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REVIEW 4 major objections 5 minor 27 references

Analysis of Image-and-Text Uncertainty Propagation in Multimodal Large Language Models with Cardiac MR-Based Applications

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the overall uncertainty of a multimodal large language model's prediction can be written as a linear combination of image-only uncertainty, text-only uncertainty, and their covariance, and that a single fitted…

desk verdict A sensible uncertainty-propagation framework for medical MLLMs whose headline transferability claim rests on null ANOVA results rather than a direct transfer experiment. read the letter →

arxiv 2507.12945 v1 pith:EFXM27ZY submitted 2025-07-17 cs.CV

Yucheng Tang , Yunguan Fu , Weixi Yi , Yipei Wang , Daniel C. Alexander , Rhodri Davies , Yipeng Hu This is my paper
classification cs.CV
keywords uncertaintypropagationmultimodallargelanguagemodelscardiacMRItest-timeaugmentationvisualquestionansweringcalibrationtransferability
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 proposes and tests a simple linear law for how input uncertainties combine in a multimodal large language model (MLLM) that reads cardiac MR images together with text health records. The law, which the authors call the multimodal uncertainty propagation model (MUPM), states that the overall variance of the model's output is approximately a weighted sum of the image-only output variance, the text-only output variance, and their covariance. Because computing the partial derivatives behind this law is numerically unstable, the authors fit the three weights as a least-squares regression from augmented samples. Their main evidence is that the fitted weights stay statistically the same across altered data-quality conditions and across 1-, 3-, and 5-year cardiac disease prediction tasks, so a model fit once can estimate uncertainty for novel tasks without refitting. If this transferability holds, uncertainty estimation for new clinical prediction tasks becomes a matter of collecting a small number of resampled inputs rather than recomputing full model uncertainty.

What carries the argument

The load-bearing object is the MUPM regression equation $s^2_{F_{I,T}} = \beta_1 s^2_{F_I} + \beta_2 s^2_{F_T} + \beta_3 s_{F_I}s_{F_T} + \epsilon$, a linear model whose independent variables are sample variances of MLLM outputs under image-only augmentation, text-only augmentation, and a covariance term, and whose coefficients are fitted by least squares. It is derived from a first-order Taylor expansion of the model output $F(x,y)$, which yields the variance-propagation formula $\sigma^2_{F_{I,T}} \approx (a/a_I)^2 \sigma^2_{F_I} + (b/b_T)^2 \sigma^2_{F_T} + 2(ab/(a_I b_T))\rho\sigma_{F_I}\sigma_{F_T}$. The machinery is model-agnostic: uncertainties are estimated by resampling and augmentation (affine transforms and Gaussian noise for images, synonym replacement for text) and computing sample variances of one-hot outputs, and the linear fit sidesteps the unstable derivative computation.

What would settle it

Fit the MUPM regression on one cardiac prediction task, then use the fitted coefficients to predict overall uncertainty on a different task or data distribution where the benchmark uncertainty is computed directly from a large number of resamples; if the predicted variances deviate systematically from the benchmark beyond the calibration error reported for the fitted setting, the transferability claim breaks. A more targeted test: apply the same procedure to a different multimodal architecture and see whether the fitted coefficients remain the same, since the paper's explanation of transferability invokes shared pretraining and light fine-tuning.

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Extended reading notes

Core claim

The central discovery on the paper's own terms is that the variance of an MLLM's one-hot-encoded output under joint image-text resampling can be modelled as a linear function of three measurable quantities: the variance under image-only resampling, the variance under text-only resampling, and their cross-covariance, where the coefficients are fitted rather than computed from derivatives. The authors derive this relation from a first-order Taylor expansion of the model output, replacing the unstable partial derivatives with regression coefficients estimated by least squares. They report that the fitted coefficients are statistically indistinguishable across four data-distribution settings and across three prediction horizons, with all pairwise ANOVA p-values above 0.05, and that the resulting model reproduces the benchmark overall uncertainty to $R^2 \approx 0.8$. They also show that the text-only coefficient dominates, that overall uncertainty rises with prediction horizon, and that removing either modality substantially lowers accuracy.

