# Tractable Shapley Values and Interactions via Tensor Networks

arXiv: https://arxiv.org/abs/2510.22138 · HTML: https://mlsanity.com/paper/2510.22138/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 72 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [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)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [RKHS-SHAP: Shapley Values for Kernel Methods](https://mlsanity.com/paper/2110.09167/) (2021)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values](https://mlsanity.com/paper/2506.11849/) (2025)
- [ProxySPEX: Inference-Efficient Interpretability via Sparse Feature Interactions in LLMs](https://mlsanity.com/paper/2505.17495/) (2025)
- [SHAP values via sparse Fourier representation](https://mlsanity.com/paper/2410.06300/) (2024)
- [Exact Shapley Attributions in Quadratic-time for FANOVA Gaussian Processes](https://mlsanity.com/paper/2508.14499/) (2025)
- [Interaction Decompositions for Tensor Network Regression](https://mlsanity.com/paper/2208.06029/) (2022)
- [Tensor Product Neural Networks for Functional ANOVA Model](https://mlsanity.com/paper/2502.15215/) (2025)
- [SHAP-based Explanations are Sensitive to Feature Representation](https://mlsanity.com/paper/2505.08345/) (2025)
- [Informative Post-Hoc Explanations Only Exist for Simple Functions](https://mlsanity.com/paper/2508.11441/) (2025)
- [Algorithmic Bayesian Epistemology](https://mlsanity.com/paper/2403.07949/) (2024)

## Built on by (most cited first, 2 of 2)

- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)
- [TN-SHAP-G: Graph-Structured Tensor Network Surrogates for Shapley Values and Interactions](https://mlsanity.com/paper/2606.01540/) (2026)

## Abstract (arXiv)

We show how to replace the O(2^n) coalition enumeration over n features behind Shapley values and Shapley-style interaction indices with a few-evaluation scheme on a tensor-network (TN) surrogate: TN-SHAP. The key idea is to represent a predictor's local behavior as a factorized multilinear map, so that coalitional quantities become linear probes of a coefficient tensor. TN-SHAP replaces exhaustive coalition sweeps with just a small number of targeted evaluations to extract order-k Shapley interactions. In particular, both order-1 (single-feature) and order-2 (pairwise) computations have cost O(n*poly(chi) + n^2), where chi is the TN's maximal cut rank. We provide theoretical guarantees on the approximation error and tractability of TN-SHAP. On UCI datasets, our method matches enumeration on the fitted surrogate while reducing evaluation by orders of magnitude and achieves 25-1000x wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts.