Constraint-Aware Synthetic Tabular Data Generation via Inter-Column Constraint Discovery with LLM Agents

Jianxing Zhao; Mao Guan; Dongyu Liu

cs.AIAug 15, 2026

Constraint-Aware Synthetic Tabular Data Generation via Inter-Column Constraint Discovery with LLM Agents

Authors: Jianxing Zhao, Mao Guan, Dongyu Liu

Organizations: University of California, Davis · independent researcher

Abstract

Generating structurally valid synthetic tabular data remains difficult: outputs with high statistical fidelity and downstream utility can still violate semantically meaningful domain constraints. We study the discovery and enforcement of three complementary inter-column constraint families---equations, linear inequalities, and logical dependencies. Our unified tool-grounded workflow represents all three as machine-executable hypotheses and applies a common interface for full-table validation, deterministic diagnosis, and counterexample-guided revision. A generator-agnostic postprocessor coordinates family-specific repairs on outputs from unchanged tabular generators. Across curated behavioral audits and end-to-end evaluations, the complete workflow improves held-out violation detection over one-shot direct prompting, while postprocessing yields zero measured violations for every retained, applicable constraint, improves downstream utility on most datasets, and largely preserves univariate marginals.

Figures & tables

Figure 1: Overview of the LLM-guided constraint discovery workflow.

Type	Model	Method	Acc.	Prec.	Rec.
Linear	GPT-5.6	Baseline	.842 (.016)	.741 (.032)	.684 (.032)
	GPT-5.6	Ours	.917 (.096)	.911 (.181)	.833 (.193)
	Claude-5	Baseline	.815 (.033)	.729 (.089)	.633 (.067)
	Claude-5	Ours	.959 (.016)	.975 (.031)	.919 (.032)
Equational	GPT-5.6	Baseline	.975 (.037)	.950 (.075)	.950 (.075)
	GPT-5.6	Ours	1.000 (.000)	1.000 (.000)	1.000 (.000)

Table 1: Held-out behavioral violation-detection results over five discovery–audit splits (mean and standard deviation). The audit tasks are constructed from 17 inequalities, 12 equations, and 13 logical dependencies.

Metric		flights	heloc	nba	news	steel	taxi	url
Constraint # (LD/Eq/Lin)		3/7/2–5	1/0/11–13	0/10–12/3–11	7–16/4/0–17	1/2/11–25	2/2/0	2/0/17–29
LD	CVR (%) $\downarrow$	65.9 $\rightarrow$ 0	4.0 $\rightarrow$ 0	–	20.2 $\rightarrow$ 0	11.7 $\rightarrow$ 0	12.2 $\rightarrow$ 0	2.2 $\rightarrow$ 0
LD	sCVC (%) $\downarrow$	40.0 $\rightarrow$ 0	4.0 $\rightarrow$ 0	–	2.2 $\rightarrow$ 0	11.7 $\rightarrow$ 0	6.3 $\rightarrow$ 0	1.1 $\rightarrow$ 0
Eq.	CVR (%) $\downarrow$	100.0 $\rightarrow$ 0	–	99.9 $\rightarrow$ 0	100.0 $\rightarrow$ 0	98.2 $\rightarrow$ 0	100.0 $\rightarrow$ 0	–
	sCVC (%) $\downarrow$	99.3 $\rightarrow$ 0	–	94.4 $\rightarrow$ 0	86.1 $\rightarrow$ 0	63.7 $\rightarrow$ 0	96.6 $\rightarrow$ 0	–
	$R^{2}$ $\uparrow$	0.31 $\rightarrow$ 1	–	$-1.30$ $\rightarrow$ 1	$-0.19$ $\rightarrow$ 1	0.65 $\rightarrow$ 1	0.58 $\rightarrow$ 1	–

Table 2: End-to-end constraint enforcement across seven public datasets. Constraint-metric cells show raw

\rightarrow

postprocessed means; exact optima are written as

0

1

. Dataset means average samples within each generator and split, then generators and splits equally. Constraint counts span splits; dashes denote unavailable families.

Figure 2: Generator-wise raw constraint metrics (mean $\pm$ standard deviation across applicable datasets). Blue and vermillion cells mark the best and worst means, respectively, within each constraint family.

Figure 3: Raw-to-postprocessed TSTR utility and Column Shapes. TSTR uses ROC-AUC for classification datasets and $R^{2}$ otherwise; only within-dataset changes are comparable.

