Improving Medical Diagnostics with Vision-Language Models: Convex Hull-Based Uncertainty Analysis

Ferhat Ozgur Catak; Murat Kuzlu; Taylor Patrick

REVIEW 4 major objections 5 minor 42 references

Improving Medical Diagnostics with Vision-Language Models: Convex Hull-Based Uncertainty Analysis

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper proposes that the total convex hull area of a vision-language model's response embeddings is a measure of its uncertainty, and reports that this measure increases with sampling temperature in medical chest X-ray question…

desk verdict A transparent but unvalidated hull-area diversity metric applied to a medical VLM: the temperature trend is real but trivial, and the 'uncertainty' claim is unsupported, with the appendix showing contradictory responses in the supposedly least-uncertain case. read the letter →

arxiv 2412.00056 v1 pith:42LMUBKF submitted 2024-11-24 cs.CV cs.AI

Ferhat Ozgur Catak , Murat Kuzlu , Taylor Patrick This is my paper · ORCID

classification cs.CVcs.AI

keywords uncertaintyquantificationvision-languagemodelsconvexhullvisualquestionansweringtemperaturesamplingLLM-CXRchestX-rayDBSCAN

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

The paper aims to give medical AI users a simple, model-agnostic way to see when a vision-language model is uncertain. It proposes measuring the geometric spread of generated radiology reports: the model answers the same prompt 30 times, encodes the answers with BERT, projects them into two dimensions, clusters them, and sums the convex hull areas of the clusters. That sum, $A(p,t)$, is claimed to quantify the uncertainty of the model's responses to prompt $p$ at temperature $t$. Applying this to the LLM-CXR model on chest X-rays, the paper reports that uncertainty is nearly zero at very low temperature and grows steadily as temperature rises to 1.00. If valid, the measure would offer a cheap way to flag unreliable answers before a model is used in a clinical setting.

What carries the argument

The central object is the total convex hull area $A(p,t)$, defined as the sum of the areas of the convex hulls of all DBSCAN clusters (excluding noise points) found among the two-dimensional PCA projections of BERT embeddings of the model's 30 responses to prompt $p$ at temperature $t$. The machinery works in three stages: BERT converts each generated radiology report into a high-dimensional semantic vector; PCA projects these vectors to two dimensions for visualization and clustering; DBSCAN groups nearby points; and the convex hull area of each cluster is summed to a single scalar uncertainty score. The claim is that the scalar tracks the diversity, and therefore the uncertainty, of the model's outputs.

What would settle it

Generate a labeled set of chest X-ray questions with known correct answers, run the same 30-response pipeline at a fixed temperature, and compute both the total convex hull area and the proportion of correct answers. If images whose responses are tightly clustered (small hull area) are not more likely to be answered correctly than those with large hull area, then the claimed uncertainty interpretation is falsified.

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Extended reading notes

Core claim

The paper's central claim is that the total convex hull area over DBSCAN clusters of BERT-encoded, PCA-projected response embeddings is a measure of the uncertainty of a VLM's responses to a given prompt. Formally, $A(p,t) = \sum_{c \in L, c \neq -1} \text{Area}(\text{ConvexHull}(c))$, where larger area means higher uncertainty. The authors argue this follows because diversity of responses increases with uncertainty, and the convex hull area reflects the spatial spread of embeddings. They demonstrate the measure on LLM-CXR generating 30 radiology reports per chest X-ray at temperatures 0.001, 0.25, 0.50, 0.75, and 1.00, observing that mean uncertainty rises monotonically with temperature, from 0.0001 to 0.3117. They also note that the model produces confident-sounding reports even for noisy or irrelevant images, which they attribute to poor data quality affecting reliability.

Load-bearing premise

The load-bearing premise is that the geometric spread of response embeddings, after BERT encoding, PCA projection, and DBSCAN clustering, faithfully tracks how uncertain the model really is in a clinical setting; the paper never validates this against accuracy, calibration, or expert judgment.

