CTSyn: A Foundational Model for Cross Tabular Data Generation

## Abstract

Abstract Generative Foundation Models (GFMs) have produced synthetic data with remarkable quality in modalities such as images and text. However, applying GFMs to tabular data poses significant challenges due to the inherent heterogeneity of table features. Existing cross-table learning frameworks are hindered by the absence of both a generative model backbone and a decoding mechanism for heterogeneous feature values. To overcome these limitations, we introduce the Cross-Table Synthesizer (CTSyn), a diffusion-based foundational model tailored for tabular data generation. CTSyn introduces three major components: an aggregator that consolidates heterogeneous tables into a unified latent space; a conditional latent diffusion model for sampling from this space; and type-specific decoders that reconstruct values of varied data types from sampled latent vectors. Extensive testing on real-world datasets reveals that CTSyn not only significantly outperforms existing table synthesizers in utility and diversity, but also uniquely enhances performances of downstream machine learning beyond what is achievable with real data, thus establishing a new paradigm for synthetic data generation.

## 1 Introduction

Generative Foundation Models (GFMs) have revolutionized fields such as Computer Vision (CV) and Natural Language Processing (NLP)[, , , , , ]. Trained on vast datasets [, , ] and with versatile model backbones [, ], these models excel across a diverse range of domains and tasks. They can generate valuable synthetic training examples to boost performances of various downstream applications [, , , , ].

GFMs also hold immense potential for generating tabular data, a modality integral to core real-world applications [, , ]. Despite the ubiquity of tables, modeling often encounters a shortage of high-quality samples. Although tabular data synthesizers have increasingly gained attention [, , ], they bring little performance gains in downstream models [, ].This limitation stems from a fundamental constraint: literally synthesizers cannot add information not included in the original training data. Tabular GFMs has the potential of overcoming that limitation by leveraging more diverse pre-training data.

Despite such opportunities, the implementation of tabular GFMs remains particularly challenging and largely overlooked, due to the heterogeneity between column structures, features sets and ranges of values [, , , , , ]. Existing methods for transferable tabular learning either model tables with language models [, , , ], or attempt to learn a unified latent space across datasets [, , , ]. They neither possess generative capability, nor include a unified decoding mechanism that reconstructs heterogeneous table values from row-level representations.

In response to all these limitation, we propose CTSyn, a foundation model framework specifically designed for the generation of heterogeneous tables. CTSyn has the following main components:

- •
Unified Table Representation: We developed a unified aggregator that tokenizes and embeds heterogeneous table rows, and projects them into a unified latent space. Utilizing self-supervised contrastive learning, regularized by magnitude-aware loss, this approach enhances the preservation of numerical information and facilitates the training of models across tabular formats, thereby overcoming the barrier of data-specific structural needs.
- •
Generative Foundation Model: Our versatile conditional diffusion model backbone efficiently samples from unified latent spaces, allowing for improved flexibility and applicability across various tabular domains without the need for domain-specific adaptations.
- •
Data Type-specific Decoder: We trained separate decoder networks that extract column values from latent row embeddings be it numerical values or refined representations of categorical levels. This modular approach in decoding allows us to accommodate different output formats and loss functions tailored to specific column types, effectively eliminating the constraints imposed by traditional data-specific output schemas.

Through extensive experiments with real-world datasets, we demonstrate that CTSyn extends the pre-train/fine-tuning paradigm to the tabular data generation and sets a new benchmark, surpassing the existing State-Of-The-Art (SOTA). Crucially, by effectively leveraging prior knowledge, our model unlocks unprecedented potential in synthetic tabular data generation.

## 2 Related Work

### 2.1 Table Representation Learning

Self-supervised learning can significantly enhance the informativeness of representations for various downstream tasks [, , , ]. In the tabular domain, methods like VIME [] train an encoder using a combination of supervised reconstruction loss and mask-array prediction loss, and SCARF [] employs contrastive loss by utilizing randomly corrupted feature vectors as positive pairs. Subtab [] and SSP [] integrates contrastive and reconstruction losses. However, these approaches do not produce transferable representations across tables as they rely on data-specific feature encoding and structures.
Xtab [] and TabRet [] introduce transformer-based backbones with separate data-specific featurizer or projection heads for each downstream task. These models achieve transferability at the expense of high model complexity.

Pre-trained Language Models (PLMs) can be used to unify representation dimensions of heterogeneous features. TransTab [] extends Subtab’s methodology by tokenizing and then encoding column names and categories, creating a latent space that can be shared across tables. Combining tokenization with masked-value-prediction objective, transformer-based models can be trained to perform predictive task across tables [, , , ]. However, such methods include neither a generative model backbone, nor a fixed-dimensional row representation and decoding strategy that could be integrated with other generative model.

Another line of research involving PLMs converts tabular features to sentences and model regression/classification problems as NLP tasks [, , , , , ]. Despite enabling transfer learning, these methods face challenges with accurately modeling continuous values and tend to overlook the intrinsic structural properties of tables [].

