# Aumann-SHAP: The Geometry of Counterfactual Interaction Explanations in Machine Learning

arXiv: https://arxiv.org/abs/2603.14014 · HTML: https://mlsanity.com/paper/2603.14014/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)

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

- [GRALIS: Fusing Coalition and Gradient Attribution with Closed-Form Conservation Error and Finite-Sample Guarantees](https://mlsanity.com/paper/2605.05480/) (2026)

## Abstract (arXiv)

We introduce Aumann-SHAP, an interaction-aware framework that decomposes counterfactual transitions by restricting the model to a local hypercube connecting baseline and counterfactual features. Each hypercube is discretized into a grid to construct an induced micro-player cooperative game in which elementary grid-step moves become players. Shapley and LES values on this TU-micro-game yield geometry-aware within-pot attributions that converge to the diagonal Aumann--Shapley / Integrated Gradients limit under grid refinement, and recover equal-split Shapley as the degenerate m=1 special case. An exact grid-state closed form gives polynomial-time computation for fixed interaction order. On a synthetic benchmark with known ground truth, equal-split Shapley carries an irreducible bias while Aumann-SHAP converges to the correct decomposition. On German Credit, interaction geometry changes feature priority rankings in 12.3% of instances. On UCI Heart Disease, equal-split misattributes a cholesterol suppressor as a positive contributor, which is a sign error Aumann-SHAP corrects. On MNIST, game-theoretic attribution reaches target confidence with 3.5× fewer edits than magnitude-based ordering, with micro-game Shapley achieving the best efficiency across all budgets.