Editorial extensions

If this is right

If $A(p,t)$ is a valid uncertainty measure, low-temperature generation (near 0.001) should be preferred when deploying a medical VLM, because responses are nearly deterministic and the metric reports near-zero uncertainty.
The metric provides a way to compare the reliability of different VLMs or different prompts on the same clinical task without needing ground-truth labels.
Because the measure only requires repeatedly sampling the model and embedding its outputs, it can be applied to any black-box VLM that generates text.
The observation that noisy or irrelevant X-ray images still yield confident-looking reports implies that input data quality directly affects the usefulness of any uncertainty score on this pipeline.

Reading between the lines

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

A natural next test the paper does not run: calibrate $A(p,t)$ against answer accuracy on a labeled benchmark. If a small hull area sometimes accompanies wrong but confident answers, the metric would capture diversity but not clinical reliability.
The same geometry could serve as an abstention rule: a system could refuse to answer when the total hull area exceeds a threshold, and the threshold could be tuned per deployment.
The temperature-diversity relationship likely holds for any stochastic text generator, but the mapping from hull area to diagnostic risk may be dataset- and task-specific, so the measured values should not be compared across different prompt sets without normalization.
The paper's reliance on PCA projection means the hull area depends on the projection; testing robustness with other dimensionality reductions (e.g., UMAP) or with the BERT embedding dimension itself would clarify whether the uncertainty signal is an artifact of 2D projection.

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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

The honest summary: this is a small paper with one empirical observation — LLM-CXR produces more textually diverse reports as temperature rises — wrapped in a metric called 'uncertainty' that is never validated. The convex hull pipeline is reused from the authors' own earlier LLM work; the new part is applying it to a chest X-ray VQA model. That application is routine.

To the paper's credit, the pipeline is transparent: 30 responses per image at five temperatures, BERT embeddings, PCA to 2D, DBSCAN clustering, hull areas. The histograms show a clear monotonic trend in spread versus temperature, and that claim is believable, matching known properties of sampling temperature. Including raw responses in the appendices is also helpful for checking.

The problems are in the interpretation. The paper defines uncertainty as hull area but never shows the metric separates correct from incorrect answers, correlates with calibration, or tracks clinical risk. The mathematical justification is circular: hull area is a measure of spread, and the conclusion is that spread increases with temperature — that is built into the definition. The first lemma is also wrong as stated: larger pairwise distances do not guarantee a larger convex hull area, especially after PCA projection. The internal evidence is worse: the 'least uncertain' instance at T=1.00 (Appendix I) contains mutually contradictory reports — normal chest, right apical pneumothorax, volume overload — for the same image. If that is the most confident response set, the metric is not capturing diagnostic uncertainty. There are also numerical inconsistencies between Table I and the histograms, and the GitHub link appears malformed.

Who is this for? Someone interested in output diversity measurement might find a simple recipe, but it adds little over existing diversity metrics. The paper does not deserve a serious referee in its current form. The right move is to desk reject or send back for a major rethink, asking the authors either to validate the metric against accuracy/calibration or to reframe the paper as a study of temperature-induced output diversity and drop the 'uncertainty' and healthcare trustworthiness claims.

Referee Report

4 major / 5 minor

Summary. The paper proposes a convex-hull-based uncertainty metric for vision-language model (VLM) responses in a medical visual question answering setting. For a fixed prompt and chest X-ray image, the authors generate 30 radiology-report responses from the LLM-CXR model at temperatures 0.001, 0.25, 0.50, 0.75, and 1.00. Responses are encoded with BERT, projected to two dimensions with PCA, clustered with DBSCAN, and the sum of the convex hull areas of all non-noise clusters is defined as the uncertainty A(p,t). The paper reports histograms and descriptive statistics suggesting that A(p,t) increases with temperature and concludes that higher temperature settings lead to higher uncertainty, with implications for healthcare trustworthiness.

