MUPAX: Multidimensional, Problem-Agnostic XAI

• The paper introduces a deterministic, perturbation-based method with a measure-theoretic formulation, ensuring model-agnostic and convergent explainability.
• The method uses structured perturbation analysis over masked inputs to filter out spurious features and highlight consistent, generalizable input patterns.
• Empirical evaluations demonstrate that MUPAX preserves or improves performance across audio, image, and volumetric data, outperforming methods like LIME and GradCAM.

Searching arXiv for the cited MUPAX-related papers and adjacent XAI framework work. arXiv query: "MUPAX Multidimensional Problem Agnostic eXplainable AI (Dentamaro et al., 17 Jul 2025)" Multidimensional Problem Agnostic Explainable AI (MUPAX) most specifically denotes a deterministic, model agnostic explainability technique with guaranteed convergency, formulated through structured perturbation analysis over a measure-theoretic space of masked inputs and evaluated across 1D, 2D, and 3D settings (Dentamaro et al., 17 Jul 2025). In the surrounding XAI literature, however, the same acronym or near-equivalent label has also been used for broader problem-agnostic explainability programs, including exemplar synthetization for black-box models and requirements-analysis frameworks organized around explanatory dimensions. The result is a term that is simultaneously a specific perturbation-based method and a wider label for multidimensional, problem-agnostic XAI design (Barbalau et al., 2020).

1. Terminological scope and historical usage

The acronym has been used for distinct XAI formulations. In its 2025 usage, MUPAX is a deterministic, model agnostic, convergence-guaranteed perturbation method defined over masked inputs and chunk-based structured perturbations (Dentamaro et al., 17 Jul 2025). In an earlier black-box explainability setting, a generic and model-agnostic exemplar synthetization framework was described as synthesizing “prototypical” inputs that maximally activate a desired response, using a generative model as a prior and a zero-order evolutionary strategy with momentum (Barbalau et al., 2020). In requirements analysis, a unified, problem-agnostic XAI framework was organized around three explanatory dimensions—Source, Depth and Scope—with explanations represented by a score triple $(S(E), D(E), P(E))$ (Sheh et al., 22 Feb 2026).

Usage	Core idea	Representative paper
Deterministic perturbation-based MUPAX	Structured perturbation analysis with guaranteed convergence across dimensions	"MUPAX: Multidimensional Problem Agnostic eXplainable AI" (Dentamaro et al., 17 Jul 2025)
Exemplar synthetization framework	Generative-prior search for prototypical black-box inputs	"A Generic and Model-Agnostic Exemplar Synthetization Framework for Explainable AI" (Barbalau et al., 2020)
Requirements-analysis framework	Source, Depth and Scope for specifying explanatory requirements	"Defining Explainable AI for Requirements Analysis" (Sheh et al., 22 Feb 2026)

This terminological overlap matters because “problem-agnostic” and “multidimensional” refer to different technical commitments in different papers. In the perturbation-based method, multidimensionality refers to the same theory and code running unmodified on 1D signals, 2D images, 3D volumes, or even higher-dimensional arrays. In the requirements-analysis formulation, multidimensionality refers to explanatory requirements. In the exemplar framework, problem-agnosticism refers to portability across images, text sequences or tabular features via a suitable generator.

2. Measure-theoretic formulation of the 2025 method

The 2025 MUPAX paper defines a formal measure space over structured perturbations of an input $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$ (Dentamaro et al., 17 Jul 2025). The set $\Omega$ is the set of all filtered inputs $X^s$ obtained by masking chunks of the original data $X$, $\mathcal{F}$ is the $\sigma$-algebra induced by all measurable subsets of $\Omega$, and $\mu$ is a base probability measure over selection vectors $s \in \{0,1\}^m$, for example uniform or stratified uniform on chunk-masks.

The original input is partitioned into $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$0 non-overlapping axis-aligned “chunks.” Each binary vector $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$1 induces a mask $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$2 with $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$3 and $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$4, so that

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$5

For a frozen predictor $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$6, target $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$7, and loss $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$8, the model error is

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$9

with inverse-error weight

$\Omega$0

The attribution function is defined through conditioning on low-error masked inputs. A threshold $\Omega$1 is fixed, for example the 20th percentile of $\Omega$2 under $\Omega$3. Using rejection sampling, one draws $\Omega$4 i.i.d. from $\Omega$5 and accepts only those with $\Omega$6, yielding accepted samples i.i.d. under the conditional distribution $\Omega$7. For each coordinate $\Omega$8,

$\Omega$9

and the empirical importance is

$X^s$0

As $X^s$1, this converges almost surely to

$X^s$2

The paper further decomposes the limit using an indicator for whether $X^s$3 is retained:

$X^s$4

Within the paper’s interpretation, structured perturbation analysis discovers inherent input patterns and eliminates spurious relationships. By conditioning on low-error masked inputs, MuPAX systematically discards spurious or non-generalizable features and highlights only those patterns that consistently reduce the model loss (Dentamaro et al., 17 Jul 2025).