### 2.2 Synthetic Tabular Data Generation

Synthetic Tabular Data Generation(STDG) has long been studied by statisticians [, , ].
Recent success of deep generative models significantly advanced its boundary [, , ].
In particular, CTGAN [] combines conditional Generative Adversarial Network(GAN) and model-speicif normalization to model highly imbalanced and non-Gaussian columns. CtabGAN+[, ] proposed a solution for mixed-type and long-tailed variable problems. Autodiff [] and Tabsyn [] used a combination of latent-diffusion and data-specific autoencoder structure, which is the most similar work to ours but missing the critical transferable encoding/decoding ability. TabDDPM [] achieved the current state-of-the-art in tabular generation with separate diffusion process for numerical and categorical columns.
Some models also synthesizes data with Differential Privacy guarantee [, , ]
Despite their effectiveness in modeling column distributions, none of the above methods is able to effectively boost the training of machine learning models with synthesized data, greatly limiting their usage in data augmentation [].

GReaT [] and Tabula [] generate tables with PLMs, by treating tables rows as natural language text.
Despite showing evidences of transferrability, they do not consider cross-table pre-training and generation, introduce risk of producing out-of-bound examples due to their unconstrained sampling of output token, and face the well-known challenge of modeling numeracy in discrete token space [].

## 3 Methodology

Figure: Figure 1: Overview of the proposed framework.
Refer to caption: extracted/5650322/figures/Overview.png

In this section, we outline CTSyn, our solutions to the challenges involved in creating a tabular GFM. Figure 1 provides an overview of the proposed framework.

### 3.1 Feature Embedding

Let a row in a mixed-type table be $\bm{x}=[c_{1},x_{1},c_{2},x_{2},\ldots,c_{D},x_{D}]$, where $c_{i}$ for $i=1,2,\ldots,D$ are the feature names, $x_{i}$ for $i=1,2,\ldots,D$ are the feature values which can be either numerical or categorical, $D$ denotes the number of features in this row. Let $m$ be the text metadata describing the context of the table.

To enable the transfer of knowledge across tables, a unified representation must preserve all such information. Since dimensions differ across variable types, we tokenize and encode them into vectors of the same dimension. First, we consolidate all text metadata, column names, and categories, ensuring all integer class labels and abbreviations are converted to complete text reflecting their original meanings. Then, we create embeddings as follows:

$$ $\displaystyle e_{m}$ $\displaystyle=\textbf{LM}(m),\quad e_{c_{i}}=\textbf{LM}(c_{i}),$ $\displaystyle e_{x_{i}}$ $\displaystyle=\begin{cases}\textbf{LM}(x_{i})&\text{if }x_{i}\text{ is categorical},\\ \textbf{AE}_{\text{enc}}(\text{Quantile}(x_{i}))&\text{if }x_{i}\text{ is numerical}\end{cases}$ $$

where LM is a pre-trained language model for text encoding, which will only be called once for each unique category/column name. Quantile is the quantile transformer [] fitted on $d$ that transforms numerical values to a standard uniform distribution. This improves the modeling of numbers by aligning their ranges and mitigating outliers. $\textbf{AE}_{\text{enc}}$ represents the encoder part of a fully connected autoencoder pre-trained on samples from $\text{Uniform}(0,1)$ (see Appendix Section B), ensuring that quantile-transformed numbers are embedded into the same dimensional space as the language model embeddings while preserving their relative numeracy.

Finally, we interleave all embeddings as a sequence:

$$ $\bm{E}=[e_{m},e_{c_{1}},e_{x_{1}},e_{c_{2}},e_{x_{2}},\ldots,e_{c_{D}},e_{x_{D }}]\in\mathbb{R}^{(2D+1)\times M_{\text{LM}}},$ (1) $$

where $M_{\text{LM}}$ is the dimension of the language model embeddings.

### 3.2 Embedding Aggregator

We train an aggregator neural network $f(\bm{E})$ to compress a sequence of embeddings into a fixed-dimension latent vector $\bm{v}\in\mathbb{R}^{M_{\text{agg}}}$, where $M_{\text{agg}}$ is the dimension of the learned latent space.

For each row $\bm{x_{i}}$, we create a set of $K+1$ embedding sequences $s_{i}=\{\textbf{E}_{i}^{1},\textbf{E}_{i}^{2},\ldots,\textbf{E}_{i}^{K+1}\}$. $\textbf{E}_{i}^{1}$ is the embedding of all row elements according to Equation 3.1, and the remaining sequences are created by randomly selecting 50% of features in $\bm{x_{i}}$, masking their value embeddings in $\textbf{E}_{i}^{1}$ with a fixed value of $-1$, while retaining the feature names. The aggregator is then trained using a self-supervised contrastive loss:

$$ $L_{\text{con}}=-\sum_{i=1}^{B}\sum_{k=1}^{K+1}\sum_{k^{\prime}\neq k}^{K+1} \log\frac{\exp(\psi(\bm{v}_{i}^{k},\bm{v}_{i}^{k^{\prime}})/\tau)}{\sum_{j=1}^ {B}\sum_{k^{\ast}=1}^{K}\exp(\psi(\bm{v}_{i}^{k},\bm{v}_{j}^{k^{\ast}})/\tau)},$ $$

where $\bm{v}_{i}^{k}=f(\bm{E}_{i}^{k})$ is the compressed embedding of the $k$th embedding sequence of the $i$th row, $B$ is the batch size, $\psi(\cdot,\cdot)$ is the cosine similarity, and $\tau$ is the temperature constant for numerical stability.

