Interaction Tensor Shap
Hiroki Hasegawa, Yukihiko Okada
TL;DR
The paper tackles the computational intractability of exact high-order Shapley interactions (STII) in high-dimensional models by introducing IT-SHAP, a tensor-network framework that represents all interaction orders as contractions between a Value Tensor and a Weight Tensor. Under a Tensor Train (TT) representation, the MWCT weight structure and the value function can be encoded with polynomially bounded ranks, reducing STII’s exponential complexity to NC^2 parallel computability. IT-SHAP preserves the Shapley axioms and aligns with MST for first-order effects, providing a unified, axiomatic, and scalable approach to quantify main effects and higher-order interactions. The work highlights a principled pathway toward interaction-aware explainable AI for large black-box models, with explicit theoretical guarantees and a roadmap for practical TT-based implementations.
Abstract
Machine learning models have grown increasingly deep and high dimensional, making it difficult to understand how individual and combined features influence their predictions. While Shapley value based methods provide principled feature attributions, existing formulations cannot tractably evaluate higher order interactions: the Shapley Taylor Interaction Index (STII) requires exponential scale enumeration of subsets, and current tensor based approaches such as the Marginal SHAP Tensor (MST) are restricted to first order effects. The central problem is that no existing framework simultaneously preserves the axiomatic exactness of STII and avoids the exponential computational blow up inherent to high order discrete derivatives. Here we show that high order Shapley interactions can be represented exactly as tensor network contractions, enabling polynomial time and polylog depth computation under Tensor Train (TT) structure. We introduce Interaction Tensor SHAP (IT SHAP), which reformulates STII as the contraction of a Value Tensor and a Weight Tensor, and assume a finite state TT representation of the Weight Tensor with polynomial TT ranks. Under TT structured model and distribution tensors, we show that IT SHAP reduces the exponential complex Theta(4^n) of STII to NC2 parallel time. These results demonstrate that IT SHAP provides a unified, axiomatic, and computationally tractable formulation of main effects and higher order interactions in high dimensional models. This framework establishes a foundation for scalable interaction aware explainable AI, with implications for large black box models whose combinatorial structure has previously rendered interaction analysis infeasible.