Explain the Synth: Interpretable Evaluation of LLM Data Synthesis

Large language models (LLMs) are increasingly used to generate synthetic data, in which tabular data constitute a fundamental data modality across a wide range of domains. Yet, current evaluation practices often provide limited insights into whether the synthetic data preserve real data-generating relationships or introduce plausible-looking artifacts. We present a conceptually simple, interpretable auditing framework that compares the explanatory structure induced by real versus synthetic data. The key idea is to use a transparent rule-based model as a shared explanatory language: we extract rules from real data to summarize how features relate to labels, then examine how this rule structure changes when explained using LLM-generated data. Importantly, these rules are derived by an independent rule auditor rather than by the generator itself. The resulting "explanation shift" reveals which relationships are preserved, weakened, removed, or newly introduced by the generator, offering actionable diagnostics beyond aggregate fidelity scores. We further provide a theoretical perspective that links explanation shift and cross-domain predictive gaps to distribution mismatch within an interpretable hypothesis class. Overall, our approach turns synthetic data evaluation into a human-auditable comparison of explanations, improving transparency for LLM-based tabular synthesis.