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How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data
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Introduces a differentiable Constraint Layer that transforms linear-inequality background knowledge into guaranteed-compliant Constrained Deep Generative Models (C-DGMs) for tabular data, improving utility and detection and usable as an inference-time guardrail.
Problem
Deep generative models for tabular data often produce samples violating domain constraints expressed as linear inequalities, yielding unrealistic synthetic data.
Approach
A constraint layer built from a variable ordering and Fourier-Motzkin-style reduction of linear inequalities incrementally clips each feature to its computed lower/upper bounds given earlier features, guaranteeing compliance and being differentiable so it can be trained end-to-end inside any DGM.
Key results
- Standard DGMs violate constraints heavily (e.g., WGAN 100% CVR on LCLD; four of five DGMs exceed 95% CVR on WiDS), while all C-DGMs have 0% violation.
- C-DGMs improve utility and detection over their standard counterparts in nearly all cases, with up to 6.5% utility gain (F1) for C-GOGGLE over GOGGLE.
- Using the layer only at inference (P-DGMs) improves over standard models in 17 of 30 comparisons, and sample generation time overhead is negligible.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add Constraint Layer during training | WGAN · All datasets average | Utility F1: 0.463 -> 0.483 | Helped |
| Add Constraint Layer during training | TableGAN · All datasets average | Utility F1: 0.330 -> 0.375 | Helped |
| Add Constraint Layer during training | CTGAN · All datasets average | Utility F1: 0.517 -> 0.516 | Hurt |
| Add Constraint Layer during training | TVAE · All datasets average | Utility F1: 0.497 -> 0.507 | Helped |
| Add Constraint Layer during training | GOGGLE · All datasets average | Utility F1: 0.344 -> 0.409 | Helped |
| Add Constraint Layer | Standard tabular DGMs · URL, WiDS, LCLD, Heloc, FSP, News | Constraint violation rate: WGAN LCLD: 100.0$\pm$0.0 -> 0.0$\pm$0.0 | Helped |
| Add Constraint Layer as inference-time post-processing | WGAN · All datasets average | Utility F1: 0.463 -> 0.462 | Hurt |
| Add Constraint Layer as inference-time post-processing | TableGAN · All datasets average | Detection F1: 0.908 -> 0.901 | Helped |
Surprising findings
- Standard DGMs such as WGAN can produce 100% constraint-violating samples on some datasets.
- The constraint layer used only as an inference-time guardrail still yields some performance gains without retraining.
Limitations
- Only linear inequality constraints are supported; more expressive relations may require richer representations.
- Strict inequalities require an arbitrarily small epsilon, so optimality holds only in the limit in those cases.
- Gains from inference-time-only use are small compared with training-time integration.
Experimental setup
Datasets: URL WiDS LCLD Heloc FSP News
Benchmarks: URL WiDS LCLD Heloc FSP News
Metrics: constraints violation rate F1 weighted F1 AUROC explained variance mean absolute error sample generation time
Baselines: WGAN TableGAN CTGAN TVAE GOGGLE
Builds on: WGAN CTGAN TableGAN TVAE GOGGLE
Closest papers by meaning
- TabSDS: a Lightweight, Fully Non-Parametric, and Model Free Approach for Generating Synthetic Tabular Data (ICML 2025 · similarity 0.89)
- Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraints (ICLR 2025 · similarity 0.89)
- Debiasing Synthetic Data Generated by Deep Generative Models (NeurIPS 2024 · similarity 0.88)
- Tabular Foundation Model for Generative Modelling (NeurIPS 2026 · similarity 0.87)
- Synthetic Tabular Data Generation for Imbalanced Classification: The Surprising Effectiveness of an Overlap Class (AAAI 2025 · similarity 0.86)
- On the Stability of Iterative Retraining of Generative Models on their own Data (ICLR 2024 · similarity 0.86)
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