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REVIEW 5 major objections 5 minor 23 references

The paper's central claim is that explainability can be distilled into a single multidimensional score, and that an offline knowledge base can predict that score for new datasets and models.

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2026-08-02 02:26 UTC pith:OIY6EA43

load-bearing objection A clear-eyed outline for an explainability score, but the one quantitative result it reports is an artifact of SHAP's local accuracy, and the promised unified score is never actually computed. the 5 major comments →

arxiv 2607.14315 v1 pith:OIY6EA43 submitted 2026-07-15 cs.LG cs.AI

Towards a Unified Multidimensional Explainability Metric: Evaluating Trustworthiness in AI Models

Georgios Makridis , Georgios Fatouros , Athanasios Kiourtis , Dimitrios Kotios , Vasileios Koukos , Dimosthenis Kyriazis , Jonh Soldatos This is my paper
classification cs.LG cs.AI
keywords explainabilityXAI evaluationfidelitystabilitysimplicitySHAPLIMEknowledge base
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the trustworthiness of an AI explanation can be compressed into a single multidimensional score built from fidelity, simplicity, and stability, with coverage and user judgments as further components. It further argues that benchmarked scores, stored with metadata about models, datasets, and explainers, form an offline knowledge base that can estimate explainability for previously unseen configurations. The authors demonstrate the framework by scoring LIME and SHAP on three tabular datasets, reporting that SHAP wins on fidelity while LIME wins on stability. A reader should care because a reliable single score would let practitioners and regulators compare explainers objectively, without rerunning experiments or relying on subjective opinion.

Core claim

On its own terms, the paper claims that an explainability score can be computed as a weighted sum of measurable components—fidelity, stability, simplicity, coverage, user satisfaction, user trust, and user task performance—yielding one number that characterizes the overall performance of an XAI method. The second claim is that this score is context-dependent, so the paper aggregates benchmarking results and metadata into an offline knowledge base whose purpose is to predict explainability scores for new datasets and models. The experiments compare LIME and SHAP, finding SHAP fidelity near 1e-17 (nearly perfect reproduction of the model) and LIME stability at 0.56–1.0, which the paper reads a

What carries the argument

The load-bearing object is the explainability score formula, a weighted sum of fidelity, stability, simplicity, coverage, and user-perceived components, where the weights are to be set later by surveys. Fidelity is the normalized squared difference between the model's prediction and the explanation model's prediction; stability is the normalized change in explanation output under input perturbation; simplicity counts features or decision-tree nodes. The second load-bearing component is the offline knowledge base, which stores these scores alongside model and dataset metadata and is meant to estimate scores for unseen inputs. The paper also leaves the score in multidimensional form when aggre

Load-bearing premise

The quantitative conclusion that SHAP beats LIME on fidelity rests on treating the near-zero fidelity scores from the formula as meaningful evidence, even though SHAP reproduces the model's prediction by construction, making those scores a mathematical identity rather than a measured result.

What would settle it

A single decisive check: implement an intentionally vacuous explainer that outputs the original model's prediction for every sample; the fidelity formula will give it the same near-zero score as SHAP. If the framework's fidelity component cannot distinguish a vacuous explainer from SHAP, then the fidelity measure—and the headline comparison built on it—does not measure explanation quality.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • If the score is valid, organizations can choose an XAI method by a single number, making comparison between LIME and SHAP (or future methods) routine.
  • Explainability evaluation becomes less dependent on human raters for the quantitative components, though user-perceived weights remain.
  • The knowledge base would let teams estimate explainability for a new dataset without recomputing expensive experiments, lowering the cost of XAI validation.
  • Trade-offs become explicit and searchable: this paper's data shows SHAP ahead on fidelity, LIME ahead on stability, so practitioners could filter by context.
  • Regulated use cases gain a numeric artifact—an explainability grade—that can be reported alongside model accuracy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Inference: the near-zero SHAP fidelity scores follow from SHAP's defining property of reproducing the model prediction locally, so the fidelity formula makes SHAP look perfect by construction; the same score would reward any explainer that simply copies the model's output.
  • Inference: a testable extension is to evaluate whether metadata-only prediction transfers—e.g., train the knowledge base on the three used datasets, then predict scores for a held-out tabular dataset and compare against true benchmarks; the paper's evidence for transfer is limited to three small datasets.
  • Inference: adding a 'random but prediction-reproducing' baseline to the benchmark would clarify whether fidelity measures explanation quality or just mathematical mimicry.
  • Inference: the multidimensional (non-aggregated) form is arguably the more defensible contribution, since aggregating with unset weights cannot yet be validated; future user surveys are what the credibility of the single score hinges on.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes a unified multidimensional explainability score for XAI methods, combining fidelity, stability, simplicity, coverage, and human-centered metrics via a weighted sum. It reports benchmarking experiments with LIME and SHAP on Iris, Wine, and Breast Cancer datasets, presents component scores in Tables I and II, and outlines an offline knowledge base for estimating explainability of unseen models and datasets. The stated claims are that SHAP has near-perfect fidelity, LIME has higher stability, and the framework supports context-dependent XAI selection.

Significance. A validated unified explainability metric would be a valuable contribution to XAI evaluation, and the paper addresses an important problem. However, the presented support is not sufficient: the main numerical comparison is predetermined by SHAP's local-accuracy property, the stability metric is mis-defined, the unified score is never computed, and the knowledge base is only described. The manuscript has a clear structure and identifies relevant literature, but it does not establish the proposed framework.

major comments (5)
  1. [Eq. (1), Tables I–II, Section V] The SHAP fidelity values (7.29e-18, 1.27e-17, 1.23e-17) are not measured results: for SHAP, with g(x_i) taken as the additive SHAP model, the local-accuracy property gives g(x_i)=f(x_i) by construction. Substituting into Eq. (1) forces the numerator to zero up to floating-point error. Therefore the Section V conclusion that 'SHAP generally outperforms LIME in terms of fidelity' is a mathematical identity of SHAP's definition, not an empirical finding, and cannot support a comparative explainability metric.
  2. [Eq. (2), Section V] Eq. (2) defines stability as the normalized L2 distance between g(x_i) and g(x_i'). This is always nonnegative, yet the Section V range bullet states 'Stability: Range: [-1, 1]'. Moreover the equation measures the change in the explanation model's predicted value, not the change in the explanation itself. For a stability metric one would compare the explanation outputs (e.g., attribution vectors) under perturbation. As defined, the reported stability values are difficult to interpret and do not support the trade-off claims about LIME versus SHAP.
  3. [Section III-B (Explainability score)] The paper's headline deliverable is 'a single score to characterize the overall performance of the XAI method' (Section I-B). However, the weighted-sum score is never computed: the text states the weights 'will not be defined' and 'will be defined via surveys and questionnaires' in future work. Tables I and II report only components. Thus the central claim of a unified multidimensional explainability score is not demonstrated.
  4. [Abstract and Section IV] The offline knowledge base and the estimation of explainability scores for unseen datasets and models are described as goals, but no such knowledge base is constructed and no estimation experiment is performed. The paper contains no metadata analysis, rule learning, or validation against held-out datasets or models. The contribution in its current scope is a proposal, not a working framework.
  5. [Eq. (3), Tables I–II] Simplicity is defined by Eq. (3) as an average ratio of number of nodes to maximum nodes, yet Tables I and II report simplicity values 4, 13, 30 (and 28.31 for SHAP on dataset 3), which look like feature counts. The units are inconsistent with the definition, and the non-integer SHAP value is unexplained. Without a consistent component calculation, the comparison of simplicity between methods is not meaningful.
minor comments (5)
  1. [Section II-B] Typo: 'off-the-self' should be 'off-the-shelf'; Section V: 'lets start' should be 'let's start'; Acknowledgments: 'Europeans Union's' should be 'European Union's'.
  2. [Tables I and II] The tables use 'Dataset 1/2/3' but do not map to Iris, Wine, and Breast Cancer datasets in the captions or surrounding text.
  3. [Section IV] The experimental setup is underspecified: no training/test split, model hyperparameters, random seeds, or perturbation procedure for Eq. (2) is described, which prevents reproduction.
  4. [Section III-A1] Eq. (1) uses f(x_i) and g(x_i) without specifying whether these are logits, probability vectors, or predicted class labels. The definition affects the meaning of fidelity.
  5. [References] Several references are incomplete: [11] lacks venue/year details, [21] lists only '2023' with no venue, and the author name 'Jonh Soldatos' appears misspelled in the author list.

