MUPAX: Multidimensional Problem Agnostic eXplainable AI

Felice Franchini; Giuseppe Pirlo; Irina Voiculescu; Vincenzo Dentamaro

REVIEW 4 major objections 4 minor 16 references

MUPAX: Multidimensional Problem Agnostic eXplainable AI

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

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Pith's one-line read MUPAX is proposed as a deterministic, model-agnostic explainer with a convergence guarantee, and its masked inputs are reported to maintain or improve model accuracy on audio, image, 3D medical, and landmark tasks.

desk verdict MUPAX's reported accuracy gains come from selecting masks with the ground-truth label and then measuring accuracy on exactly those masks; the convergence theorem is a standard SLLN application and the comparison against label-free baselines is not fair. read the letter →

arxiv 2507.13090 v1 pith:OREY2UOE submitted 2025-07-17 cs.LG cs.AIcs.CV

Vincenzo Dentamaro , Felice Franchini , Giuseppe Pirlo , Irina Voiculescu This is my paper · ORCID

classification cs.LGcs.AIcs.CV

keywords explainableAIfeatureattributionmodel-agnosticexplanationperturbation-basedconvergenceguaranteesaliencymapmedicalimaginglandmarkdetection

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

MUPAX is a proposed explainability method whose central claim is that feature importance can be computed by masking chunks of an input, keeping only masked versions whose error with respect to the true label is below a threshold, and averaging inverse-error weighted retained coordinates. The paper proves that this average converges almost surely to a limit that factorizes into the original feature value, the probability that the coordinate is retained among accepted masks, and the mean inverse error when it is retained. That convergence holds for arbitrary loss functions and arbitrary input dimensions, which the authors present as the missing combination of determinism, model agnosticism, and guaranteed convergence in XAI. On benchmarked tasks, the paper reports that masking out everything MUPAX deems unimportant leaves accuracy equal or better than the original input, in contrast to LIME, Grad-CAM, SHAP, and Integrated Gradients, and that MUPAX-based crops lower mean radial error in landmark detection. A sympathetic reader would care because this turns explanation into a form of post-hoc regularization with a stated convergence rate, not merely a visualization.

What carries the argument

The mechanism carrying the argument is chunked masking with inverse-error weighting, formalized in the MUPAX Theorem. The input is split into hyper-rectangular chunks; a selection vector $s$ keeps or zeroes each chunk; the filtered input $X_s$ is scored by $\mu(X_s)=L(f(X_s), y_{\mathrm{true}})$; and only masks whose error falls below threshold $W$ are accepted. Each accepted mask contributes the product of its inverse error $\mu'_c = 1/(\mu_c+1)$ and the retained coordinate value to the empirical average. Because accepted masks are treated as i.i.d. draws from the conditional distribution $D_W$, the Strong Law of Large Numbers gives almost sure convergence and the Lindeberg–Lévy central limit theorem gives a convergence rate of order $n^{-1/2}$. The inverse-error weight is what turns 'does this mask keep the model's error low' into a per-coordinate importance score.

What would settle it

Recompute MUPAX masks using the model's own predicted label for the original input in place of the ground-truth $y_{\mathrm{true}}$; if masked-input accuracy no longer beats the unmasked baseline, or the saliency maps become uninformative, then the accuracy-enhancement claim depends on label access rather than on the discovery of intrinsic patterns. A second check is to test the i.i.d. assumption directly: collect the sequence of accepted selection vectors and measure autocorrelation between consecutive accepted masks, since the described stratified uniform sampling and threshold estimation from an initial data-dependent phase could introduce dependence that the convergence proof does not cover.

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Extended reading notes

Core claim

The central discovery is the MUPAX Theorem. For an input $X$ partitioned into chunks, the empirical statistic $\chi_n(\alpha) = (1/n) \sum_c \mu'_c X_c(\alpha)$, computed over the first $n$ rejection-sampling accepted masks (those with $\mu(X_s) \le W$), converges almost surely to $\chi(\alpha) = X(\alpha) \, E[\mu'(X') \mid \alpha \text{ retained}] \, P(\alpha \text{ retained})$, where the expectation and probability are taken under the conditional distribution of masked inputs with error below $W$. The theorem's decomposition says a coordinate is important when it is often retained in low-error masked inputs and those inputs are on average very good according to the error function. The paper states this result in any dimension and for any loss function, and treats it as the theoretical grounding for a saliency map that is deterministic and model agnostic. Empirically the paper claims this score identifies patterns that survive masking, with masked versions of the input performing at or above the unmasked baseline across four application domains.

