TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Train

2026-01-05

arXiv.org

AI Summary

This work addresses the scalability limitations of the Faithful Shapley Interaction (FSI) index, which suffers from exponential computational and memory costs in high-dimensional settings. We reveal for the first time that the FSI linear operator admits a low-rank matrix product operator (MPO) structure with a Tensor-Train rank of only O(ℓd). Leveraging this insight, we design an efficient sweeping algorithm that achieves exponential reductions in both time and space complexity. Empirical evaluations across six datasets with coalition sizes ranging from d=8 to d=20 demonstrate up to 280× speedup and 290× memory reduction compared to baseline methods, and an 85× improvement over SHAP-IQ. Our approach successfully scales FSI to coalitions of up to one million players (d=20), marking a significant advance in practical applicability.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Shapley interaction
• computational complexity
• memory efficiency
• high-dimensional scalability
• Faithful Shapley Interaction

Innovation

• Tensor-Train
• Shapley Interaction
• Matrix Product Operator
• Scalable Attribution
• Faithful Axiom