To preserve the relative magnitudes of numerical values within the embeddings, we also modify the Magnitude-Aware Triplet Loss []. For each embedding $\bm{v}_{i}$, we randomly select two other embeddings $\bm{v}_{j}$ and $\bm{v}_{k}$ from the batch, ensuring $i\neq j\neq k$. We define the loss as:

$$ $\displaystyle L_{\text{mag}}=\max\left(\|f(\bm{v}_{i})-f(\bm{v}_{j})\|-\|f(\bm {v}_{i})-f(\bm{v}_{k})\|+m(\bm{v}_{i},\bm{v}_{j},\bm{v}_{k}),0\right),$ $\displaystyle m(\bm{v}_{i},\bm{v}_{j},\bm{v}_{k})=\frac{|x_{i,d}-x_{k,d}|-|x_{ i,d}-x_{j,d}|}{\text{range}(d)},\quad\text{s.t.}\ |x_{i,d}-x_{k,d}|>|x_{i,d}-x _{j,d}|,$ $$

where $x_{i,d}$, $x_{j,d}$, and $x_{k,d}$ are the numerical values of a selected numerical column $d$ for rows $i$, $j$, and $k$, respectively. Each epoch, one numerical column is uniformly selected for this loss calculation.

The combined training loss for the aggregator is $L_{\text{aggregator}}=L_{\text{con}}+\lambda L_{\text{mag}},$
where $\lambda=2$ is a weighting constant for the magnitude-aware loss selected by cross-validation. With this combination of masking and contrastive learning, the model learns to represent feature information as well as correlation between features as it is forced to infer closeness of masked features based on available feature values.

### 3.3 Conditional Diffusion Model for Latent Vector Generation

We employ a conditional Gaussian diffusion model to sample from learned latent distributions of tables. The forward and reverse processes of the model are characterized by Gaussian distributions:

$$ $q(v_{t}\mid v_{t-1}):=\mathcal{N}\left(v_{t};\sqrt{1-\beta_{t}}v_{t-1},\beta_{ t}\mathbf{I}_{M_{\text{agg}}}\right)$ $$

$$ $q(v_{T}):=\mathcal{N}(v_{T};\mathbf{0},\mathbf{I}_{M_{\text{agg}}})$ $$

$$ $p_{\theta}(v_{t-1}\mid v_{t},y):=\mathcal{N}\left(v_{t-1};\mu_{\theta}(v_{t},y ,t),\Sigma_{\theta}(v_{t},y,t)\right)$ $$

In the main text, $y$ is a conditioning latent vector with dimension $M_{\text{LM}}$. The variance $\Sigma_{\theta}(v_{t},y,t)$ is diagonal with a constant scalar $\sigma_{t}$. For each sample $\bm{v_{i}}$, the corresponding condition $y_{i}$ is formed by the table context embedding $e_{m}$. We report performance of generation conditioned on both table metadata and feature values in appendix section G

The mean $\mu_{\theta}(v_{t},y,t)$ is calculated using:

$$ $\mu_{\theta}(v_{t},y,t)=\frac{1}{\sqrt{\alpha_{t}}}\left(v_{t}-\frac{\beta_{t} }{\sqrt{1-\bar{\alpha}_{t}}}\epsilon_{\theta}(v_{t},y,t)\right)$ $$

where $\alpha_{t}:=1-\beta_{t}$ and $\bar{\alpha}_{t}:=\prod_{i=1}^{t}\alpha_{i}$ represent the noise schedule parameters. The function $\epsilon_{\theta}(v_{t},y,t)$ estimates the "ground truth" noise component for the noisy data sample $v_{t}$.

The objective function is simplified to:

$$ $L_{\text{simple},t}=\mathbb{E}_{v_{0},\epsilon,t}\left[\|\epsilon-\epsilon_{ \theta}(v_{t},y,t)\|^{2}\right]$ $$

### 3.4 Type-Specific Decoder

Training data-specific table decoders can significantly increase model complexity and elevate the risk of overfitting, particularly when dealing with smaller downstream datasets. Thus, we train type-specific decoders that reconstruct the original values for one cell at a time. To reconstruct the value of a column with name $c_{i}$ in row $x_{i}$ with table metadata $m$, the input to the decoders $H$ is the concatenation of embeddings $[e_{m},e_{c_{i}},v_{i}]$. This concatenation uniquely represents the value for each cell, allowing the decoder to perform accurate reconstruction. We focus on two main data types: categorical and numerical, though this framework can be seamlessly extended to various data types.

Categorical Decoder: Categorical levels vary in sets and textual representations across tables, making decoding one-hot vectors with cross-entropy loss infeasible. Decoding categories as text strings also risks generating unseen columns and losing column structures in categories. Inspired by contrastive-based classification methods in computer vision tasks [], we train the categorical decoder $H_{\text{cat}}(e_{m},e_{c_{i}},f(E_{i}))\in\mathbb{R}^{M^{\text{dec}}}$ as a projector that maps embeddings of row elements into a cell-level latent space, where cells with the same categories are clustered together.

