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

In the digital age, vast amounts of information are locked away in spreadsheets, recording everything from flight schedules and credit applications to basketball statistics and medical histories. When real data is scarce, sensitive, or difficult to share, researchers and engineers turn to synthetic data: computer-generated records that mimic the statistical patterns of the real world. These artificial datasets allow teams to build and test software, train artificial intelligence, and explore scenarios without risking privacy or exposing confidential details. However, a significant problem has long plagued this field. While computers are excellent at copying the general shape of data—ensuring that the average age or the distribution of income looks correct—they often fail to understand the deep, logical rules that bind columns together. A computer might generate a synthetic order where a package is delivered before it was even purchased, or a financial record where the total cost does not match the price multiplied by the quantity. These errors, known as structural violations, make the data look real on the surface but break down under simple logical checks, rendering it useless for serious analysis or decision-making.

A team of researchers has developed a new method to fix this flaw, creating a system that teaches artificial intelligence to discover and enforce the hidden logical rules of a dataset. Instead of trying to force the data generator to follow strict rules from the start, which often distorts the data or requires complex retraining, their approach acts as a sophisticated post-processing step. The system first uses large language models—advanced AI tools trained on vast amounts of text—to read the dataset's descriptions and sample records. These models act as curious auditors, proposing hypotheses about how different columns should relate to one another. They might suggest that a delivery date must always be later than an order date, or that a specific product type can only be shipped via certain methods.

The innovation lies in how these proposals are tested and refined. Rather than accepting the AI's guesses blindly, the system translates each idea into a strict, machine-readable instruction that can be checked against every single row of the original data. If a proposed rule fails even a few times, the system does not discard it immediately. Instead, it shows the AI the specific examples where the rule broke, allowing the model to revise its hypothesis. This cycle of proposing, testing, and correcting continues until the system settles on a set of rules that hold true for the entire dataset. The researchers focused on three main types of relationships: equations where one number is the exact result of others, inequalities where one value must be larger or smaller than another, and logical dependencies where the category of one item dictates the allowed categories of another.

Once the rules are discovered and verified, the system applies them to the synthetic data generated by any standard tool. It acts as a coordinator, fixing errors in a specific order to ensure that correcting one mistake does not create another. For instance, if a rule requires a total to be the sum of two parts, the system first fixes the total based on the parts, and only then adjusts the parts to fit within any broader limits. This careful sequencing ensures that the final dataset obeys all the discovered laws simultaneously. In their experiments, the researchers tested this workflow on seven different public datasets, ranging from flight records to steel industry energy consumption, using four different types of data generators. Before the fix, the synthetic data often contained hundreds of violations, with some datasets showing that nearly every single generated record broke at least one rule. After the system applied its corrections, the number of violations dropped to zero for every rule that could be enforced.

Crucially, this rigorous cleaning did not ruin the data's usefulness. The researchers measured how well the cleaned data performed in real-world tasks, such as training a model to predict credit risk or flight delays. In most cases, the utility of the data actually improved, and in the worst cases, the drop in performance was negligible. The system also preserved the individual characteristics of the data, ensuring that the distribution of values in each column remained faithful to the original. The study demonstrates that by treating logical rules as a system of interacting constraints rather than isolated checks, it is possible to generate synthetic data that is not only statistically similar to the real thing but also structurally sound. This approach offers a practical path forward for creating reliable synthetic data, ensuring that the artificial records used to train our future systems are built on a foundation of logical truth.