# Feature Synergy, Redundancy, and Independence in Global Model Explanations using SHAP Vector Decomposition

arXiv: https://arxiv.org/abs/2107.12436 · HTML: https://mlsanity.com/paper/2107.12436/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 11 of 11)

- [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)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Explainable AI for Trees: From Local Explanations to Global Understanding](https://mlsanity.com/paper/1905.04610/) (2019)
- [Generating Counterfactual and Contrastive Explanations using SHAP](https://mlsanity.com/paper/1906.09293/) (2019)
- [Hodge decomposition and the Shapley value of a cooperative game](https://mlsanity.com/paper/1709.08318/) (2017)

## Built on by (most cited first, 9 of 9)

- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications](https://mlsanity.com/paper/2306.04539/) (2023)
- [MMoE: Enhancing Multimodal Models with Mixtures of Multimodal Interaction Experts](https://mlsanity.com/paper/2311.09580/) (2023)
- [Unifying local and global model explanations by functional decomposition of low dimensional structures](https://mlsanity.com/paper/2208.06151/) (2022)
- [Measuring Cross-Modal Interactions in Multimodal Models](https://mlsanity.com/paper/2412.15828/) (2024)
- [Massively Multimodal Foundation Models: A Framework for Capturing Interactions with Specialized Mixture-of-Experts](https://mlsanity.com/paper/2509.25678/) (2025)
- [Foundations of Multisensory Artificial Intelligence](https://mlsanity.com/paper/2404.18976/) (2024)
- ["Mm, Wat?" Detecting Other-initiated Repair Requests in Dialogue](https://mlsanity.com/paper/2510.24628/) (2025)
- [A Vision for Multisensory Intelligence: Sensing, Science, and Synergy](https://mlsanity.com/paper/2601.04563/) (2026)

## Abstract (arXiv)

We offer a new formalism for global explanations of pairwise feature dependencies and interactions in supervised models. Building upon SHAP values and SHAP interaction values, our approach decomposes feature contributions into synergistic, redundant and independent components (S-R-I decomposition of SHAP vectors). We propose a geometric interpretation of the components and formally prove its basic properties. Finally, we demonstrate the utility of synergy, redundancy and independence by applying them to a constructed data set and model.