For each row $\bm{x_{i}}$, we create a set of $K=2$ embeddings $\{E_{i}^{1},E_{i}^{2}\}$. $E_{i}^{1}$ is the embedding of all its elements according to Equation 3.1, and $E_{i}^{2}$ is created by masking the value embedding features in $\bm{x_{i}}$ corresponding to $d$ with a fixed value of $-1$, while retaining the feature names. The presence of an embedding with the actual value absent enforces the model to learn to fill in the missing value based on available values, implicitly preserving the correlation between columns.

We apply the following supervised contrastive loss:

$$ $L_{\text{cat},d}=-\sum_{i=1}^{B}\sum_{j=1}^{B}\sum_{k=1}^{K}\sum_{k^{\prime}=1 }^{K}\mathbf{1}_{\{x_{j,d}=x_{i,d}\}}\log\left(\frac{\exp\psi(z_{i,d}^{k},z_{j ,d}^{k^{\prime}})}{\sum_{j^{\ast}=1}^{B}\sum_{k^{\ast}=1}^{K}\mathbf{1}_{\{x_{ j^{\ast},d}\neq x_{i,d}\}}\exp\psi(z_{i,d}^{k},z_{j^{\ast},d}^{k^{\ast}})} \right),$ $$

where $z_{i,d}^{k}=H_{\text{cat}}([e_{m},e_{c_{i}},f(E_{i})])$ is the output of the categorical decoder for the $k$th view of column $d$ in row $i$, and $\mathbf{1}_{\{\cdot\}}$ is the indicator function. This contrastive learning ensures that representations of cells with the same categories are clustered together.

For reconstructing column $d$ for row $i$, we first produce $z_{p,d}=H_{\text{cat}}(e_{m},e_{c_{d}},f([e_{m},e_{c_{d}},e_{p})])$ for each unique category $p$ in $d$, which are considered anchor embeddings of different categories. We then assign the category whose embedding has with the highest cosine similarity to the reconstructed cell embedding $z_{i,d}$.

Numerical Decoder: For decoding numerical values, we employ the numerical decoder $H_{\text{num}}(e_{m},e_{c_{i}},f(E_{i}))\in\mathbb{R}$ that reconstructs the quantile value of the original numerical cell. We train the decoder using the Mean Squared Error (MSE) loss. We then apply the quantile transformer fitted during training to inverse transform the normalized outputs back to their original value range.

Multi-Column Decoding:
We train decoders for different types separately and back-propagate on loss of one column at a time. Despite increasing training time, this strategy greatly reduces gradient inference between loss of decoding different columns and improves the optimization dynamics [, ]. We observe that training the decoders on multiple column at once result in little to none loss reduction during training.

### 3.5 Implementation

We use pre-trained GTE [] for encoding text and categories. The aggregator and type-specific decoders are implemented using the Perceiver Resampler [] architecture, which consists of a series of stacked Multi-Head Attention (MHA) and feed-forward layers, as specified in []. We use 1 learnable latent node, a model depth of 4, and set $M_{\text{Agg}}=128$.
For the conditional diffusion component, we utilize a Multi-Layer Perceptron (MLP) with residual connections and a depth of 4.
Details on model structures and training parameters are shown in Appendix Section B.

## 4 Experiment

### 4.1 Test Setup

In this section, we evaluate the ability of CTSyn to generate informative and diverse synthetic tabular data. Our primary research questions are: 1, Does pre-training on large general datasets enhance the quality of data generation for downstream datasets? 2, Can CTSyn generate informative data for downstream task without data-specific training?

Datasets Construction: We benchmark a set of real datasets in healthcare domains, with details shown in Table 1.
Each dataset is split into training, fine-tuning, and holdout testing sets in a 70% / 5% / 25% ratio. The training sets are pooled to form a shared pre-training set, which is used to pre-train the table aggregator, type-specific decoders, and the diffusion model within the learned latent space.
For each fine-tuning set, we randomly split the features, excluding the target column, into two subsets, creating fine-tune sets A and B. Each set contains half of the predictor features and the same target column.
Each fine-tune set is treated as a separate downstream task. Synthetic data generated for these tasks are evaluated by comparing their statistical fidelity, machine learning utility, and data diversity against the corresponding holdout testing set.
The pre-training set remains constant throughout this paper. We use 10 random seeds to create 10 splits of fine-tune and holdout test sets. We report the average metrics across all fine-tune/holdout splits. We generated synthetic tables with the same number of rows as the fine-tune set.
Results on cross-domain datasets are shown in Appendix section F

**Table 1: Summary Statistics of Datasets.**
| Dataset | Rows | Categorical | Numerical |
| --- | --- | --- | --- |
| Obesity | 2111 | 7 | 8 |
| Diabetes | 768 | 1 | 8 |
| Liver Patients | 579 | 2 | 9 |
| Sick | 3773 | 23 | 6 |
| NPHA | 715 | 15 | 0 |

Baselines: We compared our method against a wide array of baselines in synthetic data generation. These include CTGAN [] and CTGAN PLUS [] (GAN-based methods), TabDDPM [] and AutoDiff [] (state-of-the-art diffusion models), AIM [] and PATE-CTGAN [] (generators with privacy guarantees), and GReaT [] (LM-based generators with transfer learning capability).

