a bootstrap confidence interval for the difference between 74.5% and 70.1% accuracy using the confusion matrices in Figures 1 and 6; if the interval includes 0, the reported improvement is not statistically established. Alternatively, replace the MSE regression target with a cumulative-link ordinal loss that does not assume equal spacing; if accuracy and AUC do not deteriorate, the equal-spacing assumption is not essential to the gain.

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Extended reading notes

Core claim

The central claim is that coupling a standard cross-entropy classification loss with a mean-squared-error regression term on the expected severity score—computed as a fixed weighted sum of the softmax probabilities—yields a single architecture that outperforms either loss alone. On the Herlev severity dataset, the combined loss gives 74.5% overall accuracy and 94% binary normal/abnormal accuracy with an F1 of 0.96, while the plain classifier reaches 70.1% and 90.8%, respectively. The two extreme classes, normal and carcinoma in situ, show the largest AUC gains (0.98 and 0.97), correcting a known confusion between normal columnar and carcinoma in situ cells. The paper also claims that integrated-gradient attribution maps, evaluated against the dataset's nucleus and cytoplasm masks, show the malignancy scoring is driven mainly by the nucleus, with nucleus contribution increasing with severity.

Load-bearing premise

The load-bearing premise is that the five severity classes can be represented as equally spaced ordinal scores (1 to 5), so that a mean-squared-error penalty on the expected score is a meaningful regularizer; if the true clinical distances between classes are unequal, this constraint could distort the learned representation.

Editorial extensions

If this is right

If this loss works as claimed, the same trick of adding an ordinal regression constraint to cross-entropy could be applied to other medical grading tasks with ordered categories, such as diabetic retinopathy or skin lesion severity.
The improvement in extreme classes suggests that the constraint reduces confusion between normal and carcinoma in situ cells, which is the most clinically dangerous error; this could make automated screening safer.
The quantitative attribution metrics (AtN, AtC) provide a way to verify that a classifier is using medically relevant features, potentially serving as a quality-control step before deployment.
The paper's binary accuracy of 94% matches the earlier reported binary result on Herlev, suggesting the method preserves binary performance while adding explainable severity grading.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The equal-spacing assumption (1 to 5) may be too coarse; if class distances are actually unequal, the regression penalty could distort the learned representation. A natural extension would be to learn the spacing or use an ordinal cumulative-link loss, then compare accuracy and calibration.
The attribution result—that nucleus contribution rises with severity—could be turned into a weak localization signal, potentially flagging images where the model looks outside the nucleus as cases deserving manual review.
The approach is not limited to cancer screening; any classification problem with ordered classes and a natural score interpretation could benefit from the same loss, though the magnitude of the gain would likely depend on how well the classes align with the score scale.
The reported accuracy gain of 4.4 percentage points is based on a single test split; re-running the comparison with multiple random seeds and a bootstrap confidence interval would tell whether the gain is robust or partly noise.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The one-sentence take: this is a sensible, small idea with a plausible accuracy bump, but the reported gain isn't statistically grounded, and the paper's own numbers disagree about how well the binary task went.

What's actually new: applying a known ordinal-loss trick (CE + MSE on class indices) to the 5-class Herlev severity problem, and the quantitative attribution metrics AtN/AtC computed from the dataset's masks. The attribution analysis goes beyond the usual saliency maps by actually measuring where the gradients land relative to nucleus and cytoplasm. That is a useful, reproducible way to sanity-check what the model sees. The method itself is a simple combination of losses, so the novelty is modest, but the evaluation on Herlev severity with public masks is a legitimate addition.

The paper does a few things well. The loss formulation is clear and easy to reimplement. The AUC distributions in Figure 7, even if not fully numeric, suggest the regression constraint helps most on the extreme classes, which matches the confusion matrices. The motivation to avoid misclassifying carcinoma in situ as normal is medically sensible.

Now the soft spots. The headline improvement—70.1% to 74.5% accuracy, 90.8% to 94% binary—comes from a single train/test split. There are no error bars, no multiple seeds, no statement of the split ratio. With 917 images, the 4.4-point gain is roughly 8 test images; split variance alone can generate that. The only multi-run evidence is Figure 7, but the numeric AUC values and paired statistics are missing. That is the load-bearing weakness. The ordinal equal-spacing assumption (1 to 5) is a legitimate modeling choice; it's not the main risk. Also, the binary accuracy is reported as 94% with F1 0.96 in Section 3.2.3 and 96.7% with F1 0.95 in the Conclusion. That inconsistency needs to be resolved before anyone can trust the abstract numbers. No code is released, which makes the exact split question impossible to audit.

