# Permutation-Invariant Tabular Data Synthesis

arXiv: https://arxiv.org/abs/2211.09286 · HTML: https://mlsanity.com/paper/2211.09286/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 19 of 19)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Generating Multi-label Discrete Patient Records using Generative Adversarial Networks](https://mlsanity.com/paper/1703.06490/) (2017)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [CTAB-GAN: Effective Table Data Synthesizing](https://mlsanity.com/paper/2102.08369/) (2021)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks](https://mlsanity.com/paper/1810.00825/) (2018)
- [CTAB-GAN+: Enhancing Tabular Data Synthesis](https://mlsanity.com/paper/2204.00401/) (2022)
- [Conditional Wasserstein GAN-based Oversampling of Tabular Data for Imbalanced Learning](https://mlsanity.com/paper/2008.09202/) (2020)
- [Quantifying Translation-Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/1801.01450/) (2017)
- [Advancements in Image Classification using Convolutional Neural Network](https://mlsanity.com/paper/1905.03288/) (2019)
- [SYNC: A Copula based Framework for Generating Synthetic Data from Aggregated Sources](https://mlsanity.com/paper/2009.09471/) (2020)
- [Regularizing Towards Permutation Invariance in Recurrent Models](https://mlsanity.com/paper/2010.13055/) (2020)
- [Deep Learning for Target Classification from SAR Imagery: Data Augmentation and Translation Invariance](https://mlsanity.com/paper/1708.07920/) (2017)

## Built on by (most cited first, 6 of 6)

- [TabuLa: Harnessing Language Models for Tabular Data Synthesis](https://mlsanity.com/paper/2310.12746/) (2023)
- [SynthEval: A Framework for Detailed Utility and Privacy Evaluation of Tabular Synthetic Data](https://mlsanity.com/paper/2404.15821/) (2024)
- [Masked Diffusion Models are Secretly Learned-Order Autoregressive Models](https://mlsanity.com/paper/2511.19152/) (2025)
- [Toward Real-World Table Agents: Capabilities, Workflows, and Design Principles for LLM-based Table Intelligence](https://mlsanity.com/paper/2507.10281/) (2025)
- [Multimodal synthesis of MRI and tabular data with diffusion in a joint latent space via cross-attention](https://mlsanity.com/paper/2605.06699/) (2026)
- [On Privacy in Data-Space Tabular Diffusion Models: Influential Factors, Attacker Knowledge, and Metrics](https://mlsanity.com/paper/2605.06835/) (2026)

## Abstract (arXiv)

Tabular data synthesis is an emerging approach to circumvent strict regulations on data privacy while discovering knowledge through big data. Although state-of-the-art AI-based tabular data synthesizers, e.g., table-GAN, CTGAN, TVAE, and CTAB-GAN, are effective at generating synthetic tabular data, their training is sensitive to column permutations of input data. In this paper, we first conduct an extensive empirical study to disclose such a property of permutation invariance and an in-depth analysis of the existing synthesizers. We show that changing the input column order worsens the statistical difference between real and synthetic data by up to 38.67% due to the encoding of tabular data and the network architectures. To fully unleash the potential of big synthetic tabular data, we propose two solutions: (i) AE-GAN, a synthesizer that uses an autoencoder network to represent the tabular data and GAN networks to synthesize the latent representation, and (ii) a feature sorting algorithm to find the suitable column order of input data for CNN-based synthesizers. We evaluate the proposed solutions on five datasets in terms of the sensitivity to the column permutation, the quality of synthetic data, and the utility in downstream analyses. Our results show that we enhance the property of permutation-invariance when training synthesizers and further improve the quality and utility of synthetic data, up to 22%, compared to the existing synthesizers.