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REVIEW 3 major objections 2 minor 55 references

Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index

T0 review · 3 major / 2 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Two novel game-theoretic feature importance scores, built on the Shapley value and the Banzhaf index with a WAXp-based characteristic function that accounts for non-WAXp sets, quantify how effective each feature is at excluding adversarial

desk verdict The submission bundle is mismatched—supplied full text is a GR paper—so this is a review of an abstract and a metadata error, and the actual paper deserves a fair shot only after the record is fixed. read the letter →

arxiv 2508.11959 v1 pith:GSWICKQ2 submitted 2025-08-16 cs.AI

Xuanxiang Huang , Olivier Létoffé , Joao Marques-Silva This is my paper · ORCID
classification cs.AI
keywords featureimportanceShapleyvalueBanzhafindexweakabductiveexplanationsadversarialexamplesformalexplainableAIcomputationalcomplexity
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 two new feature importance scores for machine-learning models, built on the Shapley value and the Banzhaf index. The scores use a characteristic function derived from weak abductive explanations (WAXps) that, unlike earlier work, also counts the contribution of feature sets that are not WAXps. Because of the known link between formal explanations and adversarial examples, the resulting scores measure how effective each feature is at excluding adversarial examples. The paper also states formal properties of the scores and analyzes their computational complexity. A sympathetic reader would take the proposal as a step toward attribution methods with documented formal guarantees.

What carries the argument

The characteristic function built from weak abductive explanations (WAXps), together with the Shapley value and Banzhaf index from cooperative game theory. The WAXp machinery turns feature subsets into payoffs by checking whether the subset is a weak formal explanation for a prediction; the novel step extends the payoff to non-WAXp sets, so that features contributing through non-explaining subsets are not assigned zero importance. The Shapley value and Banzhaf index then aggregate these payoffs into per-feature scores.

What would settle it

Give a concrete classifier and a set of adversarial examples; compute the proposed scores and compare them with the empirically measured reduction in the number of adversarial examples when each feature is removed. If a feature that the scores rank high does not reduce the adversarial region, or if the characteristic function violates a Shapley axiom such as the dummy-player axiom on a simple example, the claimed properties would fail.

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Extended reading notes

Core claim

We introduce two feature importance scores, based on the Shapley value and the Banzhaf index, where the underlying characteristic function is defined on WAXp sets but also accounts for non-WAXp sets. The scores quantify how effective each feature is at excluding adversarial examples. We identify properties of the scores and study the computational complexity of computing them.

Load-bearing premise

The construction assumes that a feature set's importance can be faithfully summarized by how well it excludes adversarial examples within the WAXp logic, i.e., that this game-theoretic payoff correctly captures feature contribution.

Editorial extensions

If this is right

  • If the scores measure adversarial-exclusion effectiveness, they give practitioners a formally grounded way to rank features for robustness analysis.
  • The stated properties let users compare the two scores and know which game-theoretic axioms each satisfies.
  • The complexity results tell when the scores can be computed exactly and when approximation is necessary.
  • By including non-WAXp sets, the scores avoid the blind spot of earlier WAXp-only attribution.
  • The scores connect feature attribution to adversarial robustness, offering a duality-based explanation for why a feature matters.

Reading between the lines

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

  • A natural testable extension is to benchmark the new scores against existing attribution methods on models where adversarial examples are known; one expects features ranked high by the scores to be exactly those whose removal shrinks the adversarial region the most.
  • Because Banzhaf and Shapley differ in how they weight coalitions, the two scores could disagree on which feature matters most; comparing their rankings may reveal which aggregation matches human notions of feature contribution.
  • The complexity bounds suggest that for large models exact computation may be prohibitive, so approximate computation of the scores, with error guarantees, is a likely next step the paper leaves implicit.
  • If the explanation–adversarial-example duality holds more broadly, the same characteristic function could be adapted to other robust-explanation notions, such as AXps or formal explanations for regression.
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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

3 major / 2 minor

Summary. The submission, arXiv:2508.11959, is represented by an abstract announcing two novel feature importance scores based on the Shapley value and the Banzhaf index, using a WAXp-based characteristic function that includes non-WAXp feature sets. The claimed scores are said to quantify how effectively each feature excludes adversarial examples, and the paper is said to identify properties and study computational complexity. The full text supplied with the submission is, however, E. Minguzzi's mathematical physics paper "The representation of spacetime through time functions" (arXiv:2508.11956), which is unrelated to explainable AI. None of the formal objects announced in the abstract—the characteristic function, the two scores, the stated properties, or the complexity results—appear in the supplied text. The abstract is therefore the only part of the submission that concerns the claimed contribution, and it asserts results without providing definitions, theorem statements, proofs, experiments, or datasets.