The attribution results are suggestive, not conclusive. The AtN/AtC distributions are interesting, but without a baseline (e.g., a random model or a model trained without the regression constraint) it's hard to know whether the nucleus focus is specific to this loss. Minor, but worth saying.

Who should read this: anyone working on ordinal classification for small medical image datasets, and people thinking about how to evaluate attribution methods quantitatively. It deserves a serious referee—the idea is reasonable and the dataset is public—but the revision needs repeated-split statistics and a corrected, consistent set of numbers. Send it to review, but expect to send it back.

Referee Report

3 major / 5 minor

Summary. The paper addresses automatic classification of squamous cervical cells from the public Herlev dataset. It proposes a 'classification + regression' pipeline in which a ResNet-101 classifier is trained with the standard cross-entropy loss plus an MSE penalty that encourages the softmax-derived expected score to match an ordinal severity score (1 to 5). The authors report that this constraint improves five-class severity accuracy from 70.1% to 74.5% and binary normal/abnormal accuracy from 90.8% to 94%, while preserving a probabilistic output. They also apply Integrated Gradients with a white baseline and use the dataset's nucleus/cytoplasm masks to quantify where the attribution falls, concluding that the model focuses increasingly on the nucleus as severity increases.

Significance. If the claimed accuracy improvement is statistically sound, the paper would make a modest but practically relevant contribution to automated cervical cancer screening, and the ordinal-constraint idea is a reasonable way to inject clinical knowledge into a standard classifier. The attribution analysis is a strength: it uses annotated cell masks to quantify the fraction of Integrated Gradient attribution inside the nucleus and cytoplasm, going beyond typical qualitative saliency maps. The paper also builds on a public dataset and reports comparisons with prior work. However, the central empirical claim currently rests on single-split point estimates without error bars or repeated-seed statistics, and the binary accuracy is reported inconsistently across sections. The attribution results are more convincing but cannot compensate for the lack of a rigorous evaluation of the headline accuracy improvement.

major comments (3)

[Sections 3.2.1 and 3.2.3] The central claim that the MSE regression constraint improves severity accuracy from 70.1% to 74.5% and binary accuracy from 90.8% to 94% is supported only by single-point estimates on an unspecified train/test split. With 917 images, a 4.4-point severity-accuracy gap corresponds to roughly 8 images on a typical 80/20 split, so split-to-split variance and class imbalance could easily produce this difference. Figure 7 shows 4-fold AUC distributions but does not report the numeric AUC values, per-fold results, or paired statistics, so it does not establish a significant difference for AUC either. Please provide repeated random-split results with means and standard deviations (or confidence intervals) for all reported metrics, and state the exact train/test protocol and number of seeds.
[Section 3.2.3 vs. Section 5] The binary accuracy is reported as 94% with F1 = 0.96 in Section 3.2.3, but Section 5 reports 96.7% with F1 = 0.95 for the same setting. This internal inconsistency makes it impossible to determine the actual headline result and must be corrected. If the two numbers refer to different evaluation conditions (e.g., different folds or a single best run), that distinction needs to be explicit.
[Sections 3.2.2 and 3.2.3] The method assumes that the five severity classes can be represented on an equally spaced interval scale (scores 1 through 5) for the MSE penalty. If the true clinical distances between classes are not equal, the regularizer could bias the learned representation. Since the regression constraint is the paper's main contribution, this assumption needs at least a discussion, and ideally a robustness check with alternative score spacing (e.g., ordinal logistic or unequal spacing) to show that the accuracy improvement is not an artifact of the specific score assignment.

minor comments (5)

[Abstract and throughout] There are several typos: 'adresses' should be 'addresses' in the abstract, 'descibes' should be 'describes' in Section 3.2, and 'model agonistic' in Section 4 should be 'model agnostic'.
[Section 3.2.3, loss equation] The notation yx is used for both the one-hot label in the cross-entropy term and the scalar score in the MSE term. Please define separate symbols (e.g., y and s) to avoid ambiguity.
[Section 3.2.3, text before Figure 5] The statement 'our Resnet-101, Classifier + Regressor, makes less misclassifications than the classifier and lower MSE than the regressor' would benefit from specific numerical comparisons; as written, it is not clear which numbers support it.
[Section 4, Equations (1) and (2)] The notation \sum_i could be clearer; specify that the sum runs over pixel indices in the corresponding region, and define N and C as sets of pixel indices rather than just 'nucleus and cytoplasm pixels'.
[References] Several references are incomplete or inconsistently formatted (e.g., [6], [7], [9]); please ensure each entry includes author list, venue, year, and page numbers where applicable.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the accuracy comparison is empirical and self-contained, with no fitted quantity renamed as a prediction.