As methods that enable transfer learning, CTSyn and GReaT are first trained on the pre-train set, with the pre-trained checkpoint used as the common initialization for fine-tuning on all downstream tasks. Other methods that are unable to learn from heterogeneous tables are trained only on the fine-tuning sets with partial features and then tested on the corresponding holdout test sets. Implementation of baselines are detailed in section C

During CTSyn pre-training, we construct training batches so that each batch contains examples from the same table, with the order of columns randomly perturbed, and 15% of columns randomly dropped. This approach reduces unnecessary comparisons between rows from different tables, prevents the models from learning the order of columns rather than their features values, and creates a realistic pre-training set of heterogeneous tables.
For fine-tuning CTSyn, we train the conditional diffusion model, while freezing the pre-trained aggregator and decoders to maintain alignment in the latent space.

For CTSyn, we introduce two novel generation scheme in addition to fine-tuning:
- Conditional generation (Cond Gen): The pre-trained model generates data for downstream tasks by conditioning on the table metadata correspond to the fine-tune set.
- Conditional column augmentation (Cond Aug): From the conditionally generated latent vector, we decode not only the columns in the fine-tune set but also the other columns included in the test set. The synthetic data with augmented columns are then evaluated utilizing all columns in the test set.
These unique generation schemes, enabled by our flexible decoding structures where columns are reconstructed separately, allow CTSyn to adapt to various feature compositions in downstream tasks, without data-specific fine-tuning.

### 4.2 Statistical Fidelity

**Table 2: Statistical fidelity of synthetic tables. The best score for each dataset is shown in bold text.**
| Model | NPHA | Obesity | Diabetes | Liver | Sick | Avg Rank |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Column | Corr | Column | Corr | Column | Corr | Column | Corr | Column | Corr | Column | Corr |  |
| Real | 0.92 | 0.84 | 0.94 | 0.86 | 0.88 | 0.83 | 0.88 | 0.80 | 0.98 | 0.81 | 1.20 | 2.00 |
|  | (0.02) | (0.03) | (0.01) | (0.02) | (0.02) | (0.03) | (0.02) | (0.04) | (0.00) | (0.03) |  |  |
| CTGAN | 0.88 | 0.79 | 0.83 | 0.69 | 0.71 | 0.72 | 0.70 | 0.65 | 0.93 | 0.72 | 7.20 | 8.00 |
|  | (0.03) | (0.04) | (0.04) | (0.03) | (0.05) | (0.03) | (0.07) | (0.03) | (0.01) | (0.05) |  |  |
| CTABGANPlus | 0.93 | 0.87 | 0.85 | 0.72 | 0.78 | 0.78 | 0.77 | 0.77 | 0.91 | 0.74 | 6.40 | 5.00 |
|  | (0.01) | (0.02) | (0.03) | (0.03) | (0.05) | (0.05) | (0.03) | (0.02) | (0.02) | (0.05) |  |  |
| Autodiff | 0.82 | 0.68 | 0.71 | 0.58 | 0.60 | 0.65 | 0.60 | 0.62 | 0.75 | 0.59 | 10.00 | 10.20 |
|  | (0.04) | (0.06) | (0.08) | (0.05) | (0.08) | (0.07) | (0.07) | (0.09) | (0.04) | (0.08) |  |  |
| TabDDPM | 0.89 | 0.79 | 0.90 | 0.79 | 0.82 | 0.77 | 0.80 | 0.73 | 0.96 | 0.79 | 3.60 | 6.20 |
|  | (0.03) | (0.05) | (0.02) | (0.02) | (0.03) | (0.03) | (0.04) | (0.07) | (0.01) | (0.04) |  |  |
| AIM | 0.62 | 0.40 | 0.53 | 0.52 | 0.33 | 0.49 | 0.25 | 0.45 | 0.79 | 0.67 | 11.00 | 11.00 |
|  | (0.09) | (0.11) | (0.07) | (0.04) | (0.05) | (0.17) | (0.06) | (0.13) | (0.03) | (0.05) |  |  |
| PATECTGAN | 0.87 | 0.77 | 0.55 | 0.61 | 0.27 | 0.68 | 0.30 | 0.42 | 0.73 | 0.56 | 10.40 | 10.00 |
|  | (0.03) | (0.04) | (0.14) | (0.02) | (0.04) | (0.03) | (0.06) | (0.03) | (0.06) | (0.06) |  |  |
| GReaT | 0.82 | 0.68 | 0.86 | 0.75 | 0.80 | 0.77 | 0.81 | 0.72 | 0.36 | 0.29 | 8.20 | 8.80 |
|  | (0.05) | (0.09) | (0.03) | (0.03) | (0.04) | (0.02) | (0.03) | (0.04) | (0.00) | (0.21) |  |  |
| GReaT (Fine-tuned) | 0.84 | 0.70 | 0.89 | 0.77 | 0.81 | 0.79 | 0.82 | 0.75 | 0.37 | 0.29 | 6.80 | 7.60 |
|  | (0.06) | (0.10) | (0.02) | (0.04) | (0.04) | (0.04) | (0.02) | (0.05) | (0.01) | (0.21) |  |  |
| CTSyn (Fine-tuned) | 0.89 | 0.81 | 0.89 | 0.78 | 0.85 | 0.79 | 0.83 | 0.80 | 0.94 | 0.86 | 3.40 | 3.20 |
|  | (0.05) | (0.07) | (0.01) | (0.04) | (0.00) | (0.06) | (0.04) | (0.06) | (0.02) | (0.02) |  |  |
| CTSyn (Cond Gen) | 0.88 | 0.80 | 0.91 | 0.85 | 0.79 | 0.79 | 0.85 | 0.77 | 0.93 | 0.89 | 4.60 | 3.20 |
|  | (0.05) | (0.06) | (0.01) | (0.01) | (0.01) | (0.01) | (0.01) | (0.08) | (0.03) | (0.06) |  |  |
| CTSyn (Cond Aug) | 0.88 | 0.80 | 0.89 | 0.84 | 0.81 | 0.83 | 0.81 | 0.84 | 0.93 | 0.84 | 5.20 | 2.80 |
|  | (0.02) | (0.03) | (0.01) | (0.01) | (0.01) | (0.11) | (0.06) | (0.01) | (0.01) | (0.04) |  |  |

