# Refutation of Shapley Values for XAI -- Additional Evidence

arXiv: https://arxiv.org/abs/2310.00416 · HTML: https://mlsanity.com/paper/2310.00416/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 47 references that are in the map.
- First posted on arXiv 30 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [On Tackling Explanation Redundancy in Decision Trees](https://mlsanity.com/paper/2205.09971/) (2022)
- [Minimal Adversarial Examples for Deep Learning on 3D Point Clouds](https://mlsanity.com/paper/2008.12066/) (2020)
- [On Efficiently Explaining Graph-Based Classifiers](https://mlsanity.com/paper/2106.01350/) (2021)
- [Adversarial Example Defenses: Ensembles of Weak Defenses are not Strong](https://mlsanity.com/paper/1706.04701/) (2017)
- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Feature Necessity & Relevancy in ML Classifier Explanations](https://mlsanity.com/paper/2210.15675/) (2022)
- [Explainability is NOT a Game](https://mlsanity.com/paper/2307.07514/) (2023)
- [From Robustness to Explainability and Back Again](https://mlsanity.com/paper/2306.03048/) (2023)
- [Disproving XAI Myths with Formal Methods -- Initial Results](https://mlsanity.com/paper/2306.01744/) (2023)
- [A Refutation of Shapley Values for Explainability](https://mlsanity.com/paper/2309.03041/) (2023)

## Built on by (most cited first, 4 of 4)

- [From SHAP Scores to Feature Importance Scores](https://mlsanity.com/paper/2405.11766/) (2024)
- [Logic-Based Explainability: Past, Present & Future](https://mlsanity.com/paper/2406.11873/) (2024)
- [Binary Spiking Neural Networks as Causal Models](https://mlsanity.com/paper/2604.27007/) (2026)
- [Towards Rigorous Explainability by Feature Attribution](https://mlsanity.com/paper/2604.15898/) (2026)

## Abstract (arXiv)

Recent work demonstrated the inadequacy of Shapley values for explainable artificial intelligence (XAI). Although to disprove a theory a single counterexample suffices, a possible criticism of earlier work is that the focus was solely on Boolean classifiers. To address such possible criticism, this paper demonstrates the inadequacy of Shapley values for families of classifiers where features are not boolean, but also for families of classifiers for which multiple classes can be picked. Furthermore, the paper shows that the features changed in any minimal l0 distance adversarial examples do not include irrelevant features, thus offering further arguments regarding the inadequacy of Shapley values for XAI.