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REVIEW 4 major objections 6 minor 36 references

Meta-evaluating stability measures: MAX-Senstivity & AVG-Sensitivity

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Stability metrics report pure noise as perfectly stable.

desk verdict A useful benchmark idea, but the central ROT result looks like an implementation artifact, not a property of the metrics. read the letter →

arxiv 2412.10942 v1 pith:JQEYXSJM submitted 2024-12-14 cs.CV

Miquel Miró-Nicolau , Antoni Jaume-i-Capó , Gabriel Moyà-Alcover This is my paper · ORCID
classification cs.CV
keywords explainableAIXAIrobustnessstabilitymeasuresMAX-SensitivityAVG-Sensitivitymeta-evaluationRandomOutputTestPerfectExplanation
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 introduces two benchmark tests, the Perfect Explanation Test and the Random Output Test, to meta-evaluate XAI stability measures, and applies them to MAX-Sensitivity and AVG-Sensitivity. The tests give each metric a known target value: exact explanations from a decision tree should be scored perfectly stable, while Gaussian-noise explanations with uniform-noise predictions should be scored maximally unstable. Both metrics score 0.000 on the perfect case, but on the random case they return 0.011 and 0.010 instead of the expected 1.0, which the paper takes as evidence that they cannot detect an obvious lack of stability. If the argument holds, low values of these metrics should not be used as evidence that an explanation is stable.

What carries the argument

The central objects are the two sensitivity formulas: MAX-Sensitivity, the maximum over Monte-Carlo perturbations with $\|x_j-x_i\|<\epsilon$ of $\|f(x_j)-f(x_i)\|$, and AVG-Sensitivity, the average over the same perturbation set, where $f(x)$ is the explanation for input $x$. The meta-evaluation machinery is the oracle-test design: in the Perfect Explanation Test the true explanation is known exactly, so any correct stability metric must return its perfect value, and in the Random Output Test the explanation and prediction are pure noise, so any correct metric must report maximal instability. Each metric is judged by whether its value and confidence interval match the known expected value.

What would settle it

Re-run the Random Output Test on the same Gaussian-noise explanations with an implementation that samples perturbations strictly by $\|x_j - x_i\| < \epsilon$, records $\epsilon$ and the Monte Carlo count, and prints the individual norms $\|f(x_j)-f(x_i)\|$. If the resulting MAX- and AVG-Sensitivity values are near 1 rather than 0.011 and 0.010, the reported near-perfect scores are an artifact of the sampling condition, not a property of the metrics.

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Extended reading notes

Core claim

The paper claims that MAX-Sensitivity and AVG-Sensitivity pass the Perfect Explanation Test but fail the Random Output Test. With random Gaussian explanations and uniform-noise predictions, where a correct instability measure should return 1.0, both metrics returned near-zero values (0.011 and 0.010), so the paper says they depict the results as perfect. The paper attributes this failure to the way the metrics define their locality, namely that only perturbations whose prediction difference is below a threshold $\epsilon$ enter the computation, which masks the randomness. On the paper's argument, neither metric can be used to certify explanation stability.

Load-bearing premise

The conclusion rests on the authors' implementation of the two sensitivity formulas matching their definitions, namely sampling perturbations within an $\epsilon$-ball and taking the max or average of explanation differences, so the near-zero Random Output Test scores are a property of the metrics and not a coding or sampling artifact.

Editorial extensions

If this is right

  • Any stability metric that fails the Random Output Test cannot be trusted to certify explanation stability in real applications, because it cannot detect the most basic failure mode.
  • The two tests provide an objective benchmark: a metric that cannot handle the simple perfect and random scenarios is not reliable in complex scenarios either.
  • Because the failure is attributed to the $\epsilon$-neighborhood sampling, other stability measures built on the same local perturbation idea should be screened with the same benchmark before use.
  • The expected-value-plus-confidence-interval procedure gives future stability metrics a pass/fail rule that does not require new axioms about what robustness should mean.

Reading between the lines

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

  • The failure mode likely extends beyond these two formulas: any stability measure whose perturbation set is restricted by a small output or prediction change will tend to under-report instability when explanations are noisy, because the noisy samples that survive the filter are the ones that look similar.
  • A direct testable extension is to run the same two tests on other stability measures; the benchmark is metric-agnostic and does not depend on the specific choice of decision tree or synthetic dataset.
  • In practice, a low MAX- or AVG-Sensitivity value on a real model should be accompanied by a randomized-explanations control; without such a control, a near-zero score cannot be read as evidence of explanation stability.
  • The paper's own explanation of the near-zero Random Output Test scores says the perturbation set is restricted by prediction difference, but Equation 1 conditions on input distance; if the implementation follows Equation 1, the near-zero result needs a different explanation, and if it follows the prose, the result does not apply to the published metric.
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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 / 6 minor

Summary. The paper proposes two a-priori tests, the Perfect Explanation Test (PET) and the Random Output Test (ROT), to meta-evaluate the stability measures MAX-Sensitivity and AVG-Sensitivity introduced by Yeh et al. In PET, a decision tree trained on the TXUXIv3 dataset with the ssin attribution function is used to supply supposedly perfect explanations; in ROT, explanations are drawn from a Gaussian distribution and predictions from a uniform distribution. Reported results are perfect scores (0.000) in PET and near-perfect scores (0.011 and 0.010) in ROT, from which the authors conclude that both stability measures fail to detect random, unrobust explanations and are therefore unreliable.