Load-bearing premise

The load-bearing premise is that deciding which masked inputs are 'good' by comparing model output with the ground-truth label $y_{\mathrm{true}}$, and then measuring how accurate the resulting masked inputs are, is a fair comparison against explanation methods that do not see the label; if label-based selection is what inflates the masked accuracy, the reported accuracy enhancement would be an artifact of that choice.

Editorial extensions

If this is right

If MUPAX's convergence claim holds, users get an explainer whose per-coordinate importance scores have a stated almost-sure convergence and an $n^{-1/2}$ error rate, for any differentiable or non-differentiable loss and any input dimension.
MUPAX-masked inputs can act as a post-hoc denoiser: in the paper's experiments the masked versions match or exceed the original model's F1 on 1D, 2D, and 3D classification, which is what motivates the phrase 'enhance accuracy.'
In landmark detection, restricting the search area to the roughly 42% of pixels retained by MUPAX lowers the overall mean radial error from about 13.8 px to 9.3 px, suggesting a practical cropping procedure for localization tasks.
Because the method is model agnostic and does not require gradients, direct corollaries include applicability to non-differentiable pipelines and generative or regression losses, where Grad-CAM and Integrated Gradients are not available.

Reading between the lines

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

An implication the paper leaves implicit: the threshold $W$ and chunk size are free parameters, and the reported superiority could be sensitive to them; a natural extension is a data-driven rule for choosing $W$ and chunk granularity, for instance by stabilizing the resulting saliency map across repeated runs.
Because the error $\mu(X_s)$ uses the ground-truth label, the method as described is a supervised explainer; a testable extension is to replace $y_{\mathrm{true}}$ with pseudo-labels or a calibration set and check whether the convergence and accuracy effects survive, which would separate genuine pattern discovery from label leakage.
The theorem establishes pointwise convergence of coordinate scores; a further step would be to prove convergence of the full saliency map under a norm and to derive confidence intervals for ranking differences between coordinates, which would make the method directly usable for hypothesis testing about which features drive a model.

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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

Short version: the accuracy-enhancement result is an artifact of using the ground-truth label to select the masks. MUPAX keeps only masks on which the frozen model already agrees with the label, then reports accuracy on exactly those masks. The baselines get no such label-conditioned selection, so Table 1 compares apples to oranges.

What is actually here: a clean SLLN proof for a conditional distribution defined by an error threshold, a minor twist of inverse-error weighting, and a wide multi-modal evaluation including landmark detection. The theorem is correct as far as it goes, though it is a textbook application of bounded i.i.d. SLLN. The landmark crop idea is a legitimate direction worth exploring.

The biggest problem is circularity, as above. A second issue is that the paper never acknowledges RISE, which is the obvious prior art for random masking with importance weighting; missing that citation undermines the novelty claim. Also, the "deterministic" label sits oddly with random rejection sampling, and the i.i.d. assumption conflicts with the stratified sampling and data-dependent threshold W. No code or data is provided, which makes verification harder. The ablation table has a confusing threshold mapping (0.5 vs 0.8) that looks like an internal inconsistency.

This paper is not a reliable foundation for the stated claims. The convergence theorem holds but does not validate the oracle. It would be a useful candidate for an XAI evaluation-methods reading group as a cautionary example. A serious referee could ask for a redesign: either split the data so masks are selected on a validation set and evaluated on a held-out test set, or drop the accuracy-enhancement claim and evaluate faithfulness by the standard perturbation test.

I would not send this to peer review in its current form. The result needs rework before it is refereeable.