Significance. If the announced results were established, they would be a useful contribution to rigorous, logic-based feature attribution: extending WAXp-based importance by including non-WAXp sets is a sensible motivation, and formal Shapley/Banzhaf scores with stated properties and complexity bounds would be valuable for high-stakes XAI. However, the significance cannot be assessed from this record. There are no machine-checked proofs, reproducible code, parameter-free derivations, or falsifiable predictions to examine; the only full text is a different paper. Any judgment about novelty or correctness would be speculation. I therefore cannot credit the claimed contribution beyond the abstract's own assertion.

major comments (3)
  1. [Full Text / Abstract] The full text supplied is E. Minguzzi's "The representation of spacetime through time functions", not the announced cs.AI manuscript. The WAXp-based characteristic function, the Shapley/Banzhaf scores, the properties, and the complexity bounds asserted in the Abstract are completely absent. This mismatch is load-bearing: there is no technical content to verify, so the central claim is unsupported by the record.
  2. [Abstract] The Abstract states that the paper "leverages Shapley value and Banzhaf index" and "takes into account non-WAXp sets," but it does not define the characteristic function v(S) that is the input to these game-theoretic values. Without a definition of the payoff over feature subsets, the scores are undefined and none of their claimed properties can be checked.
  3. [Abstract] The Abstract claims "identifies properties and studies the computational complexity," but no theorem, proposition, proof, algorithm, or complexity-class statement is present. The asserted complexity results are therefore no more than claims.
minor comments (2)
  1. [Header] The arXiv number shown in the supplied full text is 2508.11956, not 2508.11959; if this is a packaging error, the correct manuscript must be submitted.
  2. [General] No datasets, experimental protocol, or code are mentioned. If the intended paper includes empirical evaluation, that material is also missing.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity assessable: supplied full text does not match the target paper

full rationale

The supplied full text is not the text of arXiv:2508.11959; it is E. Minguzzi's 'The representation of spacetime through time functions' (arXiv:2508.11956). The target paper's abstract promises Shapley/Banzhaf feature importance scores with a WAXp-based characteristic function, but none of the formal definitions, properties, or complexity claims appear in the record. Without the actual manuscript, I cannot identify any equation that is equivalent by construction to an input, any fitted parameter renamed as prediction, or any load-bearing self-citation that reduces to itself. The only notable finding is the document mismatch, which is a review-integrity issue, not a circularity. Under the hard rule requiring a quotable reduction, no circular step can be exhibited; the honest finding is therefore no significant circularity (0).

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

The abstract rests on two implicit premises: the WAXp-based formalization is faithful enough to serve as the characteristic function for feature contribution, and the explanation and adversarial-example duality transfers to the score definitions. No free parameters or invented entities are visible from the abstract. The full text required for a complete ledger is missing.

assumptions (2)
  • domain assumption WAXp (weak abductive explanation) sets, used as the characteristic function, faithfully capture the contribution of feature subsets to a model decision
    The abstract defines the new scores on top of WAXp-based feature contribution; if this formalization misrepresents practical importance, the scores inherit the error. Invoked in the abstract's description of the characteristic function.
  • domain assumption The duality between formal explanations (XPs) and adversarial examples (AExs) supports equating feature importance with effectiveness at excluding adversarial examples
    The abstract motivates non-WAXp sets by this relationship; the scores quantify how effective each feature is at excluding AExs. If the duality does not hold in the model class considered, the interpretation of the scores fails.

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Cite this review

Pith. "Pith review of Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index." pith.science (2026). https://pith.science/paper/GSWICKQ2

@misc{pith2026250811959,
  author       = {Pith},
  title        = {Pith review of: Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GSWICKQ2}},
  note         = {Machine review of arXiv:2508.11959}
}
read the original abstract

Feature attribution methods based on game theory are ubiquitous in the field of eXplainable Artificial Intelligence (XAI). Recent works proposed rigorous feature attribution using logic-based explanations, specifically targeting high-stakes uses of machine learning (ML) models. Typically, such works exploit weak abductive explanation (WAXp) as the characteristic function to assign importance to features. However, one possible downside is that the contribution of non-WAXp sets is neglected. In fact, non-WAXp sets can also convey important information, because of the relationship between formal explanations (XPs) and adversarial examples (AExs). Accordingly, this paper leverages Shapley value and Banzhaf index to devise two novel feature importance scores. We take into account non-WAXp sets when computing feature contribution, and the novel scores quantify how effective each feature is at excluding AExs. Furthermore, the paper identifies properties and studies the computational complexity of the proposed scores.

Discussion (0). Continue with ORCID to comment.

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