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arxiv: 2604.15898 · v1 · submitted 2026-04-17 · 💻 cs.AI

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Towards Rigorous Explainability by Feature Attribution

Olivier L\'etoff\'e , Xuanxiang Huang , Joao Marques-Silva
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Pith reviewed 2026-05-10 09:12 UTC · model grok-4.3

classification 💻 cs.AI
keywords explainable AIfeature attributionShapley valuessymbolic methodsXAIrigorous explanationsmachine learning interpretability
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The pith

Symbolic methods can provide rigorous feature importance assignments in explainable AI unlike non-symbolic approaches such as Shapley values

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

The paper argues that non-symbolic methods have served as the default option for explaining complex machine learning models for about a decade, yet they lack rigor and can mislead human decision-makers, a problem that is especially acute in high-stakes applications. It identifies the use of Shapley values in tools such as SHAP as a clear case of provable lack of rigor. The work surveys ongoing efforts to develop and apply rigorous symbolic methods as a concrete alternative for assigning relative feature importance.

Core claim

Non-symbolic methods such as Shapley values lack rigor and can mislead, while symbolic methods provide rigorous alternatives for feature importance assignment.

What carries the argument

Rigorous symbolic methods of XAI for assigning relative feature importance

If this is right

  • High-stakes ML applications would gain explanations that carry formal guarantees rather than approximations.
  • Decision-makers could act on feature importance scores with reduced risk of being misled.
  • Development of symbolic XAI tools would replace current non-rigorous practices in domains requiring accountability.

Where Pith is reading between the lines

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

  • Symbolic methods could be paired with formal verification to strengthen overall AI safety pipelines.
  • Hybrid systems might address scalability limits and allow symbolic rigor on larger models.
  • Regulatory requirements for AI explainability could shift toward demanding provable rather than heuristic attributions.

Load-bearing premise

That symbolic methods can be made practical and scalable for the complex, high-dimensional models used in real-world machine learning.

What would settle it

A concrete case in a high-stakes domain where a symbolic feature attribution method yields an incorrect or incomplete assignment, or where a non-symbolic method such as SHAP produces explanations that never mislead users.

Figures

Figures reproduced from arXiv: 2604.15898 by Joao Marques-Silva, Olivier L\'etoff\'e, Xuanxiang Huang.

Figure 1
Figure 1. Figure 1: Classification model M1 represented as a decision tree. row # x1 x2 π2(x) 1 0 0 −1/2 2 0 1 3/2 3 1 0 1 4 1 1 1 (a) Tabular representation x1 x2 −1/2 3/2 1 ∈ {0} ∈ {0} ∈ {1} ∈ {1} 1 2 4 5 3 (b) Regression tree (RT) S rows(S) υe(S) ∅ 1, 2, 3, 4 3/4 {1} 3, 4 1 {2} 2, 4 5/4 {1, 2} 4 1 (c) Expected values [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Regression model M2 represented as a regression tree. An explanation problem is a tuple E = (M, I), where M can either be a classification or a regression model, and I = (v, p) is a given instance, with v ∈ F. (Observe that p = π(v), with p ∈ V.) Running examples [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Computation of SHAP scores for E1. i = 1 S υe(S) υe(S ∪ {1}) ∆1(S) ς(S) ς(S) × ∆1(S) ∅ 3/4 1 1/4 1/2 1/8 {2} 5/4 1 −1/4 1/2 −1/8 Sve(1) = 0 i = 2 S υe(S) υe(S ∪ {2}) ∆2(S) ς(S) ς(S) × ∆2(S) ∅ 3/4 5/4 1/2 1/2 1/4 {1} 1 1 0 1/2 0 Sve(2) = 0.25 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Computation of SHAP scores for E2. no observable difference exists between the ML model’s output for x and v. 6 For regression problems, we write instead σ as the instantiation of a template 6 Throughout the paper, parameterization are shown after the separator ’;’, and will be elided when clear from the context [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Example of regression model that is Lipschitz continuous. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
read the original abstract

For around a decade, non-symbolic methods have been the option of choice when explaining complex machine learning (ML) models. Unfortunately, such methods lack rigor and can mislead human decision-makers. In high-stakes uses of ML, the lack of rigor is especially problematic. One prime example of provable lack of rigor is the adoption of Shapley values in explainable artificial intelligence (XAI), with the tool SHAP being a ubiquitous example. This paper overviews the ongoing efforts towards using rigorous symbolic methods of XAI as an alternative to non-rigorous non-symbolic approaches, concretely for assigning relative feature importance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper claims that non-symbolic feature attribution methods such as Shapley values and the SHAP tool lack rigor and can mislead human decision-makers, especially in high-stakes ML applications. It positions rigorous symbolic methods as preferable alternatives and overviews ongoing efforts to apply them for assigning relative feature importance.

Significance. If the overview accurately catalogs viable symbolic techniques and their advantages, the paper could help redirect XAI research toward more trustworthy methods. As a survey without new derivations, proofs, or experiments, its significance rests on synthesis quality and whether it substantiates the practicality of symbolic approaches for real-world models.

major comments (1)
  1. Abstract and introduction: The central positioning of symbolic methods as practical alternatives to non-symbolic ones (e.g., SHAP) for complex ML models is load-bearing, yet the manuscript provides no concrete scaling arguments, complexity bounds, or references to benchmarks demonstrating that cited symbolic techniques avoid exponential blow-up in high-dimensional settings. This leaves the 'alternative' claim unsubstantiated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our survey. We address the single major comment below and will revise the manuscript to strengthen the relevant sections.

read point-by-point responses

  1. Referee: Abstract and introduction: The central positioning of symbolic methods as practical alternatives to non-symbolic ones (e.g., SHAP) for complex ML models is load-bearing, yet the manuscript provides no concrete scaling arguments, complexity bounds, or references to benchmarks demonstrating that cited symbolic techniques avoid exponential blow-up in high-dimensional settings. This leaves the 'alternative' claim unsubstantiated.

    Authors: We agree that the survey would benefit from more explicit discussion of practicality and scalability. As an overview paper, the manuscript synthesizes existing literature rather than deriving new bounds; however, the referee is correct that the current text does not sufficiently reference or summarize complexity results or benchmarks for the cited symbolic techniques. In revision we will expand the introduction and add a dedicated subsection on computational considerations. This will include citations to relevant analyses of symbolic feature attribution methods (e.g., work on decision diagrams and satisfiability-based approaches that demonstrate polynomial scaling under restricted model classes or via approximations) and note both successful high-dimensional applications and remaining limitations regarding exponential blow-up. The revised text will also qualify the 'alternative' claim to distinguish rigor advantages from universal practicality. revision: yes

Circularity Check

0 steps flagged

No circularity: survey paper with no derivations or self-referential reductions

full rationale

The paper is an overview surveying symbolic XAI methods as rigorous alternatives to non-symbolic approaches like Shapley values/SHAP. It contains no equations, fitted parameters, predictions, or derivation chains that could reduce to the paper's own inputs by construction. Claims rest on external references rather than internal self-definition, fitted-input renaming, or load-bearing self-citations. This matches the default expectation for non-circular survey papers.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a survey paper. No free parameters, axioms, or invented entities are introduced because no new technical claims or derivations are made.

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