OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators

A new method called OperatorSHAP promises to make Shapley value explanations practical for neural operators, a class of models used in safety-critical physical applications where data often arrives on irregular grids [1]. The technique, detailed in a preprint submitted to arXiv on June 26, 2026, addresses a long-standing bottleneck. Shapley values are prized as an attribution method because they satisfy many desirable theoretical properties, but their computational cost during inference has limited their real-world deployment [1]. Current amortized explainers, such as FastSHAP, can speed up this process but are restricted to homogeneous inputs, a significant limitation for physical applications involving irregular geometries [1]. OperatorSHAP is a grid-agnostic training procedure that enables FastSHAP-like explainers to work with neural operators. The researchers establish a theoretical framework for attributions in function space, drawing a connection to Aumann-Shapley values [1]. The paper further demonstrates that OperatorSHAP's explanations remain consistent with state-of-the-art discrete Shapley values across different resolutions and can transfer across grid sizes without retraining [1]. The work appears on arXiv, an open-access repository of electronic preprints that, as of late 2024, receives about 24,000 submissions per month and has surpassed two million total articles [6]. The platform is not peer-reviewed, and papers are posted after moderation [6]. The repository also hosts a framework called arXivLabs, which allows community collaborators to develop and share experimental tools on the site, such as bibliographic explorers and code finders, under guidelines that emphasize openness and user data privacy [5]. The need for interpretable models in physical domains is acute. The authors note that outputs from these systems often inform safety-critical decisions, including structural load assessment, weather warnings, and clinical diagnosis [1]. By making Shapley value estimation both fast and accurate for neural operators, OperatorSHAP targets a gap where the cost of explanation has previously hindered adoption.