# Towards Attributions of Input Variables in a Coalition

arXiv: https://arxiv.org/abs/2309.13411 · HTML: https://mlsanity.com/paper/2309.13411/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 23 Sep 2023.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [Model Agnostic Supervised Local Explanations](https://mlsanity.com/paper/1807.02910/) (2018)
- [Detecting Statistical Interactions from Neural Network Weights](https://mlsanity.com/paper/1705.04977/) (2017)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Hierarchical interpretations for neural network predictions](https://mlsanity.com/paper/1806.05337/) (2018)
- [Accelerating Self-Play Learning in Go](https://mlsanity.com/paper/1902.10565/) (2019)
- [Discovering and Explaining the Representation Bottleneck of DNNs](https://mlsanity.com/paper/2111.06236/) (2021)
- [Joint Shapley values: a measure of joint feature importance](https://mlsanity.com/paper/2107.11357/) (2021)
- [Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs](https://mlsanity.com/paper/2304.13312/) (2023)
- [Can We Faithfully Represent Masked States to Compute Shapley Values on a DNN?](https://mlsanity.com/paper/2105.10719/) (2021)
- [Batch Normalization Is Blind to the First and Second Derivatives of the Loss](https://mlsanity.com/paper/2205.15146/) (2022)

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

- [Explaining How a Neural Network Play the Go Game and Let People Learn](https://mlsanity.com/paper/2310.09838/) (2023)

## Abstract (arXiv)

This paper focuses on the fundamental challenge of partitioning input variables in attribution methods for Explainable AI, particularly in Shapley value-based approaches. Previous methods always compute attributions given a predefined partition but lack theoretical guidance on how to form meaningful variable partitions. We identify that attribution conflicts arise when the attribution of a coalition differs from the sum of its individual variables' attributions. To address this, we analyze the numerical effects of AND-OR interactions in AI models and extend the Shapley value to a new attribution metric for variable coalitions. Our theoretical findings reveal that specific interactions cause attribution conflicts, and we propose three metrics to evaluate coalition faithfulness. Experiments on synthetic data, NLP, image classification, and the game of Go validate our approach, demonstrating consistency with human intuition and practical applicability.