Significance. If the proposed metric were shown to track predictive uncertainty in a clinically meaningful sense, it could offer a simple, model-agnostic tool for evaluating VLM reliability. The paper makes its code available and applies the method to a concrete medical VQA task, which is a strength. However, the significance is currently limited because the metric is not validated against correctness, calibration, or expert judgment, and the paper's own appendix contains examples that contradict the interpretation of low hull area as low uncertainty.

major comments (4)

[Section IV.B.1, Lemma] The proof of the lemma is invalid. The claim that larger pairwise distances between embedding points imply a larger convex hull area is false in general: a set of collinear points has zero hull area regardless of how far apart the points are, and adding a single outlier can increase hull area in a way that is not monotonic in pairwise distances. Furthermore, the proof does not account for the PCA projection to two dimensions, which does not preserve distances and can change the ordering of hull areas. Thus the 'mathematical justification' does not establish that A(p,t) measures uncertainty.
[Section IV.A, definition of A(p,t)] The central claim that A(p,t) is 'a measure of the uncertainty of the model's responses' is asserted rather than demonstrated. The metric is never compared against diagnostic accuracy, calibration, or expert judgment. This is not merely a philosophical issue: Appendix I, labeled 'Least Uncertain Instance at the Temperature Setting of 1.00', lists clinically contradictory responses for the same image — 'Lungs are fully expanded and clear', '1. Small right apical pneumothorax', 'Findings concerning for volume overload' — which a clinically useful uncertainty metric should identify as highly uncertain, not as the least uncertain instance. Without evidence that hull area separates reliable from unreliable answers, the abstract's claim about healthcare trustworthiness is unsupported.
[Table I and Figures 2-10] The numerical results in Table I are inconsistent with the histograms. For T=0.50, Figure 6 shows a normal distribution centered around a convex hull area of 25; for T=0.75, Figure 8 shows a main peak around 30; for T=1.00, Figure 10 shows a distribution spanning roughly 10-60. Yet Table I reports means of 0.1698, 0.2473, and 0.3117 for those temperatures. The paper does not explain whether the histograms are normalized, per-cluster, or in different units. Additionally, no error bars, confidence intervals, or statistical tests are reported across the images, so the claimed monotonic increase in uncertainty with temperature is not supported by the presented evidence.
[Section IV.A, experimental setup] The experimental setup omits several details that are needed to evaluate the method: the number of chest X-ray images used is not stated, the number of DBSCAN clusters and the proportion of noise points excluded from A(p,t) are not reported, and only two illustrative 'most uncertain' instances per temperature are shown. Because the total area is a sum over clusters, the number of clusters and the noise exclusion rule can dominate the result; without aggregate statistics over all images, the central empirical claim cannot be assessed.

minor comments (5)

[Throughout] The manuscript contains several typos and misspellings, including 'Evalaution' in the Section IV.A heading, 'resonances' in Section V, 'antipicated' in Section IV.C.5, and 'diffrence' in the discussion of Table I. A careful proofreading pass is needed.
[Table I] The column labeled '0.001-1.00' contains ratios (e.g., 3115, 114, 31) but the header does not state what is being divided by what; the intended computation should be explicitly defined.
[Figures 3, 5, 7, 9, 11] The contour plots are difficult to interpret because the axes are unlabeled and no colorbar is provided, so the reader cannot determine what the background colors represent in terms of uncertainty values.
[Section IV.A] The GitHub URL 'https://github.com/ocatak/VLM Uncertainty' contains a space and is likely broken; please provide a valid link.
[References] The paper would benefit from citing prior work on semantic entropy or embedding-diversity-based uncertainty estimation in language models, to clarify the novelty of the proposed convex-hull metric relative to existing approaches.