3. Algorithmic procedure, determinism, and convergence guarantees

The method is designed to meet four desiderata simultaneously: Determinism, Model-agnosticism, Guaranteed convergence, and Multidimensional applicability (Dentamaro et al., 17 Jul 2025). Determinism is defined as: the same input and hyperparameters always yield the same explanation, with no random seeds once $X^s$5 is fixed. Model-agnosticism means applicability to any frozen predictor $X^s$6 (black-box), any loss $X^s$7, and any output type, including classification, regression, and landmark heatmaps.

The algorithmic description is explicit. Inputs are $X^s$8, black-box $X^s$9, loss $X$0, a chunk partition of $X$1 into $X$2 blocks, threshold $X$3, and desired $X$4. One sets $X$5 and initializes $X$6 for all $X$7. While $X$8, one draws $X$9, computes $\mathcal{F}$0, computes $\mathcal{F}$1, and if $\mathcal{F}$2, computes $\mathcal{F}$3 and accumulates $\mathcal{F}$4 into $\mathcal{F}$5 for each coordinate. The final explanation map is $\mathcal{F}$6.

Its complexity is given as

$\mathcal{F}$7

forward passes, where $\mathcal{F}$8, and the method is fully parallelizable across $\mathcal{F}$9 (Dentamaro et al., 17 Jul 2025). The key theorem assumes: (a) $\sigma$0 is bounded for each coordinate $\sigma$1; (b) $\sigma$2 so $\sigma$3 and hence $\sigma$4; and (c) the acceptance probability $\sigma$5. Under these assumptions, $\sigma$6 are i.i.d. bounded random variables with finite mean $\sigma$7, and by the Strong Law of Large Numbers,

$\sigma$8

almost surely as $\sigma$9. By the Central Limit Theorem,

$\Omega$0

where

$\Omega$1

A plausible implication is that the paper positions explainability not merely as a visualization layer, but as an estimator with an explicit sampling distribution, bounded random variables, and asymptotic guarantees.

4. Empirical evaluation across modalities

The reported experiments cover four modalities: 1D audio-spectrogram classification on GTZAN with a ResNet-50 on $\Omega$2 Mel-spectrograms; 2D Cat vs. Dog classification on 3,000 images with ConvNeXtXLarge; 3D CT COVID-19 detection on MosMedData with a custom 3D-CNN; and 2D cephalometric landmark detection on CephAdoAdu with ConvNeXt-Tiny plus decoder (Dentamaro et al., 17 Jul 2025). The stated claim is that MUPAX demonstrates dimension agnostic effectiveness across audio classification (1D), image classification (2D), volumetric medical image analysis (3D), and anatomical landmark detection.

Setting	Reported comparison	Result
1D audio classification	Macro F1, Full Input vs MuPAX Mask	$\Omega$3
2D Cat vs. Dog	Macro F1, Full Input vs MuPAX Mask	$\Omega$4
3D CT COVID-19 detection	Macro F1, Full Input vs MuPAX Mask	$\Omega$5

The same section reports mask-based comparisons against LIME, GradCAM, SHAP, and IntGrads. In 1D, the corresponding Macro F1 values after masking are LIME Mask $\Omega$6, GradCAM Mask $\Omega$7, SHAP Mask $\Omega$8, and IntGrads $\Omega$9. In 2D, they are LIME Mask $\mu$0, GradCAM Mask $\mu$1, SHAP Mask $\mu$2, and IntGrads $\mu$3. In 3D, the reported values are GradCAM Mask $\mu$4 and IntGrads $\mu$5, while LIME and SHAP are marked as unavailable. For landmark detection, mean radial error over 10 points is $\mu$6 for Full Image, $\mu$7 for MuPAX Crop, and $\mu$8 for GradCAM Crop (Dentamaro et al., 17 Jul 2025).

The paper’s summary claim is direct: MuPAX not only preserves but often improves model performance when retaining only its most “useful” features; other XAI masks sharply degrade accuracy. The stated explanation is a post-hoc regularization effect: by conditioning on low-error masked inputs, the method highlights only those patterns that consistently reduce the model loss. This suggests that, in the paper’s experimental setup, explanation and selective input retention are coupled rather than opposed.

