arXiv:2512.05338cs.LGcs.AI2025-12被引 1

提出可高效计算高阶交互作用的张量方法,让复杂模型解释变得可行。

Interaction Tensor SHAP

  • 用张量代数重构高阶交互指数,显式表达权重结构。
  • 在张量列车假设下,计算复杂度降至NC²,实现并行化加速。
  • 揭示无结构时计算本质困难,为可扩展解释提供理论依据。

本文提出交互张量SHAP(IT-SHAP),一种将谢帕利泰勒交互指数(STII)形式化为张量代数的方法,使计算结构清晰可见。STII将谢帕利值推广至高阶交互,但其指数级组合定义导致大规模计算不可行。我们将STII重构成作用于值函数的线性变换,并推导出其权重张量的显式代数表达式。该权重张量表现出由离散有限差分算子诱导的多重线性结构。当值函数具有张量列车(Tensor Train)表示时,高阶交互指数可在并行复杂度类NC²内计算;而在无结构性假设的通用张量网络表示下,同一计算被证明为P#-hard。主要贡献有三:第一,建立STII权重张量的精确张量列车表示;第二,在张量列车假设下开发可并行评估的算法,并给出明确复杂度界;第三,证明无结构性假设时计算不可行性不可避免。这些结果表明,高阶交互分析的计算难度取决于底层代数表示,而非交互指数本身,为高维模型的可扩展解释提供了理论基础。

原文摘要 · Abstract (English)

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.

模型解释张量计算交互分析

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