# Fair feature attribution for multi-output prediction: a Shapley-based perspective

arXiv: https://arxiv.org/abs/2602.22882 · HTML: https://mlsanity.com/paper/2602.22882/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [Is Attention Interpretable?](https://mlsanity.com/paper/1906.03731/) (2019)
- [Top-down Neural Attention by Excitation Backprop](https://mlsanity.com/paper/1608.00507/) (2016)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [SHAP values through General Fourier Representations: Theory and Applications](https://mlsanity.com/paper/2511.00185/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Hierarchy of Entropy-Shapley Games for Multivariate Predictive Uncertainty](https://mlsanity.com/paper/2609.35217/) (2026)

## Abstract (arXiv)

In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the theoretical necessity of this practice has remained unclear. By extending the classical Shapley axioms to vector-valued cooperative games, we establish a rigidity theorem showing that any attribution rule satisfying efficiency, symmetry, dummy player, and additivity must necessarily decompose component-wise across outputs. Consequently, any joint-output attribution rule must relax at least one of the classical Shapley axioms. This result identifies a previously unformalized structural constraint in Shapley-based interpretability, clarifying the precise scope of fairness-consistent explanations in multi-output learning. Numerical experiments on a biomedical benchmark illustrate that multi-output models can yield computational savings in training and deployment, while producing SHAP explanations that remain fully consistent with the component-wise structure imposed by the Shapley axioms.