Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks

2026-05-22

AI Summary

Accurately computing SHAP values for neural networks has long been considered intractable due to the exponential growth of feature coalitions. This work introduces, for the first time, formal verification techniques from neural network analysis into SHAP value computation, proposing an algorithm that yields provably tight upper and lower bounds. By leveraging efficient pruning strategies, the method substantially expands the tractable search space. Compared to existing exact approaches, it handles problems orders of magnitude larger and successfully recovers exact SHAP values across multiple tasks, thereby establishing a reliable benchmark for evaluating approximate methods.

Abstract

Shapley additive explanations (SHAP) are widely recognised as computationally intractable for neural networks, since they induce an exponential search space over the input features. In this work, we take a first step towards scaling exact SHAP computation to larger search spaces by introducing an algorithm that leverages recent advances in neural network verification to compute arbitrarily tight exact lower and upper bounds on SHAP values for neural networks, ultimately recovering the exact SHAP values. We demonstrate that our approach scales to orders of magnitude larger search spaces than state-of-the-art exact methods. This provides an important first step towards exact SHAP computation and establishes a principled cornerstone for evaluating statistical approximation methods on larger search spaces.

Problem

• SHAP
• Shapley values
• neural networks
• computational intractability
• exact computation

Innovation

• Exact SHAP
• Neural Network Verification
• Provable Bounds
• Scalable Explanation
• Shapley Values