Figure 4: Discovery sensitivity on news (three-split means; GPT-5.6 Luna). Each variant changes one component of the default $(3,100,20)$ ; dashed lines mark it. Higher yield and lower token use are better.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Total	Train	Test	Cat.	Num.
flights	60,000	42,000	18,000	9	14
heloc	9,084	6,358	2,726	3	21
nba	14,062	9,843	4,219	0	26
news	38,458	26,920	11,538	9	45
steel	34,993	24,495	10,498	3	7
taxi	59,996	41,997	17,999	7	15

Appendix

Table 3: Dataset sizes and column-type counts for the frozen end-to-end evaluation splits. Column counts include the utility target. Anxiety is not included in the end-to-end evaluation task.

#	Ground-truth logical dependency
1	Anxiety Band = Very high (9--10) $\rightarrow$ Caffeine Band = 294 mg or more
2	Anxiety Band = Very high (9--10) $\rightarrow$ Breathing Rate Band = 20 breaths/min or higher
3	Anxiety Band = Very high (9--10) $\rightarrow$ Heart Rate Band = 85 bpm or higher
4	Anxiety Band = Very high (9--10) $\rightarrow$ Alcohol Band = 5 or more drinks
5	Anxiety Band = Very high (9--10) $\rightarrow$ Diet Quality Band = Low (1--4)
6	Anxiety Band = Very high (9--10) $\rightarrow$ Therapy Band = 3 or more sessions

Appendix

Table 4: The 13 annotator-verified logical dependencies used as ground truth for the anxiety detection task.

CTGAN hyperparameter	Setting
Training epochs	300
Batch size	500
Noise/embedding dimension	128
Generator hidden layers	$[256,256]$
Discriminator hidden layers	$[256,256]$
Generator learning rate	$2\times 10^{-4}$

Appendix

Table 7: CTGAN training configuration.

TVAE hyperparameter	Setting
Training epochs	300
Batch size	500
Latent/embedding dimension	128
Encoder/compression layers	$[128,128]$
Decoder/decompression layers	$[128,128]$
Optimizer	Adam

Appendix

Table 8: TVAE training configuration.

Gaussian Copula hyperparameter	Setting
Default numerical marginal distribution	Beta

Appendix

Table 9: Gaussian Copula configuration.

TabDDPM hyperparameter	Setting
Optimizer updates	30,000
Maximum training batch size	4,096
Optimizer	AdamW
Initial learning rate	$1\times 10^{-3}$
Learning-rate schedule	Linear decay toward zero
Denoising MLP hidden layers	$[256,256]$

Appendix

Table 10: TabDDPM training configuration, including the flights -specific override.

Dataset	Generator	Raw	Postprocessed	$\Delta$
		Column Shapes $\uparrow$
flights	CTGAN	$0.906\;(0.008)$	$0.912\;(0.010)$	+0.006
	Gaussian Copula	$0.931\;(0.001)$	$0.931\;(0.001)$	0.000
	TabDDPM	$0.968\;(0.004)$	$0.969\;(0.003)$	+0.001
	TVAE	$0.932\;(0.002)$	$0.935\;(0.004)$	+0.003
heloc	CTGAN	$0.906\;(0.014)$	$0.900\;(0.016)$	-0.006

Appendix

Table 11: Column Shapes for all dataset–generator combinations before and after constraint postprocessing. Entries are means, with standard deviations in parentheses; each entry aggregates nine runs across three independent data splits. The final column gives

\Delta=\text{Postprocessed}-\text{Raw}

for the displayed means; green and orange denote gains and losses, respectively. Higher is better.

Dataset	Task / metric	Selected evaluation model	Generator	TRTR $\uparrow$	Raw TSTR $\uparrow$	Postprocessed TSTR $\uparrow$	$\Delta$
flights	Regression ( $R^{2}$ )	Linear regression	CTGAN	$0.986\;(0.000)$	$0.645\;(0.037)$	$0.661\;(0.040)$	+0.016
			Gaussian Copula		$0.963\;(0.008)$	$0.964\;(0.002)$	+0.001
			TabDDPM		$0.839\;(0.052)$	$0.745\;(0.111)$	-0.094
			TVAE		$0.875\;(0.078)$	$0.874\;(0.077)$	-0.001
heloc	Classification (ROC-AUC)	Logistic regression	CTGAN	$0.802\;(0.003)$	$0.720\;(0.028)$	$0.720\;(0.029)$	0.000
			Gaussian Copula		$0.775\;(0.020)$	$0.784\;(0.004)$	+0.009

Appendix

Table 12: Complete downstream utility results (mean; standard deviation in parentheses). TRTR aggregates three splits for the selected dataset-level model; TSTR aggregates nine runs across three splits for each dataset–generator pair. The final column reports

\Delta=\text{Postprocessed}-\text{Raw}

for displayed TSTR means (green: gain; orange: loss). Regression uses

R^{2}

and classification uses ROC-AUC; higher is better.