Significance. The conceptual idea of testing stability metrics against scenarios with known ground-truth robustness is useful and complements existing axiomatic meta-evaluation approaches. The proposed tests are simple, intuitive, and potentially cheap to apply to other stability metrics. If the ROT finding were established under a faithful implementation of Eqs. (1) and (2), it would be a significant negative result for two widely used sensitivity measures. The paper also honestly states the scope limitation that the tests work only as a benchmark. However, the empirical claim is not currently verifiable: the manuscript omits key experimental parameters, asserts rather than derives the expected robustness values, and contains an internal contradiction about whether 0 or 1 denotes perfect robustness. The central negative conclusion is therefore not supported by the evidence as presented.

major comments (4)
  1. [§3.1–3.2, Tables 3–4] The robustness scale is defined inconsistently across the two tests. Section 3.2 states that 'r = 0, where 0 value indicated a completely unrobust explanation' and that 'any robustness metric r_hat ≠ 0 is clearly an erroneous result.' Section 3.1 and Table 3 instead treat 0.0 as the perfect value ('where the least the better, being 0 the perfect value'), while Table 4 lists the expected ROT value as 1.0. The manuscript never reconciles whether a correct metric should output 0 or 1 in perfect versus random scenarios, so the claim that MAX- and AVG-Sensitivity 'failed' the ROT test has no coherent interpretation.
  2. [§5.2 vs. Eqs. (1)–(3)] The explanation of the near-zero ROT values contradicts the metric definitions. Equation (3) defines the perturbation set by input distance, ||x_j - x_i|| < epsilon, and Eq. (1) takes the maximum over that input ball. Section 5.2 instead says the low values arise because 'the perturbation samples toke into account are the ones with a prediction difference, respect to the original data, lower than a threshold epsilon.' If the implementation selected samples by output difference, it did not compute the metrics as defined; near-zero values would then be a mechanical artifact of selecting only near-identical outputs. The paper reports no epsilon, no Monte Carlo sample count, no image dimensionality, and no norm normalization, so the experiment cannot be reproduced. For a Gaussian explanation field that is independent across inputs, the expected value of ||f(x_j) - f(x_i)|| over an input ball is positive and grows with explanation dimension, so a faithful implementation of Eqs. (1)–(3) would not obviously produce values near 0.01.
  3. [§4.1, PET ground truth] The PET asserts that the decision-tree explanation is perfect, but the explanation used is an ad-hoc Gini-importance vector (Eqs. 6–8), not a defined ground-truth explanation for the ssin attribution function (Eqs. 11–12). No argument is given for why this vector equals the true contribution of each feature to the prediction, so the claim that r = 1 in PET is not derived from known ground truth. Moreover, because the explanation is a deterministic function of the tree path, any perturbed input that stays in the same leaf yields exactly the same explanation; the perfect PET score (0.000) may therefore be tautological rather than evidence that the metrics correctly measure robustness.
  4. [§3, expected-value derivation] The central methodological claim is that the proposed tests are 'completely verifiable, without depending on any novel axiom.' This requires that the expected robustness values be derived from the definitions of robustness and the test construction. The manuscript asserts these values but never proves them: it does not specify how the random explanation field enters the expectation in Eqs. (1)–(2), what the norm is normalized by, or why the expected ROT value should be exactly 1.0 rather than some other constant. Without such a derivation, the pass/fail criterion is an unsubstantiated assumption, not a verifiable benchmark.
minor comments (6)
  1. [Title and abstract] There are several typos in the title and abstract, including 'MAX-Senstivity', 'AVG-Sensitiviy', and the header 'MAX-S ENSTIVITY'; these should be corrected.
  2. [Eqs. (9)–(10)] The summation index in both equations reads 'Pn i=i' and should be 'Σ_{i=1}^n'.
  3. [Table 4] The confidence-interval notation is internally inconsistent: '0.011 ± 0.003 (0.011, 0.011)' cannot all be true, and the construction of the interval and the meaning of the ± term should be stated explicitly.
  4. [§6] The conclusion says the ROT values are '0.11 and 0.010', but Table 4 reports 0.011 and 0.010; this numerical typo should be fixed.
  5. [§3.2 vs. §4.4] The test is called 'Random Output Test' in Section 3.2 but 'Random Explanation Test' in Section 4.4; the names should be consistent throughout.
  6. [References] Reference [11] contains an empty author entry (', , Vedaldi'); the reference list should be checked for such formatting errors.