Load-bearing premise

The validity of the whole construction rests on the assumption that the resampling-and-augmentation procedure produces output variances that faithfully capture the clinically relevant input uncertainty, and that the first-order Taylor approximation is accurate enough for the linear law to hold for the nonlinear MLLM.

Editorial extensions

If this is right

  • A fitted MUPM can estimate overall prediction uncertainty for novel cardiac disease prediction tasks without refitting, as long as the output is one-hot encoded in the same token format.
  • Uncertainty estimates stabilize with roughly 20 resamples per input, so overall uncertainty can be computed efficiently on unseen downstream data instead of running hundreds of augmentations.
  • The relative sizes of the fitted coefficients reveal which modality drives overall uncertainty—here text dominates—so data-improvement efforts can be directed to the more influential modality.
  • The covariance term and coefficient magnitudes can flag redundant factors, although in the tested cardiac tasks both image and text proved essential.
  • Transferability across data distributions implies that quality perturbations such as image-view changes, signal-to-noise changes, and text-style changes do not require refitting the uncertainty model within the tested range.

Reading between the lines

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

  • The transferability claim suggests the fitted coefficients are a property of the MLLM's pretraining and fine-tuning rather than of the specific task; an out-of-domain test on non-cardiac medical image-text pairs would show whether the law is a general feature of such models.
  • The paper's text augmentation uses a generative language model for synonym replacement, which introduces sampling randomness; a controlled comparison with deterministic lexical substitution would test how much the fitted coefficients depend on the augmentation distribution.
  • Because the covariance coefficient is consistently negative in the reported fits, a natural extension would examine whether this reflects complementary information between modalities and whether it strengthens or weakens for tasks where the modalities are more or less aligned.
  • The first-order derivation is local, so the linear law should degrade for very large input perturbations; measuring output variance under progressively larger image rotations or text rewrites would map the regime in which the approximation holds.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a multimodal uncertainty propagation model (MUPM), a linear regression model in Eq. (4) motivated by first-order Taylor uncertainty propagation in Eqs. (2)-(3), to relate image-only uncertainty, text-only uncertainty, and their covariance to the overall output uncertainty of a multimodal large language model (MLLM). Using UK Biobank cardiac MR images and digital health records, the authors fit MUPM for closed-ended cardiac disease prediction tasks at 1-, 3-, and 5-year horizons, and claim that the fitted MUPM is robust across input data distributions and downstream tasks, supports efficient estimation of overall uncertainty with small resample sizes, and can identify redundant factors. The paper includes code release and uses a real clinical dataset.

Significance. If transferability were convincingly established, MUPM would be a low-cost post hoc estimator of overall uncertainty for multimodal clinical predictions, and the paper addresses an underexplored and practically relevant question. The first-order propagation derivation is standard, the use of a fitted linear model to avoid unstable derivative computation is sensible, and the clinical setting (cardiac MR plus electronic health records) is meaningful. Credit is also due for releasing code. However, the central claim that fitted MUPMs generalize across data distributions and tasks is currently supported only by non-significant ANOVA results with small per-group sample sizes and no direct transfer experiment, so the practical significance of the contribution is not yet established.