Circularity Check

2 steps flagged · score 7.0 of 10

Central result is essentially a definitional restatement: uncertainty is defined as convex hull area of embedding spread, and temperature is known to increase output diversity, so the reported temperature-uncertainty trend is built into the operationalization.

self definitional [Section IV.A (definition of A(p,t)) and Section IV.B.2 (Temperature Sensitivity)]
"The total area is a measure of the uncertainty of the model’s responses to the given prompt. ... In this context, a larger area indicates a higher uncertainty, while a smaller area indicates a lower uncertainty. ... As t increases, the model produces more diverse and uncertain responses. Formally, for a higher temperature t, the spread of the embedding points increases, leading to larger convex hulls: ∂A(p,t)/∂t > 0"

Uncertainty is never measured independently; it is defined as A(p,t), the summed DBSCAN-cluster convex hull areas of BERT/PCA response embeddings. Temperature is introduced as the sampling knob that controls output diversity, and the paper's own 'mathematical justification' proves only the analytic fact that increasing pairwise embedding distance increases hull area. The reported conclusion that uncertainty increases with temperature therefore follows from substituting the definition of uncertainty (embedding spread) into the known effect of temperature (more diverse outputs).
other [Appendix I (Least Uncertain Instance at Temperature Setting 1.00)]
"I. Least Uncertain Instance at the Temperature Setting of 1.00 ... -- Lungs are fully expanded and clear. ... -- 1. Small right apical pneumothorax. ... -- Findings concerning for volume overload."

The instance is labeled 'least uncertain' because its summed convex hull area is smallest. But the quoted responses are clinically contradictory: a clear lung, a right apical pneumothorax, and volume overload cannot all describe the same radiograph. This shows that the 'uncertainty' label is assigned by the geometry of the embedding clusters, not by any property related to diagnostic reliability. The paper has simply renamed geometric dispersion as uncertainty, so the quantity it claims to evaluate remains the same quantity it defined; no external validation step breaks the definitional loop.

full rationale

The paper's derivation chain is: define uncertainty as the summed convex hull area of clustered response embeddings; note (correctly) that temperature is a knob that increases output diversity; and conclude that uncertainty increases with temperature. The second and third links are connected by the definitional equation A(p,t) = geometric spread, so the central claim is largely tautological. The 'mathematical justification' in Section IV.B.1 proves only a geometric monotonicity fact (larger pairwise distances imply larger hull area), and Section IV.B.2 asserts ∂A(p,t)/∂t > 0 from the temperature-diversity relationship rather than from any independent uncertainty measurement. Appendix I exposes the consequence: an instance called 'least uncertain' contains mutually contradictory clinical findings, confirming that the label tracks embedding spread rather than diagnostic reliability. There is also a self-citation to the authors' prior convex-hull uncertainty work [40], but the core issue is not the citation chain; it is that the paper's operational definition of uncertainty already contains the reported result. Consequently, the abstract's healthcare-trustworthiness conclusion is not independently supported, though the underlying observation that higher temperature increases response diversity remains true.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central claim rests on the operationalization of uncertainty as the summed area of 2D convex hulls around DBSCAN clusters of BERT embeddings. The method introduces several arbitrary hyperparameters and an unvalidated equivalence between output diversity and predictive uncertainty. The lemmas in Section IV.B assume monotonicity that does not hold in general, and the conclusion about temperature is essentially built into the definition.

free parameters (6)

DBSCAN epsilon = 0.25
Chosen for 2D PCA embeddings with no sensitivity analysis. It determines which responses are clustered and therefore which hull areas are summed.
DBSCAN min_samples = 3
Arbitrary choice that affects cluster membership and noise points, hence the computed hull area.
PCA dimensionality = 2
Projection to 2D for visualization and clustering alters pairwise distances and hull areas; no robustness check is reported.
Number of responses per image = 30
Sample size per prompt, chosen without justification or variance analysis.
Temperature values = 0.001, 0.25, 0.50, 0.75, 1.00
Five manually selected settings; conclusions are limited to these values.
BERT embedding model
Choice of embedding model affects the geometry of the response space; no comparison with other embedding models is provided.

assumptions (5)

ad hoc to paper Area of a convex hull increases monotonically with the pairwise distances of its points.
Used in Lemma 1 proof; false in general, especially after PCA projection, so the derivation does not go through.
domain assumption Higher temperature sampling increases the semantic diversity of generated radiology reports.
Standard property of softmax temperature, but the paper treats it as part of the derivation of ∂A/∂t > 0 rather than as an empirical check.
domain assumption BERT embeddings and PCA projection preserve enough structure for hull area to represent semantic spread.
No validation that 2D PCA hull areas are stable across random seeds, projections, or embedding choices.
domain assumption DBSCAN with fixed epsilon and min_samples yields meaningful clusters of responses.
Cluster structure determines the summed area; no sensitivity analysis is reported.
ad hoc to paper The variability of responses to the same prompt and image is equivalent to predictive uncertainty.
This equates output variability with uncertainty, which is the core unvalidated move in the paper.