Circularity Check

1 steps flagged · score 7.0 of 10

The ROT verdict is an artifact of the perturbation-selection rule reported in §5.2; near-zero MAX/AVG values are forced by construction, so the central claim against the metrics is not established.

  1. self definitional [Section 5.2 (Experiment 2), contrasted with Equations 1–3 in Section 2]
    "This error happens due to the nature of both metrics analysed in Section 2: the fact that in both Equation 1 and Equation 2 the perturbation samples toke into account are the ones with a prediction difference, respect to the original data, lower than a threshold ϵ, produced an artificial mitigation of the lack of robustness of the methods."

    Equation 3 defines the perturbation set as S^ϵ_xi = {x_j sampled using Monte-Carlo algorithm | ||x_j − x_i|| < ϵ}, i.e., proximity in input space. The paper's explanation of the ROT result instead says the samples admitted are those whose prediction/explanation difference is below ϵ. With that filter, the quantities ||f(x_j) − f(x_i)|| in Equations 1 and 2 are computed only over outputs that are already nearly identical, so MAX- and AVG-Sensitivity are forced toward 0 regardless of the metric's definition. The reported 'failure' is therefore not an empirical property of the Yeh et al. metrics but a logical consequence of the sample-selection rule described; the result reduces by construction to the paper's own (mis)stated filtering criterion.

full rationale

The central claim that MAX- and AVG-Sensitivity are unreliable rests on the Random Output Test values (0.011 and 0.010) being near zero for noise. On the face of the paper's own Section 5.2, those values arise because the perturbation samples retained are those with a prediction difference below ϵ, which would make near-zero sensitivity a definitional tautology rather than evidence against the metrics as defined in Equations 1–3. This is a self-definitional/circular step in the experimental derivation, not a self-citation issue: the Yeh et al. metric definitions and the ROT expectation come from external sources, and the authors' previous dataset/attribution work is not what forces the ROT outcome. There are also non-circular correctness inconsistencies (Section 3.2 asserts r=0 for unrobust but Table 4 lists expected value 1.0; Table 3 expects 0.0 while Section 3.1 demands r=1), which should be weighed as validity problems but do not themselves constitute circularity. Because the headline conclusion about metric unreliability is not independently established once the §5.2 filtering explanation is taken literally, the score is elevated to 7 rather than 0–2.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central ROT result rests on asserted target values and on unreported implementation details, plus reuse of the authors' own synthetic benchmark. No new physical entities are introduced.

free parameters (2)
  • Perturbation radius epsilon
    Radius that defines S_epsilon_xi in Eqs. 1-3; never reported in the paper, yet it directly determines the sensitivity values.
  • Monte Carlo sample count |S_epsilon_xi|
    Number of perturbed samples per input used to estimate MAX and AVG sensitivity; not reported, so the confidence intervals and point values cannot be reproduced.
assumptions (3)
  • domain assumption A correct stability metric must return zero sensitivity in the Perfect Explanation Test.
    Assumes the decision-tree importance explanation is the perfect ground-truth explanation, so any change is metric error.
  • domain assumption Random explanations and random predictions imply completely unrobust behavior, encoded as r=0 in Section 3.2 but expected value 1.0 in Table 4.
    The test's ground truth is asserted, not derived; the two scale conventions contradict each other.
  • domain assumption The TXUXIv3 dataset and its ssin attribution function provide valid ground-truth explanations.
    The dataset and attribution function come from the authors' own prior work [23,24]; the explanations of the decision tree are taken as perfect by construction.

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Cite this review

Pith. "Pith review of Meta-evaluating stability measures: MAX-Senstivity & AVG-Sensitivity." pith.science (2026). https://pith.science/paper/JQEYXSJM

@misc{pith2026241210942,
  author       = {Pith},
  title        = {Pith review of: Meta-evaluating stability measures: MAX-Senstivity & AVG-Sensitivity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JQEYXSJM}},
  note         = {Machine review of arXiv:2412.10942}
}
read the original abstract

The use of eXplainable Artificial Intelligence (XAI) systems has introduced a set of challenges that need resolution. The XAI robustness, or stability, has been one of the goals of the community from its beginning. Multiple authors have proposed evaluating this feature using objective evaluation measures. Nonetheless, many questions remain. With this work, we propose a novel approach to meta-evaluate these metrics, i.e. analyze the correctness of the evaluators. We propose two new tests that allowed us to evaluate two different stability measures: AVG-Sensitiviy and MAX-Senstivity. We tested their reliability in the presence of perfect and robust explanations, generated with a Decision Tree; as well as completely random explanations and prediction. The metrics results showed their incapacity of identify as erroneous the random explanations, highlighting their overall unreliability.

Figures

Figures reproduced from arXiv: 2412.10942 by the authors.

Figure 1
Figure 1. Samples from TXUXIv3 dataset [23] and their respective explanations from a Decision Tree. We can see the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Samples from TXUXIv3 dataset [23], we can see the different background from DTD dataset [11]. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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Reviewed August 11, 2026 · model on record in the stance chip above.