major comments (4)
  1. [Section 3, 'Robustness of MUPM across various input data distributions' and 'Robustness of MUPM in different cardiac…] The headline claim that fitted MUPMs are generalisable across data distributions and downstream tasks (Abstract) is never directly tested. Tables 1 and 2 report ANOVA p-values for separately fitted regression coefficients, but failure to reject the null hypothesis is not evidence of invariance, especially with standard errors on the coefficients as large as ±0.40 and only five fitted models per group. A direct test would fit MUPM on one distribution or task, then use those fixed coefficients to predict overall uncertainty on a different distribution or task, and compare the resulting error with refitting. As written, the closest experiment, Fig. 2(a), uses the same augmentation protocol and does not perform such a fixed-coefficient transfer test.
  2. [Table 1 and accompanying text] The text states that 'improving the quality of health record text alone resulted in a more significant reduction in overall uncertainty as shown in Table 1,' but Table 1 contains no column for overall uncertainty, such as the average L2 norm of s^2_FI,T. The table only reports averaged regression coefficients, R², ECE, and ANOVA p-values. The claimed reduction in overall uncertainty is therefore not visible in the cited evidence; either remove this claim or add the relevant overall uncertainty metrics to the table.
  3. [Section 2.2, Eq. (4)] Because Eq. (4) is an unconstrained least-squares fit rather than the derived Eq. (3), the fitted coefficients absorb all experiment-specific choices: the MLLM, the one-hot output encoding, the augmentation ranges, the resampling protocol, and the prompt template. Consequently, the ANOVA invariance reported in Tables 1 and 2 is conditional on all these choices being shared across the compared settings. The abstract's broader claim of transferability to novel tasks and differing input distributions requires either an explicit transfer experiment that varies these factors or a clearly stated limitation of the invariance claim to the current M3D-based setup.
  4. [Section 3, 'Identifying Redundant Factors'] The redundancy criterion is not precisely defined: the text says a completely redundant factor is 'more likely' to have a very low regression coefficient and large covariance with other modalities, but it does not give a decision rule or demonstrate the criterion on a known-redundant input. The validation experiment (removing one modality and measuring accuracy drop) confirms that both image and text contribute to accuracy, but it does not test the paper's proposed redundancy criterion. Please specify the criterion and evaluate it, for example on synthetic inputs with controlled redundancy or by comparison with a baseline method.
minor comments (5)
  1. [Section 2.1, Eq. (1)] Equation (1) omits the increments in the Taylor expansion; it should read F(x,y) ≈ F(x0,y0) + ∂F/∂x (x - x0) + ∂F/∂y (y - y0) unless x0 and y0 are assumed to be zero. Please clarify.
  2. [Figure 2(a)] The horizontal and vertical axes of Fig. 2(a) are not described in the caption; please add axis labels and units, including the definition of the L2-norm of overall uncertainty used.
  3. [Throughout] Please correct typographical errors, including 'Insti-tute' in the affiliation line and 'predication tasks' in the Section 3 heading.
  4. [Section 3, ECE description] The calibration measure ECE is computed using a log-sigmoid mapping from uncertainty L2-norms to confidence, but the mapping is not defined precisely and no confidence intervals are given. Please define the mapping and report calibration with uncertainty, e.g., bootstrap intervals.
  5. [Section 3, benchmark computation] The benchmark for overall uncertainty is computed as the average of 100 augmentation runs; the text does not justify why this average is the ground truth or how the benchmark's own sampling variability compares with the MUPM estimates. Please clarify or provide error bars for the benchmark.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MUPM is an explicitly fitted linear model, and the downstream evaluations use unseen pairs and independent ablations.

full rationale

The derivation chain is self-contained. Equation (2) is the standard first-order variance propagation formula; Equation (3) is algebra from Equation (2) with the indicated substitutions. Equation (4) is then introduced explicitly as a linear regression: 'we formulate MUPM as a linear regression model in Eq.(4), with independent variables (s2FI, s2FT, sFI*sFT), and dependent variable (s2FI,T)' and the coefficients are 'estimated using least squares'. This is an empirical fit, not a hidden restatement of the prediction target. The efficiency experiment estimates image-only and text-only uncertainties from '60 unseen image-text pairs' and compares MUPM-computed overall uncertainty against a benchmark obtained by 100 augmentations; that is a genuine transfer test on held-out data rather than a fitted-input-called-prediction. The redundancy analysis first reads the fitted coefficients but then independently validates by removing each modality and measuring accuracy (Fig. 2b), so the conclusion does not rest solely on the fitted values. The only same-author citation, CineMA [10], appears in the future-work sentence and is not load-bearing. The ANOVA-based generalisability claim may be statistically under-powered or over-interpreted—failure to reject the null is not proof of coefficient invariance—but that is a correctness/evidence concern, not a circularity. No step in the paper reduces by construction to its own inputs.

