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

arXiv: https://arxiv.org/abs/2606.08736 · HTML: https://mlsanity.com/paper/2606.08736/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [TabSynDex: A Universal Metric for Robust Evaluation of Synthetic Tabular Data](https://mlsanity.com/paper/2207.05295/) (2022)
- [SynthEval: A Framework for Detailed Utility and Privacy Evaluation of Tabular Synthetic Data](https://mlsanity.com/paper/2404.15821/) (2024)
- [The DCR Delusion: Measuring the Privacy Risk of Synthetic Data](https://mlsanity.com/paper/2505.01524/) (2025)
- [LLM-TabLogic: Preserving Inter-Column Logical Relationships in Synthetic Tabular Data via Prompt-Guided Latent Diffusion](https://mlsanity.com/paper/2503.02161/) (2025)
- [Benchmarking Synthetic Tabular Data: A Multi-Dimensional Evaluation Framework](https://mlsanity.com/paper/2504.01908/) (2025)
- [RelDiff: Relational Data Generative Modeling with Graph-Based Diffusion Models](https://mlsanity.com/paper/2506.00710/) (2025)
- [IRG: Modular Synthetic Relational Database Generation with Complex Relational Schemas](https://mlsanity.com/paper/2312.15187/) (2023)
- [Sequentially Constrained Monte Carlo](https://mlsanity.com/paper/1410.8209/) (2014)
- [Hierarchical Conditional Tabular GAN for Multi-Tabular Synthetic Data Generation](https://mlsanity.com/paper/2411.07009/) (2024)
- [Self-Reinforcing Controllable Synthesis of Rare Relational Data via Bayesian Calibration](https://mlsanity.com/paper/2604.16817/) (2026)

## Abstract (arXiv)

We study a capability the dominant paradigm in synthetic tabular data does not provide: exact satisfaction of a declared analytical outcome with no source data. Imitation methods (copulas, GANs, diffusion) learn a real distribution and sample from it, and are judged on fidelity to real data. A large, practical class of needs is different: generating data with no source data ("cold start") that reproduces a declared outcome (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. 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. We name this task outcome-conformant synthesis, argue its evaluation axis is conformance rather than fidelity, and show the two axes are orthogonal. We contribute: (1) a formal account showing 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 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, the rest being shape-family mismatch; (2) SpecBench, to our knowledge the first benchmark to measure conformance to analytical outcomes for cold-start relational synthesis; and (3) a closed-form, deterministic reference system. Exact aggregation alone is trivial; the contribution is conformance jointly with closed-form marginals, integrity, determinism, and zero source data. We concede fidelity to imitation where real data exists.