Circularity Check

1 steps flagged

SHAP's near-zero fidelity is a tautology: Eq. (1) combined with SHAP's defining local-accuracy property forces g(x_i)=f(x_i), so the headline comparison is predetermined by construction.

specific steps
  1. self definitional [Eq. (1) in Section III-A1; SHAP definition in Section II-A1; interpretation in Section V (Tables I-II).]
    "Fidelity measures the extent to which the explanation model accurately reflects the behavior of the underlying model... where ... f(x_i) is the prediction of the original model for sample i, and g(x_i) is the prediction of the explanation model for the same sample. ... SHAP values are based on game theory and provide a unified measure of feature importance for individual predictions, fairly distributing the prediction output among input features. ... the fidelity scores for SHAP are extremely close to zero (on the order of 1e-17), indicating that SHAP provides a nearly perfect fit with the glo"

    Eq. (1) defines fidelity as the normalized distance between the model prediction f(x_i) and the explanation-model prediction g(x_i). For SHAP, the explanation model is the additive SHAP model, whose defining local-accuracy property (the 'fairly distributing the prediction output among input features' property, from the cited Lundberg & Lee work) enforces g(x_i) = f(x_i) up to floating-point error. Plugging this identity into Eq. (1) forces every summand to zero, so Table II's ~1e-17 fidelity scores are not measured outcomes but mathematical identities. Hence 'SHAP generally outperforms LIME in terms of fidelity' is a consequence of SHAP's definition, not an empirical benchmark result. This makes the fidelity component of the proposed metric unable to compare SHAP with any explanation that

full rationale

The paper's only quantitative comparison is the SHAP-vs-LIME fidelity result, and that result is circular: fidelity is defined in Eq. (1) as the distance between f(x_i) and the explanation model g(x_i), while SHAP's defining property guarantees g(x_i)=f(x_i) on every instance. The near-zero entries in Table II therefore follow by construction, not from benchmarking. The simplicity and stability measurements are not circular, and no self-citation is load-bearing for them; but they do not rescue the headline fidelity claim or the proposed unified metric, which is never actually assembled (weights are deferred to future surveys, and the knowledge base is not built). The central 'SHAP outperforms LIME in fidelity' conclusion is thus forced by definition, warranting a score of 8 rather than a lower partial-circularity score.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 3 invented entities

The central claimed deliverable, a unified explainability score, depends on undefined weights and unvalidated metric definitions. The most consequential empirical result, SHAP's near-zero fidelity, is forced by the choice of SHAP's additive model in the fidelity formula. The knowledge base and human-validation components are described only as future work, so the paper's contribution is an outline rather than a functioning metric.

