Declarative Outcome-Conformant Synthesis: Exact, Closed-Form Specification Satisfaction and a Conformance Benchmark

A formal account and benchmark for cold-start relational synthesis that exactly satisfies declared analytical outcomes, orthogonal to fidelity.

Muhammed Rasin· 2026· DOI 10.48550/arXiv.2606.08736

The core problem

Synthetic tabular data generation has been dominated by imitation methods—copulas, GANs, and diffusion models—that learn a real distribution and sample from it, evaluated on fidelity to real data. However, a large class of practical needs is fundamentally different: generating data with **no source data** ("cold start") that reproduces a **declared analytical outcome** (e.g., a revenue curve, a churn rate, a group share) across a relational schema. Off-the-shelf imitation tools offer no interface for such targets, and no sampler can hit an exact aggregate because sampling has variance. The paper names this task **outcome-conformant synthesis**, argues its evaluation axis is **conformance** rather than fidelity, and shows the two axes are orthogonal. On a real public dataset, off-the-shelf learned synthesizers trained on that very data miss the declared monthly aggregate by 74 to 86 percent; a per-period steelman cuts the miss to about 19 percent and still cannot reach 0; a closed-form generator reaches exactly 0.

The empirical evaluation on a real public dataset demonstrates the stark contrast between imitation and conformance. Off-the-shelf learned synthesizers trained on the very data they are meant to imitate miss the declared monthly aggregate by **74 to 86 percent**. A per-period steelman approach reduces the miss to about **19 percent** but still cannot achieve exactness. In contrast, the closed-form generator achieves **exactly 0** miss. The controlled experiment further quantifies the cost of enforcing the exact aggregate: at most **0.006 in 1-Wasserstein distance** to an arbitrary external marginal, with the remaining discrepancy attributed to shape-family mismatch. This shows that exact aggregation is achievable with minimal distortion to the marginal distribution, and that the primary challenge is not aggregation but conformance jointly with other desiderata.

Synthetic tabular data generation has been dominated by imitation methods—copulas, GANs, and diffusion models—that learn a real distribution and sample from it, evaluated on fidelity to real data. However, a large class of practical needs is fundamentally different: generating data with **no source data** ("cold start") that reproduces a **declared analytical outcome** (e.g., a revenue curve, a churn rate, a group share) across a relational schema. Off-the-shelf imitation tools offer no interface for such targets, and no sampler can hit an exact aggregate because sampling has variance. The paper names this task **outcome-conformant synthesis**, argues its evaluation axis is **conformance** rather than fidelity, and shows the two axes are orthogonal. On a real public dataset, off-the-shelf learned synthesizers trained on that very data miss the declared monthly aggregate by 74 to 86 percent; a per-period steelman cuts the miss to about 19 percent and still cannot reach 0; a closed-form generator reaches exactly 0.

The paper provides a formal account showing that a widely-used family of exact-aggregate generators is exactly **conditional-sum sampling of a Gamma population** (via Lukacs' characterization), with closed-form exactness, a closed-form marginal coefficient of variation (CV), and scale-invariance. A controlled experiment maps the boundary: enforcing the exact aggregate costs at most 0.006 in 1-Wasserstein distance to an arbitrary external marginal, with the rest being shape-family mismatch. The authors contribute:

The paper argues that conformance and fidelity are **orthogonal axes**. Fidelity measures how closely synthetic data resembles real data, while conformance measures how exactly synthetic data satisfies declared analytical outcomes. Imitation methods excel at fidelity but fail at conformance, especially in cold-start scenarios where no real data exists. The proposed closed-form approach achieves exact conformance, closed-form marginals, integrity, determinism, and zero source data—properties that are essential for applications such as scenario planning, privacy-preserving data sharing, and testing analytical pipelines. The authors concede that when real data exists, fidelity to imitation may be preferable. However, for cold-start settings, outcome-conformant synthesis fills a critical gap. The introduction of **SpecBench** provides a standardized way to measure conformance, enabling future research. The formal characterization via Lukacs' theorem offers theoretical grounding, and the scale-invariance property ensures robustness across different scales. The 1-Wasserstein distance bound of 0.006 indicates that the cost of exact aggregation is negligible, making the approach practical. Overall, the work shifts the paradigm from imitation to specification satisfaction, with broad implications for synthetic data generation.

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