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

The paper's contribution is the empirical fit and its claimed transferability, which rest on hand-chosen augmentations, linearity assumptions, and the validity of one-hot output variance as uncertainty. No new physical entities are introduced.

free parameters (4)
  • MUPM regression coefficients (beta1, beta2, beta3) = beta1 about 0.20-0.24, beta2 about 0.88-0.93, beta3 about -0.19 to -0.22 across Tables 1 and 2
    Fitted by least squares (Eq. 4) to predict overall uncertainty; the fitted coefficients are the core parameters of MUPM.
  • Number of resamples n = 20
    Chosen for uncertainty estimation and fitting; Fig. 2a suggests stability beyond n=20. This is a hand-set hyperparameter affecting variance estimates.
  • Augmentation ranges for cardiac MR images = rotation 15 degrees, zoom 0.2, shear 5, shift 0.15, Gaussian noise StD=10
    Chosen by hand; these define what counts as image-only uncertainty.
  • Text augmentation settings = 5-6 or 10-12 patient items, GPT temperature 0.8 or 0.4
    Chosen by hand to simulate text variability; affects the estimated text-only uncertainty.
assumptions (4)
  • standard math First-order Taylor expansion variance propagation (Eq. 2) approximates the nonlinear MLLM over the augmentation range.
    Eqs. (1)-(3) assume the MLLM is approximately linear in x and y; no verification of the approximation's accuracy is provided.
  • domain assumption Augmented samples represent realistic input variability.
    Section 2.2 defines image-only and text-only uncertainties through affine transformations, Gaussian noise, and GPT synonym replacements; the clinical meaningfulness of these perturbations is assumed.
  • ad hoc to paper The linear regression Eq. (4) is an adequate stand-in for the derivative-based Eq. (3).
    The paper fits a linear model because derivative computation is unstable, but never validates that the linear form and independent beta coefficients satisfy the structural constraints of Eq. (3).
  • domain assumption Image-text pairs describe the same clinical entity.
    Section 3 constructs pairs by timestamp alignment of cardiac MR and health-record diagnoses; misalignment would break the covariance interpretation.

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Cite this review

Pith. "Pith review of Analysis of Image-and-Text Uncertainty Propagation in Multimodal Large Language Models with Cardiac MR-Based Applications." pith.science (2026). https://pith.science/paper/EFXM27ZY

@misc{pith2026250712945,
  author       = {Pith},
  title        = {Pith review of: Analysis of Image-and-Text Uncertainty Propagation in Multimodal Large Language Models with Cardiac MR-Based Applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EFXM27ZY}},
  note         = {Machine review of arXiv:2507.12945}
}
read the original abstract

Multimodal large language models (MLLMs) can process and integrate information from multimodality sources, such as text and images. However, interrelationship among input modalities, uncertainties due to individual uni-modal data and potential clinical applications following such an uncertainty decomposition are yet fully understood in the context of large-scale MLLMs. In this work, we propose a multimodal uncertainty propagation model (MUPM) based on uncertainty propagation, to characterise the relationship among the uncertainties arising from image-only, text-only, and joint image-text variations in MLLM inputs. Using real clinical data consisting of cardiac MR scans and digital health records, we describe that MUPMs can be optimised robustly with a few samples. We then show that the fitted MUPMs are generalisable across different input data distributions and, perhaps surprisingly, across different downstream tasks. Such a transferability may be explained by the shared pretraining, comparatively light MLLM fine-tuning, along with the low-dimensional nature of the MUPMs. More importantly, this learned transferability, quantifying the relationship between these uncertainties, led to direct clinical applications in which uncertainties may be estimated and thus analysed robustly for varying data or even a novel set of cardiac disease prediction tasks. In addition, we show experimentally the efficiency in multimodal data required for estimating the overall uncertainty and its ability to identify redundant factors, both of which are considered practical yet clinically useful applications with the proposed MUPMs. Codes are available at https://github.com/yucheng722/MUPM.

Figures

Figures reproduced from arXiv: 2507.12945 by the authors.

Figure 1
Figure 1. Uncertainty estimation and MUPM fitting process. We compute the sample variances of one-hot encoded outputs of MLLM when applying image-only, text-only, and image-text data resampling and augmentation. The covariance term is computed from the outputs of the image-only and text-only branches. We then fit the linear MUPM in Eq. (4) using the sample variances and the covariance term. The regression coefficients are est… view at source ↗
Figure 2
Figure 2. (a) Experimental results on the efficient uncertainty estimation of downstream data: the purple line represents the average L2-norms of the overall uncertainties (with StDs) computed by MUPM, when n = 2, 5, 8, 11, 14, 17, 20, 23. The red line represents the benchmark overall uncertainty. (b) Box plot of the average accuracy (with StDs) when removing cardiac MR image inputs (text-only), removing health record text in… view at source ↗

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