This study proposes Interaction Tensor SHAP (IT-SHAP), a tensor algebraic formulation of the Shapley Taylor Interaction Index (STII) that makes its computational structure explicit. STII extends the Shapley value to higher order interactions, but its exponential combinatorial definition makes direct computation intractable at scale. We reformulate STII as a linear transformation acting on a value function and derive an explicit algebraic representation of its weight tensor. This weight tensor is shown to possess a multilinear structure induced by discrete finite difference operators. When the value function admits a Tensor Train representation, higher order interaction indices can be computed in the parallel complexity class NC squared. In contrast, under general tensor network representations without structural assumptions, the same computation is proven to be P sharp hard. The main contributions are threefold. First, we establish an exact Tensor Train representation of the STII weight tensor. Second, we develop a parallelizable evaluation algorithm with explicit complexity bounds under the Tensor Train assumption. Third, we prove that computational intractability is unavoidable in the absence of such structure. These results demonstrate that the computational difficulty of higher order interaction analysis is determined by the underlying algebraic representation rather than by the interaction index itself, providing a theoretical foundation for scalable interpretation of high dimensional models.

翻译：本研究提出了交互张量SHAP（IT-SHAP），这是Shapley泰勒交互指数（STII）的张量代数表述，使其计算结构显式化。STII将Shapley值推广至高阶交互，但其指数级组合定义使得直接计算在大规模问题上难以处理。我们将STII重新表述为作用于价值函数的线性变换，并推导出其权重张量的显式代数表示。该权重张量被证明具有由离散有限差分算子诱导的多线性结构。当价值函数允许张量列车表示时，高阶交互指数可在并行复杂度类NC平方内计算。相比之下，在没有结构假设的一般张量网络表示下，同一计算被证明是P sharp困难的。主要贡献有三方面。首先，我们建立了STII权重张量的精确张量列车表示。其次，我们在张量列车假设下开发了具有显式复杂度界的可并行化评估算法。第三，我们证明了在缺乏此类结构时计算不可行性是不可避免的。这些结果表明，高阶交互分析的计算难度由底层代数表示决定，而非交互指数本身，从而为高维模型的可扩展解释提供了理论基础。