Referee Report

4 major / 4 minor

Summary. MUPAX is presented as a deterministic, model-agnostic, dimension-agnostic explainability method. It partitions an input into chunks, draws random selection vectors from a base distribution, computes the frozen model's loss relative to the ground-truth label for each masked input, retains only masks whose loss is below a threshold W, and forms a saliency map as the average of inverse-error-weighted masked inputs. The MUPAX Theorem claims almost-sure convergence of this average to a conditional expectation, with a CLT convergence rate (Section 3.1, Appendix A). Experiments benchmark masked-input accuracy against LIME, SHAP, GradCAM, and Integrated Gradients on audio (1D), images (2D), CT volumes (3D), and cephalometric landmark detection, reporting that MUPAX preserves or improves accuracy while baselines degrade (Tables 1-2). The formal convergence result is a standard SLLN statement, but the empirical central claim is undermined by the use of ground-truth labels in both mask selection and evaluation.

Significance. If the claims held, this would be an important contribution: formal convergence guarantees, model-agnosticism, and dimension-agnostic demonstrations across four modalities. The SLLN/CLT core is mathematically sound as far as it goes, and the paper has genuine breadth in its experimental coverage. However, the reported accuracy enhancement is not supported by the evaluation protocol, because the same ground-truth labels are used both to select the masks and to measure the resulting accuracy, while the baseline methods do not receive this label information. The practical advantage of MUPAX over existing XAI methods is therefore unsubstantiated as submitted.

major comments (4)

[Section 3 (Setup) and Section 3.1, with Section 4.2 and Table 1] The error function is defined as mu(X_arg) = L(f(X_arg), y_true), and acceptance of a mask requires mu(X_s) <= W. Table 1 then evaluates accuracy on the same labeled test samples used to generate those masks. This makes the reported accuracy enhancement a consequence of selecting masks on which the frozen model already agrees with the ground-truth label, rather than evidence that MUPAX identifies the 'most important patterns' of the input. The evaluation is circular and cannot support the claim that MUPAX preserves or enhances model accuracy.
[Section 4.2 and Table 1] The comparison with LIME, SHAP, GradCAM, and Integrated Gradients is informationally unfair: those baselines generate masks from the input and model only, whereas MUPAX receives y_true for every test sample when computing mu. The baselines' large F1 drops therefore reflect an unequal access to the ground-truth answer, not an inherent superiority of MUPAX's feature-attribution principle.
[Section 3.1] The method as specified cannot produce an explanation when the ground-truth label is unavailable, because the acceptance condition mu(X_s) <= W cannot be evaluated. Since post-hoc XAI is normally applied to unlabeled deployment inputs, the paper needs either a label-free proxy for mu or a clear statement that MUPAX is a label-guided input-selection method; without this, the practical contribution is unproven.
[Section 3.1 and Appendix A] The convergence theorem assumes a fixed threshold W and i.i.d. selection vectors from U, but the implementation sets W as the 20th percentile from an initial data-dependent phase and uses stratified uniform sampling. The accepted samples are therefore not i.i.d. from the fixed conditional distribution D_W, so the stated almost-sure guarantee does not directly apply to the evaluated procedure; a corrected analysis or a revised protocol is needed.

minor comments (4)

[Appendix B] The ablation discussion says the number of MUPAX perturbation samples was reduced from 50,000 to 5,000, while Section 4.2 states that 2,000 perturbation samples were used for the 2D task; these numbers are inconsistent and should be reconciled.
[Appendix B] The sentence 'setting the parameter W = 1.0 - threshold = 1.0 - 0.8 = 20%' is confusing and appears to conflate a percentile with a loss threshold; please clarify what W values were actually used.
[Section 3.1] The phrase 'converges pointwise almost surely (with probability that tends to 1)' should simply say 'almost surely,' matching the proof in Appendix A.
[Figure 3 caption] The caption repeats F1 values already given in Table 1; it should instead explain what the three panels illustrate.