5. Relation to black-box exemplar synthesis and the task-agnostic XAI debate

An important precursor to MUPAX-style problem-agnostic XAI is the generic and model-agnostic exemplar synthetization framework described in 2020 (Barbalau et al., 2020). That framework seeks a latent code $\mu$9 maximizing a black-box response over a generator,

$s \in \{0,1\}^m$0

where $s \in \{0,1\}^m$1 is a pre-trained generator and $s \in \{0,1\}^m$2 is any scalar output of the black-box, such as a logit, class probability or regression score. Because neither $s \in \{0,1\}^m$3 nor $s \in \{0,1\}^m$4 is differentiated through, the method employs a zero-order evolutionary strategy with momentum:

$s \in \{0,1\}^m$5

$s \in \{0,1\}^m$6

Its claims to agnosticism are dual: model-agnostic, because only query access to the black-box is required; and problem-agnostic, because the same procedure can operate with generators for images, text, or tabular data. The reported findings include equally-good exemplars in a shorter computational time than a model-dependent gradient-descent baseline, roughly $s \in \{0,1\}^m$7 fewer $s \in \{0,1\}^m$8-evaluations than standard evolutionary strategies, and $s \in \{0,1\}^m$9–$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$00 fewer model calls for the same target score when momentum is used (Barbalau et al., 2020).

Set against that line of work, the 2023 critique “Is Task-Agnostic Explainable AI a Myth?” argues that no current method truly meets the ideal of an explainer whose design and guarantees do not depend on the particular end-use or data modality while still producing faithful, actionable explanations across all settings (Chaszczewicz, 2023). The critique identifies persistent roadblocks across saliency, attention, and graph explainers: missing method–task link, ill-defined “importance,” absent or spurious guarantees, no ground truth, unreliable metrics and sanity checks, and evaluation confounders. It also characterizes a recurring three-stage pattern: initial introduction under simplistic setups, subsequent reliability failures, and then metric proliferation without consensus.

This suggests that the breadth of modalities in MUPAX and related problem-agnostic methods should not be conflated with a universal resolution of task compatibility. Dimension agnostic effectiveness and model-agnostic deployment are specific technical claims. The broader question posed by the task-agnostic XAI critique concerns whether the explanation is faithful, actionable, and validated relative to the downstream task.

6. Multidimensional requirements, explanatory depth, and open problems

A distinct use of “multidimensional” in XAI appears in requirements analysis, where explanations are assigned a triple

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$01

corresponding to Source, Depth and Scope (Sheh et al., 22 Feb 2026). Source is defined as the fidelity of an explanation against the true decision process of $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$02, with

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$03

Depth is decomposed into attribute identity/use and attribute/model sub-levels,

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$04

and Scope is defined by the fraction of the domain over which the explanation’s claims hold,

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$05

This framework then maps application requirements to an explanation requirement vector

$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$06

and selects eligible methods satisfying threshold constraints. Its open challenges include standard benchmarks for fidelity $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$07, automating dynamic trade-offs, integrating interactive dialogue, and quantifying human-centric metrics such as time-to-understand (Sheh et al., 22 Feb 2026).

A broader multidimensional scaffold is provided by a multi-component framework for XAI design, which identifies four components—Explicit Explanation Representation, Alternative Explanations, Knowledge of the Explainee, and Interactivity—and arranges them into Levels $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$08–$X \in \mathbb{R}^{d_1 \times \dots \times d_N}$09 of explainability calibration (Atakishiyev et al., 2020). In that framework, explanation is not exhausted by feature attribution or saliency, but extends to user models, multiple explanans, and dialogue protocols.

Against these multidimensional perspectives, the open problems stated for the 2025 perturbation-based MUPAX method are notably operational: perturbation-based sampling can be expensive; runtime scales as $X \in \mathbb{R}^{d_1 \times \dots \times d_N}$10 but is highly parallelizable; and future extensions include fast Monte Carlo approximations, adaptive chunking, support for temporal sequences and graph-structured data, human-in-the-loop threshold tuning, and tackling semantic segmentation via structured set-based sampling (Dentamaro et al., 17 Jul 2025). A plausible implication is that the perturbation-based method addresses determinism, model agnosticism, convergence, and cross-dimensional data handling, while the requirements-analysis and multi-component frameworks address a different layer of the XAI problem: what kind of explanation is needed, for whom, over what scope, and with what interaction model.

In that sense, MUPAX denotes both a concrete explainability algorithm and a wider research aspiration. As a concrete method, it is a deterministic, structured perturbation framework with almost-sure convergence guarantees and reported gains under mask-based evaluation. As a wider aspiration, it aligns with attempts to organize XAI around multiple dimensions rather than a single saliency map or local attribution score.