		Logical dependency		Equational			Linear
Dataset	Generator	CVR $\downarrow$	sCVC $\downarrow$	CVR $\downarrow$	sCVC $\downarrow$	$\boldsymbol{R^{2}}$ $\uparrow$	CVR $\downarrow$	sCVC $\downarrow$	LFD $\downarrow$
flights	CTGAN	$0.826\;(0.021)$	$0.455\;(0.013)$	$1.000\;(0.000)$	$0.996\;(0.000)$	$0.301\;(0.031)$	$0.000\;(0.000)$	$0.000\;(0.000)$	$0.000\;(0.000)$
	Gaussian Copula	$0.994\;(0.002)$	$0.757\;(0.029)$	$1.000\;(0.000)$	$0.998\;(0.000)$	$-0.214\;(0.005)$	$0.000\;(0.000)$	$0.000\;(0.000)$	$0.000\;(0.000)$
	TabDDPM	$0.116\;(0.004)$	$0.057\;(0.005)$	$1.000\;(0.000)$	$0.982\;(0.001)$	$0.691\;(0.033)$	$0.000\;(0.000)$	$0.000\;(0.000)$	$0.000\;(0.000)$
	TVAE	$0.702\;(0.004)$	$0.332\;(0.002)$	$1.000\;(0.000)$	$0.994\;(0.001)$	$0.474\;(0.010)$	$0.000\;(0.000)$	$0.000\;(0.000)$	$0.000\;(0.000)$
heloc	CTGAN	$0.013\;(0.007)$	$0.013\;(0.007)$	–	–	–	$0.715\;(0.051)$	$0.095\;(0.017)$	$0.698\;(0.102)$

Appendix

Table 13: Raw constraint results for every dataset–generator combination. Entries are means, with standard deviations in parentheses, over nine runs spanning three independent data splits. CVR, sCVC, and LFD are lower-is-better metrics; equational

R^{2}

is higher-is-better. Dashes indicate that a constraint family is unavailable for a dataset. News linear metrics are computed over the two splits containing detected linear constraints; the zero-constraint split is excluded (

n=2

	Column Shapes $\uparrow$
Dataset	KS-guided	Random feasible	KS gain
flights	$0.878(0.037)$	$0.825(0.048)$	$\mathbf{+0.053(0.020)}$
nba	$0.916(0.026)$	$0.897(0.040)$	$\mathbf{+0.020(0.024)}$
news	$0.819(0.102)$	$0.818(0.101)$	$0.000(0.001)$
taxi	$0.898(0.043)$	$0.875(0.051)$	$\mathbf{+0.023(0.015)}$
steel	$0.890(0.046)$	$0.863(0.060)$	$\mathbf{+0.028(0.031)}$

Appendix

Table 14: Equational-repair scheduling ablation, aggregated by dataset over four generators, three data splits, and three synthetic samples per split (36 matched inputs per dataset; 180 total). Values are means with sample standard deviations in parentheses. KS gain is computed per matched input as KS-guided minus random feasible, so positive values favor KS guidance. Equational CVR is zero under both schedules on every input and is therefore omitted.

Generator	Metric	$E{\rightarrow}L$	$L{\rightarrow}E$
CTGAN	CVR (%) $\downarrow$	$0\;(0)$	$7.331\;(5.919)$
CTGAN	LFD $\downarrow$	$0\;(0)$	$1.583\;(2.102)$
TVAE	CVR (%) $\downarrow$	$0\;(0)$	$0.782\;(1.193)$
TVAE	LFD $\downarrow$	$0\;(0)$	$0.640\;(1.225)$
Gaussian Copula	CVR (%) $\downarrow$	$0\;(0)$	$9.919\;(3.753)$
Gaussian Copula	LFD $\downarrow$	$0\;(0)$	$1.219\;(0.755)$

Appendix

Table 15: Repair-order ablation on nba .

E{\rightarrow}L

is categorical

\rightarrow

equational

\rightarrow

linear repair;

L{\rightarrow}E

swaps the two numerical stages. The All row aggregates all 36 matched settings. Entries are means, with sample standard deviations in parentheses. Final equational CVR is zero under both orders and is therefore omitted.

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