Title: Efficient Shapley Values and Interactions Using Tensor Networks

Abstract: This study demonstrates how to substitute the computationally intensive O(2^n) coalition enumeration, traditionally required for calculating Shapley values and Shapley-style interaction indices across n features, with a highly efficient, few-evaluation approach utilizing a tensor-network (TN) surrogate, termed TN-SHAP. The core concept involves modeling the local behavior of a predictor as a factorized multilinear map, thereby transforming coalitional metrics into linear probes of a coefficient tensor. By leveraging this structure, TN-SHAP eliminates the need for exhaustive coalition sweeps, requiring only a limited number of targeted evaluations to derive order-k Shapley interactions. Specifically, the computational cost for both order-1 (single-feature) and order-2 (pairwise) analyses is reduced to O(n*poly(chi) + n^2), with chi denoting the maximum cut rank of the tensor network. We establish theoretical assurances regarding the tractability and approximation error bounds of TN-SHAP. Experimental results on UCI datasets indicate that TN-SHAP achieves accuracy levels comparable to KernelSHAP-IQ while delivering wall-clock speedups ranging from 25x to 1000x. This efficiency is realized by significantly lowering the number of required evaluations—by orders of magnitude—and by amortizing training costs across local cohorts, all while maintaining fidelity to the fitted surrogate.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC