The Faithful Shapley Interaction (FSI) index uniquely satisfies the faithfulness axiom among Shapley interaction indices, but computing FSI requires $O(d^\ell \cdot 2^d)$ time and existing implementations use $O(4^d)$ memory. We present TT-FSI, which exploits FSI's algebraic structure via Matrix Product Operators (MPO). Our main theoretical contribution is proving that the linear operator $v \mapsto \text{FSI}(v)$ admits an MPO representation with TT-rank $O(\ell d)$, enabling an efficient sweep algorithm with $O(\ell^2 d^3 \cdot 2^d)$ time and $O(\ell d^2)$ core storage an exponential improvement over existing methods. Experiments on six datasets ($d=8$ to $d=20$) demonstrate up to 280$\times$ speedup over baseline, 85$\times$ over SHAP-IQ, and 290$\times$ memory reduction. TT-FSI scales to $d=20$ (1M coalitions) where all competing methods fail.

翻译：忠实沙普利交互作用（FSI）指数在沙普利交互作用指数中唯一满足忠实性公理，但其计算需要$O(d^\ell \cdot 2^d)$时间，且现有实现需占用$O(4^d)$内存。本文提出TT-FSI方法，通过矩阵乘积算子（MPO）利用FSI的代数结构。我们的主要理论贡献是证明了线性算子$v \mapsto \text{FSI}(v)$具有TT秩为$O(\ell d)$的MPO表示，从而实现了$O(\ell^2 d^3 \cdot 2^d)$时间和$O(\ell d^2)$核心存储的扫描算法，相比现有方法实现指数级改进。在六个数据集（$d=8$至$d=20$）上的实验表明，相比基线方法获得最高280倍的加速，相比SHAP-IQ获得85倍加速，内存占用降低290倍。TT-FSI可扩展至$d=20$（100万个联盟）的规模，而所有竞争方法在此规模下均失效。