full rationale

The paper's central claims are empirical measurements on the public Herlev dataset. No equation in the paper transforms a fitted parameter into a predicted quantity: the MSE constraint is a proposed loss, and the reported 74.5% and 94% accuracies are obtained by training and evaluating on images. The regression constraint is not defined in terms of the accuracy it is claimed to improve; ordinal scoring is an assumption, not a circular definition. The qualitative attribution analysis uses the model's own integrated gradients, but this is a post-hoc explanation, not a derivation of the model's behavior from that explanation. The internal discrepancy between 94% and 96.7% binary accuracy and the absence of error bars are reproducibility and reporting concerns, not circularity. I find no load-bearing self-citation: references to previous Herlev classifiers are external works, and the comparison against them is not used to justify the present model's loss. Therefore the derivation chain is self-contained, and the correct circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The paper's assumptions are standard deep-learning transfer, dataset reliability, and two ad hoc modeling choices: equal-spaced ordinal scores and the white baseline. The free parameters are the class scores and the equal loss weighting, both chosen by hand without sensitivity analysis.

free parameters (2)

Ordinal class scores for MSE = 1, 2, 3, 4, 5
Classes normal, light dysplastic, moderate dysplastic, severe dysplastic, and carcinoma in situ are assigned equally spaced scores. No clinical justification is given for equal spacing, and the reported results depend on this encoding.
Loss weighting = 1.0 for each loss (unweighted sum)
The combined loss in Section 3.2.3 adds cross-entropy and MSE without a weighting hyperparameter; the paper does not test other weights.

assumptions (4)

domain assumption ImageNet-pretrained ResNet-101 features transfer to cervical cytology images.
Section 3.2.1 uses a model pretrained on ImageNet [10] without discussing domain shift; the success of transfer learning is assumed.
domain assumption The Herlev annotations and nucleus/cytoplasm masks are correct.
The attribution metrics in Eq. 1 and 2 rely on these masks; errors in the masks would affect the AtN/AtC numbers.
ad hoc to paper The five severity classes can be represented on an interval scale for MSE loss.
The regression and combined pipelines use scores 1 to 5 (Sections 3.2.2 and 3.2.3); this is a modeling choice specific to this paper.
ad hoc to paper A white image is a valid Integrated Gradient baseline.
Section 4 assumes white is the 'absence of object' for pap smears, but no sensitivity analysis is provided.

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Cite this review

Pith. "Pith review of Regression Constraint for an Explainable Cervical Cancer Classifier." pith.science (2026). https://pith.science/paper/SHFWM3HY

@misc{pith2026190802650,
  author       = {Pith},
  title        = {Pith review of: Regression Constraint for an Explainable Cervical Cancer Classifier},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SHFWM3HY}},
  note         = {Machine review of arXiv:1908.02650}
}

read the original abstract

This article adresses the problem of automatic squamous cells classification for cervical cancer screening using Deep Learning methods. We study different architectures on a public dataset called Herlev dataset, which consists in classifying cells, obtained by cervical pap smear, regarding the severity of the abnormalities they represent. Furthermore, we use an attribution method to understand which cytomorphological features are actually learned as discriminative to classify severity of the abnormalities. Through this paper, we show how we trained a performant classifier: 74.5\% accuracy on severity classification and 94\% accuracy on normal/abnormal classification.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

World Health Organization Comprehensive cervical can- cer control : a guide to essential practice. 2006

work page 2006
[2]

Medical Ima- ging 2015 : Computer-Aided Diagnosis, 2015

Yaniv Bar and Idit Diamant and Lior Wolf and Hayit Greenspan Deep learning with non-medical trai- ning used for chest pathology identiﬁcation. Medical Ima- ging 2015 : Computer-Aided Diagnosis, 2015

work page 2015
[3]

This is can be more easily displayed by the overall MSE of 0.58 over the test set

deriving from this distribution, this model does more mis- classiﬁcations than the categorical model, with an accuracy of 60.6%, however these misclassifcation are less severe in the scope due to their relative prognosis distance. This is can be more easily displayed by the overall MSE of 0.58 over the test set. The binary accuracy was of 91.8% and the F1...

work page
[4]

Medical Image Computing and Computer- Assisted Intervention MICCAI 2015

Olaf Ronneberger and Philipp Fischer and Thomas Brox U-Net : Convolutional Networks for Biomedical Image Segmentation. Medical Image Computing and Computer- Assisted Intervention MICCAI 2015

work page 2015
[5]

Hinton ImageNet Classiﬁcation with Deep Convolutional Neural Networks

Alex Krizhevsky and Ilya Sutskever and Geoffrey E. Hinton ImageNet Classiﬁcation with Deep Convolutional Neural Networks. Advances in Neural Information Pro- cessing Systems 25, 2012

work page 2012
[6]

2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

Kaiming He and Xiangyu Zhang and Shaoqing Ren and Jian Sun Deep Residual Learning for Image Recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

work page 2016
[7]

IEEE Journal of Biomedical and Health Informatics, 2017

Le Lu and Ling Zhang and al DeepPap : Deep Convo- lutional Networks for Cervical Cell Classiﬁcation . IEEE Journal of Biomedical and Health Informatics, 2017

work page 2017
[8]

Forslid and H

G. Forslid and H. Wieslander and al Deep Convolutional Neural Networks for Detecting Cellular Changes Due to Malignancy. IEEE International Conference on Computer Vision Workshops, 2017

work page 2017

Show all 13 references

[9]

ICML 2017

Mukund Sundararajan and Ankur Taly and al Axiomatic Attribution for Deep Networks. ICML 2017

2017
[10]

Solomon and D

D. Solomon and D. Davey and al The 2001 Bethesda System : Terminology for Reporting Results of Cervical Cytology. 2001

2001
[11]

Deng and W

J. Deng and W. Dong and al A Large-Scale Hierarchical Image Database. CVPR 2009

2009
[12]

IEEE International Conference on Big Data and Smart Computing, 2017

Jonghwan Hyeon and Ho-Jin Choi and al Diagno- sing cervical cell images using pre-trained convolutional neural network as feature extractor . IEEE International Conference on Big Data and Smart Computing, 2017

2017
[13]

Proceedings of the Tenth Indian Conference on Computer Vision, Graphics and Image Processing, 2016

Kangkana Bora and Manish Chowdhury and al Pap Smear Image Classiﬁcation Using Convolutional Neural Network. Proceedings of the Tenth Indian Conference on Computer Vision, Graphics and Image Processing, 2016

2016

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

World Health Organization Comprehensive cervical can- cer control : a guide to essential practice. 2006

work page 2006

[2] [2]

Medical Ima- ging 2015 : Computer-Aided Diagnosis, 2015

Yaniv Bar and Idit Diamant and Lior Wolf and Hayit Greenspan Deep learning with non-medical trai- ning used for chest pathology identiﬁcation. Medical Ima- ging 2015 : Computer-Aided Diagnosis, 2015

work page 2015

[3] [3]

This is can be more easily displayed by the overall MSE of 0.58 over the test set

deriving from this distribution, this model does more mis- classiﬁcations than the categorical model, with an accuracy of 60.6%, however these misclassifcation are less severe in the scope due to their relative prognosis distance. This is can be more easily displayed by the overall MSE of 0.58 over the test set. The binary accuracy was of 91.8% and the F1...

work page

[4] [4]

Medical Image Computing and Computer- Assisted Intervention MICCAI 2015

Olaf Ronneberger and Philipp Fischer and Thomas Brox U-Net : Convolutional Networks for Biomedical Image Segmentation. Medical Image Computing and Computer- Assisted Intervention MICCAI 2015

work page 2015

[5] [5]

Hinton ImageNet Classiﬁcation with Deep Convolutional Neural Networks

Alex Krizhevsky and Ilya Sutskever and Geoffrey E. Hinton ImageNet Classiﬁcation with Deep Convolutional Neural Networks. Advances in Neural Information Pro- cessing Systems 25, 2012

work page 2012

[6] [6]

2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

Kaiming He and Xiangyu Zhang and Shaoqing Ren and Jian Sun Deep Residual Learning for Image Recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

work page 2016

[7] [7]

IEEE Journal of Biomedical and Health Informatics, 2017

Le Lu and Ling Zhang and al DeepPap : Deep Convo- lutional Networks for Cervical Cell Classiﬁcation . IEEE Journal of Biomedical and Health Informatics, 2017

work page 2017

[8] [8]

Forslid and H

G. Forslid and H. Wieslander and al Deep Convolutional Neural Networks for Detecting Cellular Changes Due to Malignancy. IEEE International Conference on Computer Vision Workshops, 2017

work page 2017