We evaluate the similarity between real and synthetic tables using two main metrics: marginal column distribution and column-wise correlation. For column distribution, we compute the Kolmogorov-Smirnov (KS) Test Statistics for numerical columns and Total Variation Distance (TVD) for categorical columns. Specifically, we use $1-\text{KS}$ and $1-\text{TVD}$ to ensure that higher values indicate better similarity. For column-wise correlation, we use Pearson’s correlation coefficient for numerical columns and contingency similarity for categorical columns. For correlations between numerical and categorical columns, we first transform the continuous values into percentiles and then apply the contingency score. We calculate the absolute difference between the correlation scores of each pair of columns in the real and synthetic data, then compute $1-\frac{1}{2}\times$ the average of all pair-wise correlations.

Table 2 shows the average similarity in column distribution and correlation. CTSyn showcases superior performance in both the fine-tuned and conditional generation configurations on par with all state-of-the-art baselines. Notably, the fine-tuned version of CTSyn achieves the highest similarity in column distribution, while the conditional generation versions preserved the highest column-wsie correlation. This highlights CTSyns robust generalization capabilities without prior specific training.
Note that Autodiff method perform poorly, especially on smaller datasets, indicating potential overfitting issues arises from its data-specific autoencoder and reinforces the need for transferable decoders like ours for latent table generation.
Additional distance-based metrics are shown in table 6.

