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.
This paper introduces Wittgenstein's Rule Following (WRF) data evolution, a framework in philomatics for evolving or generating a new dataset from a sequence of previously observed datasets. The method is inspired by Ludwig Wittgenstein's rule-following considerations and his notion of family resemblance in Philosophical Investigations. Unlike standard synthetic data generation, where the goal is usually to sample from or augment a fixed distribution, WRF aims to continue the implicit rule expressed by a historical sequence of datasets while preserving resemblance to the previous datasets. WRF represents each dataset by structural descriptors rather than pointwise correspondences. These descriptors summarize geometric, distributional, clustering, and, in the supervised case, label-based properties of the data. The method predicts a rule-following target by extrapolating descriptor trajectories and a family-resemblance target by averaging historical descriptors. Candidate datasets are then generated from the observed history through balanced or bounded mixture recombination, scored according to these targets, and optionally refined through differentiable optimization in descriptor space. The proposed framework allows both sample size and feature dimension to vary over time and does not assume that the next dataset is a direct transformation of the last one. Simulations on synthetic and image datasets show that WRF can generate meaningful continuations of evolving datasets in both unsupervised and supervised settings.
Training robust multivariate time series forecasting models requires large, diverse corpora, yet many real-world domains provide only a handful of observed sequences. Existing generators fail to resolve this mismatch: prior-based approaches (e.g., CauKer, TimePFN) produce domain-agnostic samples, while data-driven methods (e.g., TimeGAN) treat references as black-box supervision, forfeiting explicit control over periodic structure, local variability, and cross-variable dynamics. We propose ReGeN, a reference-guided generative pipeline that treats observed sequences not as examples to imitate, but as structural scaffolds for controllable synthesis. ReGeN decomposes each reference into three interpretable components: a phase-aligned periodic backbone capturing dominant domain morphology; per-variable stochastic residuals modeled with a deep-kernel Gaussian process; and lag-aware cross-variable dependencies injected through a structural causal model with fitted coupling coefficients. Sampling these components at controllable temperature broadens distributional coverage while preserving domain-grounded structure. We show that ReGeN-generated data consistently substitutes for real sibling data with minimal forecasting degradation, and in strongly periodic domains such as traffic, can outperform the real source itself. We further show that a foundation model pretrained on ReGeN corpora outperforms those pretrained on prior-based and data-driven synthetic alternatives. This suggests that in low-data regimes, how reference data is structurally exploited can matter as much as how much data is available.
Tabular data synthesis aims to generate high-quality data while preserving privacy. However, we find that existing tabular generative models exhibit a clear tradeoff in the small-data regime: improving data quality typically comes at the cost of increased memorization of training samples, thereby weakening privacy protection. This tradeoff arises because small training sets make it difficult for dataset-specific generative models to distinguish generalizable structure from sample-specific patterns. To address this, we propose DiffICL, which formulates tabular data generation as an in-context learning problem. Instead of fitting each dataset from scratch,DiffICL leverages pretrained structural priors learned from a large collection of datasets, enabling it to infer data distributions from limited context rather than memorizing individual samples. We evaluate DiffICL on 14 real-world datasets. Results show that DiffICL improves both data quality and privacy, and generate synthetic data that provides effective data augmentation. Our findings suggest that the quality-privacy tradeoff can be improved through better training paradigms.