Circularity Check

2 steps flagged · score 7.0 of 10

MUPAX's headline accuracy-enhancement and landmark-improvement results reduce by construction: masks are accepted based on the same ground-truth-labeled loss that is later reported as accuracy, and label-free baselines are compared against this label-conditioned selection.

fitted input called prediction [Section 3 (Goal) and Section 4.2 (Classification Methodology for Filter Mask Evaluation)]
"Given that n masked samples {X^1, . . . ,X^n} produce error values below some threshold W (or otherwise selected), it is possible to determine which coordinates of X consistently contribute to 'good' or 'bad' performance under the model f. In practice, generating the set {X^1, . . . ,X^n} involves randomly sampling a large number Ntotal ≫ n of selection vectors s, generating the corresponding filtered inputs Xs, computing their error µs, and retaining the first n samples for which µs ≤ W ."

The acceptance event µs ≤ W uses µ(Xs) = L(f(Xs), ytrue), i.e. the frozen model's loss against ground-truth labels. The masked inputs retained are therefore only the perturbations on which the model already achieves low loss relative to y_true. Section 4.2 then evaluates classification performance on those filtered inputs and reports F1 scores. Since the same labels enter both mask construction and evaluation, the reported accuracy gain (e.g. 0.93->0.95) is an evaluation of the label-conditioned accepted subset, not of an unsupervised 'most important patterns' selection. The baselines (LIME, SHAP, GradCAM, IG) receive no labels and are not selected by this oracle; the comparison is therefore unequal and the enhancement claim is forced by construction, not by the convergence theorem.
fitted input called prediction [Section 3.1 (Interpretation) and Section 4.3 (Landmark detection)]
"for landmark detection, if µ(Xarg) measures the error between predicted and ground-truth keypoint heatmaps, masked inputs X′ with low µ are those preserving essential visual cues for locating the landmark."

In the landmark experiments, the MUPAX crop is formed from the low-µ masks, where µ is the error between predicted and ground-truth keypoint heatmaps. Table 2 then reports mean radial error against the same ground-truth landmarks. The reduction from ~13.8 px to ~9.3 px is thus measured on the very criterion used to choose the crop: patches are kept because they keep the landmark error low, and then the landmark error is shown to be low. GradCAM crops are generated without any label-based error oracle, so the comparison does not establish that MUPAX selects semantically important regions.

full rationale

The MUPAX Theorem itself is not circular: given a fixed threshold W and i.i.d. samples from the conditional distribution D_W, the SLLN/CLT argument with bounded variables is a standard and valid derivation of χ_n(α) → E_{D_W}[µ'(X')X'(α)]. No self-citation chain is load-bearing and the convergence proof does not import a uniqueness result. However, the paper's central empirical claims — that MUPAX 'preserves but actually enhances model accuracy' and improves landmark localization — reduce by construction. In Section 3, the mask set is defined by µ(X_s) = L(f(X_s), y_true) ≤ W, i.e. the labels are used as an acceptance oracle to select perturbations where the model is already correct. In Sections 4.2 and 4.3, accuracy/F1 and radial error are then measured on those same selected masks against the same y_true. The comparison against label-free baselines is unequal, so the reported gains are not evidence for principled feature selection. A secondary technical weakness, not itself circularity, is that W is estimated from an initial data-dependent sampling phase while the theory treats W as fixed and the samples as i.i.d.; stratified uniform sampling also conflicts with the i.i.d. rejection-sampling premise. These issues affect the validity of the convergence guarantee as applied, but the decisive circularity is the label-conditioned mask selection used as evidence of accuracy enhancement.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The derivation relies on a handful of standard measure-theoretic facts (SLLN, CLT, rejection sampling) and on several hand-chosen parameters: the acceptance threshold W, chunk size, number of perturbations, and the inverse-error weighting 1/(mu+1). The most consequential assumption is that ground-truth labels are available when computing explanations, which is not stated as a limitation and is what makes the accuracy improvements possible.

free parameters (4)