### 4.3 Machine Learning Utility

**Table 3: Machine learning utility of synthetic tables.**
| Model | NPHA | Obesity | Diabetes | Liver | Sick | Avg Rank |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Acc | F1 | Acc | F1 | Acc | F1 | Acc | F1 | Acc | F1 | Acc | F1 |  |
| Real | 0.39 | 0.36 | 0.56 | 0.54 | 0.65 | 0.64 | 0.65 | 0.64 | 0.84 | 0.86 | 4.20 | 3.40 |
|  | (0.04) | (0.03) | (0.10) | (0.10) | (0.03) | (0.04) | (0.03) | (0.03) | (0.02) | (0.02) |  |  |
| CTGAN | 0.40 | 0.36 | 0.14 | 0.12 | 0.61 | 0.57 | 0.59 | 0.54 | 0.80 | 0.79 | 8.00 | 8.20 |
|  | (0.05) | (0.04) | (0.02) | (0.02) | (0.05) | (0.06) | (0.05) | (0.05) | (0.02) | (0.02) |  |  |
| CTABGANPlus | 0.39 | 0.35 | 0.20 | 0.17 | 0.56 | 0.55 | 0.59 | 0.57 | 0.81 | 0.80 | 9.20 | 8.60 |
|  | (0.03) | (0.03) | (0.05) | (0.04) | (0.05) | (0.04) | (0.05) | (0.05) | (0.05) | (0.05) |  |  |
| Autodiff | 0.37 | 0.34 | 0.21 | 0.17 | 0.58 | 0.56 | 0.58 | 0.54 | 0.79 | 0.80 | 10.20 | 9.20 |
|  | (0.06) | (0.04) | (0.03) | (0.04) | (0.07) | (0.06) | (0.08) | (0.09) | (0.10) | (0.08) |  |  |
| TabDDPM | 0.41 | 0.36 | 0.47 | 0.44 | 0.61 | 0.61 | 0.63 | 0.62 | 0.82 | 0.82 | 5.40 | 5.20 |
|  | (0.05) | (0.03) | (0.08) | (0.08) | (0.05) | (0.05) | (0.03) | (0.04) | (0.03) | (0.04) |  |  |
| AIM | 0.37 | 0.32 | 0.15 | 0.08 | 0.53 | 0.45 | 0.53 | 0.41 | 0.83 | 0.83 | 10.40 | 10.80 |
|  | (0.09) | (0.08) | (0.02) | (0.02) | (0.10) | (0.11) | (0.10) | (0.10) | (0.07) | (0.06) |  |  |
| PATECTGAN | 0.39 | 0.35 | 0.14 | 0.07 | 0.50 | 0.40 | 0.58 | 0.48 | 0.86 | 0.85 | 10.00 | 10.00 |
|  | (0.05) | (0.03) | (0.03) | (0.03) | (0.08) | (0.09) | (0.07) | (0.07) | (0.08) | (0.07) |  |  |
| GReaT | 0.39 | 0.35 | 0.21 | 0.19 | 0.59 | 0.56 | 0.60 | 0.54 | 0.91 | 0.89 | 6.80 | 7.60 |
|  | (0.04) | (0.03) | (0.05) | (0.05) | (0.05) | (0.05) | (0.05) | (0.06) | (0.05) | (0.05) |  |  |
| GReaT (Fine-tuned) | 0.40 | 0.36 | 0.44 | 0.41 | 0.60 | 0.55 | 0.58 | 0.52 | 0.91 | 0.91 | 6.20 | 6.60 |
|  | (0.06) | (0.05) | (0.08) | (0.08) | (0.04) | (0.03) | (0.05) | (0.05) | (0.01) | (0.01) |  |  |
| CTSyn (Fine-tuned) | 0.49 | 0.42 | 0.49 | 0.48 | 0.63 | 0.61 | 0.61 | 0.61 | 0.89 | 0.89 | 3.80 | 3.60 |
|  | (0.05) | (0.06) | (0.13) | (0.12) | (0.05) | (0.04) | (0.11) | (0.11) | (0.05) | (0.03) |  |  |
| CTSyn (Cond Gen) | 0.41 | 0.35 | 0.54 | 0.52 | 0.68 | 0.65 | 0.63 | 0.61 | 0.93 | 0.91 | 2.40 | 3.40 |
|  | (0.03) | (0.01) | (0.13) | (0.12) | (0.01) | (0.01) | (0.00) | (0.00) | (0.01) | (0.00) |  |  |
| CTSyn (Cond Aug) | 0.43 | 0.41 | 0.68 | 0.67 | 0.70 | 0.69 | 0.65 | 0.64 | 0.92 | 0.91 | 1.40 | 1.60 |
|  | (0.04) | (0.01) | (0.10) | (0.02) | (0.04) | (0.01) | (0.01) | (0.02) | (0.01) | (0.03) |  |  |

To evaluate the utility of synthetic data for training machine learning models, we fit the following classifiers: logistic regression, Naive Bayes, decision tree, random forest, XGBoost [], and CatBoost []. The models trained on different synthetic tables are then tested on the holdout test set following the canonical Train on Synthetic and Test on Real (TSTR) framework.

Table 3 reports the average classification accuracy and micro-averaged F1 scores across models. Both the fine-tuned and conditional generation versions of CTSyn exhibit superior performance compared to other SOTA baselines. CTSyn also outperformed both pre-trained and non-pre-trained versions of GReaT. While pre-training improved performance for GReaT, its utility remains lower than both CTSyn and prior SOTA baselines such as TabDDPM indicating the inefficiency of pure text representation for tabular transfer learning.

Moreover, the conditional generation and column augmentation versions of CTSyn consistently achieve accuracy and F1 scores on par with or higher than the original fine-tune sets. This exceptional performance underscores the unique ability of CTSyn to augment datasets leveraging prior knowledge, without data-specific fine-tuning that can lead to overfitting. This also allows CTSyn to surpass traditional models by making more efficient use of the provided data via its flexible augmentation on the column dimension, broadening the scope of tabular generative models.

