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

Background

Shapley additive explanations (SHAP) are a theoretically sound method for feature attribution in machine learning, quantifying each feature's contribution to a model's prediction. However, computing exact SHAP values for neural networks is considered computationally intractable due to the exponential search space over input features. This intractability forces practitioners to rely on various approximation methods, the accuracy of which is difficult to validate on large-scale problems. Existing exact methods are limited to tiny search spaces (e.g., ≤20 features), severely restricting their practical utility.

Key Points

• The core innovation is using neural network verification techniques—traditionally used to prove robustness properties—to compute exact lower and upper bounds on SHAP values.
• The algorithm does not enumerate all possible feature subsets (the exponential search space). Instead, it formulates the SHAP value calculation as an optimization problem and applies verification tools to find arbitrarily tight bounds. In the limit, these bounds converge to the exact SHAP value.
• Scalability is dramatically improved. The method scales to "orders of magnitude larger search spaces" (e.g., 50+ features) than state-of-the-art exact approaches, moving the boundary of exact computation significantly.
• The work provides a "principled cornerstone". By establishing a feasible method for exact computation at a larger scale, it creates an essential ground-truth benchmark. This allows for a rigorous, empirical evaluation of the accuracy of numerous SHAP approximation methods (like KernelSHAP or FastSHAP) that were previously untestable on problems of this size.

Significance

This research is a first step toward practical exact SHAP computation for non-trivial neural networks. Its primary significance is not that it replaces approximations overnight (exact computation remains more expensive), but that it enables rigorous validation. For the first time, researchers can systematically measure how approximation errors behave as the search space grows, guiding the development of better, more reliable approximations. By bridging the gap between exact methods and larger models, it strengthens the foundation of explainable AI (XAI), moving the field from relying on theoretical assumptions about approximations toward empirically verifiable explanations.