W (selection threshold) = 20th percentile of initial error distribution per dataset
Controls acceptance probability p_W and thus which masks are kept; chosen empirically per dataset without a principled rule (Section 3.1).
chunk_size = 8x8 (2D), 16x16 (landmarks), 8x8x8 (3D)
Determines granularity of the mask and strongly affects performance; hand-chosen per task (Section 4.2).
N_perturb (number of perturbation samples) = 500 (1D), 2000 (2D), 200 (3D), 500 (landmarks)
Affects variance and runtime; no rule given for choosing these counts (Section 4.2).
inverse_error_weight mu' = 1/(mu+1) = 1/(mu+1)
Chosen ad hoc; no derivation or ablation justifies this specific weighting over alternatives like 1/mu or exp(-mu) (Section 3).

assumptions (6)

domain assumption Input X is nonnegative
Required for the boundedness step in the proof (Step 1, Appendix A); section 3 setup states this.
domain assumption Loss L is nonnegative
States L : Y x T -> R_{>=0}, which bounds mu' in [0,1]; section 3 setup.
standard math Rejection sampling yields i.i.d. draws from D_W
Correct for fixed W and i.i.d. proposal U, but in practice W is estimated from an initial sample and U is stratified, so the premise is only approximately met; section 3.1.
standard math Strong law of large numbers and central limit theorem
Applied to bounded i.i.d. variables in Appendix A, Step 2 and Step 3.
domain assumption Ground-truth label y_true is available when computing explanations
mu(X) is defined as L(f(X), y_true); this is the key ingredient that makes the accuracy-enhancement comparison circular, and it is not listed as a limitation in Section 5.
domain assumption Coordinates frequently retained in low-error masks are the 'important' coordinates
The interpretation step in Section 3.1 asserts a semantic meaning for chi(alpha) beyond its mathematical definition.

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Cite this review

Pith. "Pith review of MUPAX: Multidimensional Problem Agnostic eXplainable AI." pith.science (2026). https://pith.science/paper/OREY2UOE

@misc{pith2026250713090,
  author       = {Pith},
  title        = {Pith review of: MUPAX: Multidimensional Problem Agnostic eXplainable AI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OREY2UOE}},
  note         = {Machine review of arXiv:2507.13090}
}

read the original abstract

Robust XAI techniques should ideally be simultaneously deterministic, model agnostic, and guaranteed to converge. We propose MULTIDIMENSIONAL PROBLEM AGNOSTIC EXPLAINABLE AI (MUPAX), a deterministic, model agnostic explainability technique, with guaranteed convergency. MUPAX measure theoretic formulation gives principled feature importance attribution through structured perturbation analysis that discovers inherent input patterns and eliminates spurious relationships. We evaluate MUPAX on an extensive range of data modalities and tasks: audio classification (1D), image classification (2D), volumetric medical image analysis (3D), and anatomical landmark detection, demonstrating dimension agnostic effectiveness. The rigorous convergence guarantees extend to any loss function and arbitrary dimensions, making MUPAX applicable to virtually any problem context for AI. By contrast with other XAI methods that typically decrease performance when masking, MUPAX not only preserves but actually enhances model accuracy by capturing only the most important patterns of the original data. Extensive benchmarking against the state of the XAI art demonstrates MUPAX ability to generate precise, consistent and understandable explanations, a crucial step towards explainable and trustworthy AI systems. The source code will be released upon publication.

Figures

Figures reproduced from arXiv: 2507.13090 by the authors.

**Figure 1.** 1D audio classification explanation: MUPAX outperforms LIME and GradCAM in identifying important frequency features. (a) Orig. Pred: ‘cat’ (b) MUPAX Pred: ‘cat’ (c) LIME Pred: ‘cat’ (d) GradCAM Pred: ‘dog’ (e) SHAP Pred: ‘dog’ (f) Int. grads. Pred: ‘dog’ [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 2.** 2D cat-dog image classification: MUPAX preserves discriminative patterns w.r.t other methods. • 2D Image Landmark Detection: We used the CephAdoAdu dataset Wu et al. [2024], which includes 1, 000 cephalometric X-ray images evenly divided between 500 adult and 500 adolescent patients. Each image is annotated with 10 clinically significant anatomical landmarks, identified by an expert dental radiologist. The original … view at source ↗

**Figure 3.** 3D COVID-19 CT classification explanation: [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Landmark detection qualitative output for Landmarks 7 (left) and 6 (right) from using the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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