invented entities (1)

Convex hull area uncertainty score
purpose: To quantify VLM response uncertainty in medical VQA
The score is not validated against diagnostic accuracy, calibration, human expert ratings, or established UQ metrics; it is just a diversity measure.

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Cite this review

Pith. "Pith review of Improving Medical Diagnostics with Vision-Language Models: Convex Hull-Based Uncertainty Analysis." pith.science (2026). https://pith.science/paper/42LMUBKF

@misc{pith2026241200056,
  author       = {Pith},
  title        = {Pith review of: Improving Medical Diagnostics with Vision-Language Models: Convex Hull-Based Uncertainty Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/42LMUBKF}},
  note         = {Machine review of arXiv:2412.00056}
}

read the original abstract

In recent years, vision-language models (VLMs) have been applied to various fields, including healthcare, education, finance, and manufacturing, with remarkable performance. However, concerns remain regarding VLMs' consistency and uncertainty, particularly in critical applications such as healthcare, which demand a high level of trust and reliability. This paper proposes a novel approach to evaluate uncertainty in VLMs' responses using a convex hull approach on a healthcare application for Visual Question Answering (VQA). LLM-CXR model is selected as the medical VLM utilized to generate responses for a given prompt at different temperature settings, i.e., 0.001, 0.25, 0.50, 0.75, and 1.00. According to the results, the LLM-CXR VLM shows a high uncertainty at higher temperature settings. Experimental outcomes emphasize the importance of uncertainty in VLMs' responses, especially in healthcare applications.

Figures

Figures reproduced from arXiv: 2412.00056 by the authors.

**Figure 2.** Uncertainty distribution at the temperature set [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 5.** Most uncertain instances (a-b) at the temperature [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

Figures from the paper (4 more)

**Figure 6.** Figure 6: Uncertainty distribution at the temperature setting=0.50 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Most uncertain instances at the temperature set [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: Uncertainty distribution at the temperature setting=0.75 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 11.** Figure 11: Most uncertain instances at the temperature set [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]

Discussion (0). Continue with ORCID to comment.

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Y . Leung, J.-S. Zhang, and Z.-B. Xu, “Neural networks for convex hull computation,” IEEE Transactions on Neural Networks, vol. 8, no. 3, pp. 601–611, 1997

1997
[36]

Llm-cxr: Instruction- finetuned llm for cxr image understanding and generation,

S. Lee, W. J. Kim, J. Chang, and J. C. Ye, “Llm-cxr: Instruction- finetuned llm for cxr image understanding and generation,” in The Twelfth International Conference on Learning Representations , 2023

2023
[37]

Taming transformers for high- resolution image synthesis,

P. Esser, R. Rombach, and B. Ommer, “Taming transformers for high- resolution image synthesis,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , 2021, pp. 12 873–12 883

2021
[38]

Free dolly: Introducing the world’s first truly open instruction-tuned llm,

M. Conover, M. Hayes, A. Mathur, J. Xie, J. Wan, S. Shah, A. Ghodsi, P. Wendell, M. Zaharia, and R. Xin, “Free dolly: Introducing the world’s first truly open instruction-tuned llm,” Company Blog of Databricks , 2023

2023
[39]

Mimic-cxr-jpg-chest radiographs with structured labels,

A. Johnson, M. Lungren, Y . Peng, Z. Lu, R. Mark, S. Berkowitz, and S. Horng, “Mimic-cxr-jpg-chest radiographs with structured labels,” PhysioNet, 2019

2019
[40]

Covid-19 image data collection,

J. P. Cohen, P. Morrison, and L. Dao, “Covid-19 image data collection,” arXiv 2003.11597 , 2020. [Online]. Available: https: //github.com/ieee8023/covid-chestxray-dataset

2003 arXiv
[41]

Uncertainty quantification in large language models through convex hull analysis,

F. Ozgur Catak and M. Kuzlu, “Uncertainty quantification in large language models through convex hull analysis,” arXiv e-prints , pp. arXiv–2406, 2024. APPENDIX A. Least Uncertain Instance at the Temperature Setting of 0.001 X-Ray ImageResponses -- No acute intrathoracic proce...

