SHAP Distance: An Explainability-Aware Metric for Evaluating the Semantic Fidelity of Synthetic Tabular Data

Synthetic tabular data, which are widely used in domains such as healthcare, enterprise operations, and customer analytics, are increasingly evaluated to ensure that they preserve both privacy and utility. While existing evaluation practices typically focus on distributional similarity (e.g., the Kullback-Leibler divergence) or predictive performance (e.g., Train-on-Synthetic-Test-on-Real (TSTR) accuracy), these approaches fail to assess semantic fidelity, that is, whether models trained on synthetic data follow reasoning patterns consistent with those trained on real data. To address this gap, we introduce the SHapley Additive exPlanations (SHAP) Distance, a novel explainability-aware metric that is defined as the cosine distance between the global SHAP attribution vectors derived from classifiers trained on real versus synthetic datasets. By analyzing datasets that span clinical health records with physiological features, enterprise invoice transactions with heterogeneous scales, and telecom churn logs with mixed categorical-numerical attributes, we demonstrate that the SHAP Distance reliably identifies semantic discrepancies that are overlooked by standard statistical and predictive measures. In particular, our results show that the SHAP Distance captures feature importance shifts and underrepresented tail effects that the Kullback-Leibler divergence and Train-on-Synthetic-Test-on-Real accuracy fail to detect. This study positions the SHAP Distance as a practical and discriminative tool for auditing the semantic fidelity of synthetic tabular data, and offers practical guidelines for integrating attribution-based evaluation into future benchmarking pipelines.