free parameters (3)
  • Weights w1..w7 in the explainability score = undefined
    Section III states the weights will be defined in future work via surveys, so the unified score cannot actually be computed.
  • Perturbation scale for stability x'_i = unspecified
    Eq. (2) requires a perturbed version of each sample, but the paper gives no perturbation magnitude, distribution, or sampling procedure.
  • Maximum number of nodes in simplicity denominator = unspecified
    Eq. (3) normalizes by 'maximum num of nodes' but no value or per-model computation is given.
axioms (4)
  • ad hoc to paper Eq. (1), the normalized L2 difference between model and explanation predictions, measures fidelity.
    No validation links this quantity to human-understood fidelity; the paper also uses lower-is-better while calling it fidelity.
  • ad hoc to paper Eq. (2), the normalized L2 difference between explanations on original and perturbed samples, measures stability.
    The equation is nonnegative, but the paper claims stability ranges over [-1, 1], so the axiom is internally inconsistent with the stated range.
  • ad hoc to paper SHAP's additive explanation model g(x_i) may be used as the explanation model in Eq. (1).
    SHAP's local accuracy property forces ||f - g|| to be essentially zero, making the reported fidelity comparison definitional rather than empirical.
  • domain assumption Three small tabular UCI datasets are representative of diverse data types including image data.
    The paper claims coverage of tabular and image data, but only tabular datasets are used; no image dataset appears in the experiments.
invented entities (3)
  • Unified multidimensional explainability score no independent evidence
    purpose: To compress fidelity, stability, simplicity, coverage, and user metrics into a single trustworthiness score.
    The aggregation weights are not defined and no complete score is reported; it is a proposed construct with no empirical validation.
  • Offline knowledge base for explainability estimation no independent evidence
    purpose: To estimate explainability scores for unseen models and datasets from metadata.
    No schema, algorithm, construction details, or populated instance of the knowledge base is presented; it remains a future artifact.
  • Social performance score from human experts no independent evidence
    purpose: To validate the quantitative explainability score against human judgment.
    Mentioned as a possible validation methodology, but no survey, protocol, or results are provided.

pith-pipeline@v1.3.0-alltime-deepseek · 8888 in / 8506 out tokens · 87529 ms · 2026-08-02T02:26:53.204745+00:00 · methodology

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Cite this review

Pith. "Pith review of Towards a Unified Multidimensional Explainability Metric: Evaluating Trustworthiness in AI Models." pith.science (2026). https://pith.science/paper/OIY6EA43

@misc{pith2026260714315,
  author       = {Pith},
  title        = {Pith review of: Towards a Unified Multidimensional Explainability Metric: Evaluating Trustworthiness in AI Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OIY6EA43}},
  note         = {Machine review of arXiv:2607.14315}
}
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read the original abstract

In this paper, we present a comprehensive framework for assessing the explainability of various XAI methods, such as LIME and SHAP, across multiple datasets and machine learning models, with the ultimate goal of creating a unified multidimensional explainability score. Our methodology focuses on three key aspects of explainability: fidelity, simplicity, and stability. We leverage benchmarking experiments to systematically evaluate these aspects and use the insights gained to construct an offline knowledge base. This knowledge base captures the explainability scores for each registered model and serves as a valuable resource for context-dependent evaluation of explainability. By analyzing the complementary characteristics and metadata of AI models, datasets, and XAI methods, the knowledge base will enable the estimation of explainability scores for previously unseen datasets and models. Properties like fidelity, simplicity, and stability may vary significantly based on the dataset, underlying model, and domain expertise of the end user. We demonstrate our framework by applying it to three open-source datasets, discussing the implications of the obtained results in relation to the characteristics of the datasets. Our work contributes to the growing field of XAI by providing a robust and versatile tool for evaluating and comparing the explainability of various XAI methods, ultimately supporting the development of more transparent and trustworthy AI systems.

Figures

Figures reproduced from arXiv: 2607.14315 by Athanasios Kiourtis, Dimitrios Kotios, Dimosthenis Kyriazis, Georgios Fatouros, Georgios Makridis, Jonh Soldatos, Vasileios Koukos.

Figure 1
Figure 1. Figure 1: Explainability score logical architecture with quantifying XAI and performance of the model [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Benchmarking experiments for Knowledge Base devel [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

discussion (0)

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