2024
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Right internal jugular central venous line at the cavoatrial junction

Small pleural effusion on the left ,→ ,→ ,→ ,→ ,→ ,→ ,→ ,→ ,→ -- Nasogastric tube tip in the stomach. Right internal jugular central venous line at the cavoatrial junction. ,→ ,→ -- Pulmonary edema with moderate right-sided effusion.,→ -- ET tube 5.3 cm above the carina

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Gpt-4 technical report,

J. Achiam, S. Adler, S. Agarwal, L. Ahmad, I. Akkaya, F. L. Aleman, D. Almeida, J. Altenschmidt, S. Altman, S. Anadkat et al. , “Gpt-4 technical report,” arXiv preprint arXiv:2303.08774 , 2023

arXiv 2023

[2] [2]

Improved baselines with visual instruction tuning,

H. Liu, C. Li, Y . Li, and Y . J. Lee, “Improved baselines with visual instruction tuning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , 2024, pp. 26 296–26 306

2024

[3] [3]

Cogvlm: Visual expert for pretrained language models,

W. Wang, Q. Lv, W. Yu, W. Hong, J. Qi, Y . Wang, J. Ji, Z. Yang, L. Zhao, X. Song et al., “Cogvlm: Visual expert for pretrained language models,” arXiv preprint arXiv:2311.03079 , 2023

arXiv 2023

[4] [4]

Learning transferable visual models from natural language supervision,

A. Radford, J. W. Kim, C. Hallacy, A. Ramesh, G. Goh, S. Agarwal, G. Sastry, A. Askell, P. Mishkin, J. Clark et al., “Learning transferable visual models from natural language supervision,” in International conference on machine learning . PMLR, 2021, pp. 8748–8763

2021

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Assessing the utility of multimodal large language models (gpt-4 vision and large language and vision assistant) in identifying melanoma across different skin tones,

K. Cirone, M. Akrout, L. Abid, and A. Oakley, “Assessing the utility of multimodal large language models (gpt-4 vision and large language and vision assistant) in identifying melanoma across different skin tones,” JMIR Dermatology, vol. 7, 2024

work page 2024

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Gpt-4 artificial intelligence model outperforms chatgpt, medical students, and neurosurgery residents on neurosurgery written board-like questions,

G. A. Guerra, H. Hofmann, S. Sobhani, G. Hofmann, D. Gomez, D. Soroudi, B. S. Hopkins, J. Dallas, D. J. Pangal, S. Cheoket al., “Gpt-4 artificial intelligence model outperforms chatgpt, medical students, and neurosurgery residents on neurosurgery written board-like questions,” World Neurosurgery, vol. 179, pp. e160–e165, 2023

work page 2023

[7] [7]

Evaluating gpt-v4 (gpt-4 with vision) on detection of radiologic findings on chest radiographs,

Y . Zhou, H. Ong, P. Kennedy, C. C. Wu, J. Kazam, K. Hentel, A. Flanders, G. Shih, and Y . Peng, “Evaluating gpt-v4 (gpt-4 with vision) on detection of radiologic findings on chest radiographs,”Radiology, vol. 311, no. 2, p. e233270, 2024

work page 2024

[8] [8]

Llama: Open and efficient foundation language models,

H. Touvron, T. Lavril, G. Izacard, X. Martinet, M.-A. Lachaux, T. Lacroix, B. Rozi `ere, N. Goyal, E. Hambro, F. Azhar et al. , “Llama: Open and efficient foundation language models,” arXiv preprint arXiv:2302.13971, 2023

arXiv 2023