### 4.4 Diversity and Privacy

**Table 4: Distance to closest record (DCR) and proportion closer to testing (PCT) scores.**
| Model | NPHA | Obesity | Diabetes | Liver | Sick | Avg Rank |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| PCT | DCR | PCT | DCR | PCT | DCR | PCT | DCR | PCT | DCR | PCT | DCR |  |
| CTGAN | 0.92 | 0.97 | 0.82 | 2.80 | 0.80 | 16.29 | 0.83 | 21.92 | 0.83 | 6.10 | 6.60 | 6.80 |
|  | (0.04) | (0.32) | (0.04) | (1.77) | (0.07) | (10.34) | (0.09) | (16.77) | (0.03) | (4.76) |  |  |
| CTABGANPlus | 0.96 | 0.75 | 0.84 | 2.70 | 0.85 | 18.53 | 0.84 | 60.00 | 0.83 | 8.10 | 3.60 | 6.00 |
|  | (0.02) | (0.15) | (0.03) | (1.61) | (0.04) | (10.34) | (0.05) | (41.52) | (0.03) | (5.37) |  |  |
| Autodiff | 0.73 | 0.98 | 0.78 | 4.66 | 0.67 | 19.46 | 0.52 | 63.50 | 0.67 | 18.02 | 9.60 | 3.80 |
|  | (0.09) | (0.19) | (0.09) | (3.71) | (0.20) | (7.89) | (0.25) | (172.26) | (0.38) | (15.77) |  |  |
| TabDDPM | 0.64 | 0.21 | 0.56 | 1.51 | 0.21 | 2.72 | 0.30 | 5.07 | 0.77 | 5.15 | 10.40 | 10.60 |
|  | (0.20) | (0.17) | (0.08) | (1.30) | (0.07) | (1.29) | (0.16) | (2.79) | (0.03) | (2.75) |  |  |
| AIM | 0.91 | 1.29 | 0.85 | 81.59 | 0.83 | 63.39 | 0.91 | 107.10 | 0.85 | 56.05 | 4.00 | 1.20 |
|  | (0.14) | (0.56) | (0.17) | (16.32) | (0.29) | (15.70) | (0.24) | (27.49) | (0.13) | (23.55) |  |  |
| PATECTGAN | 0.93 | 0.98 | 0.92 | 23.33 | 0.84 | 46.36 | 0.95 | 67.48 | 0.89 | 4.58 | 2.40 | 4.80 |
|  | (0.05) | (0.37) | (0.11) | (22.09) | (0.33) | (34.13) | (0.23) | (47.65) | (0.24) | (2.96) |  |  |
| GReaT | 0.89 | 1.19 | 0.80 | 2.26 | 0.73 | 8.85 | 0.65 | 24.41 | 0.73 | 7.11 | 8.40 | 6.20 |
|  | (0.06) | (0.21) | (0.07) | (1.44) | (0.09) | (2.83) | (0.11) | (32.08) | (0.05) | (0.28) |  |  |
| GReaT (Fine-tuned) | 0.90 | 1.11 | 0.70 | 1.54 | 0.56 | 5.95 | 0.56 | 11.18 | 0.60 | 6.65 | 9.60 | 8.00 |
|  | (0.09) | (0.13) | (0.08) | (0.93) | (0.10) | (1.51) | (0.11) | (6.89) | (0.05) | (0.41) |  |  |
| CTSyn (Fine-tuned) | 0.94 | 0.89 | 0.82 | 1.70 | 0.84 | 12.69 | 0.89 | 34.31 | 0.85 | 4.88 | 3.80 | 8.00 |
|  | (0.04) | (0.53) | (0.04) | (1.49) | (0.04) | (9.81) | (0.05) | (24.40) | (0.00) | (1.90) |  |  |
| CTSyn (Cond Gen) | 0.94 | 0.82 | 0.83 | 1.88 | 0.80 | 5.29 | 0.83 | 19.89 | 0.87 | 7.24 | 4.20 | 8.20 |
|  | (0.03) | (0.55) | (0.01) | (1.71) | (0.07) | (1.04) | (0.03) | (10.58) | (0.03) | (3.31) |  |  |
| CTSyn (Cond Aug) | 0.96 | 1.86 | 0.82 | 3.83 | 0.85 | 29.55 | 0.84 | 90.44 | 0.85 | 19.28 | 3.40 | 2.40 |
|  | (0.05) | (0.41) | (0.02) | (1.23) | (0.03) | (0.99) | (0.03) | (6.31) | (0.04) | (4.89) |  |  |

We evaluate the diversity and privacy of the synthesized data using two metrics: L2 Distance to Closest Real record (DCR) for each synthetic dataset, and the Proportion of synthetic examples Closer to the Test set (PCT) compared with the fine-tune set on which the synthesizer is trained []. Smaller DCR or PCT values indicate that synthetic data points are too close to the training set, raising concerns about data copying. A powerful generator can easily copy its training data, achieving spuriously high fidelity and utility without actual generation, harming the generalization of downstream ML models and breaching privacy of individual data points.

Table 4 shows the diversity scores. CTSyn achieved significantly higher PCT and DCR scores compared with state-of-the-art baselines like TabDDPM, indicating that the data synthesized by CTSyn are more distinct from real data points, while the baselines show strong evidence of data copying. The high PCT scores of CTSyn are comparable to AIM and PATE-CTGAN, which are models with built-in Differential Privacy (DP) mechanisms to prevent such closeness. However, these methods have shown poor fidelity and utility in previous sections.
Therefore, we observe that CTSyn achieves a "Sweet Spot" by balancing the utility of synthetic data with diversity and privacy. This provides more evidence of pre-training acting as regularization.

We further visualize the diversity of synthesized data via data support. Figure 2 shows the 2D-tSNE projection of the pre-training set, fine-tune set A, and various synthetic datasets for the Obesity dataset. We observe that, among all the synthesizers, CTSyn produces the most diverse data distribution. CTSyn’s synthetic data not only covers the fine-tune set but also expands into regions covered by the pre-training set. This explains the source of the surprising utility of our method: the diverse pre-training data serves as implicit regularization, leading to greater generalization.

Figure: Figure 2: T-sne plot of obesity dataset from different synthesizers.
Refer to caption: extracted/5650322/figures/tsne.png

### 4.5 Ablation Study

We examine the significance of pre-training and task-specific decoders in the fine-tune setting of CTSyn. For effect of pre-training, we alternatively train the diffusion model and type-specific decoders only on fine-tune sets. For task-specific decoders, we replace type-specific decoders with an MLP decoder that reconstructs feature vectors and is trained solely on the fine-tune set. We present the utility and diversity results for each altered setting in Table 5 for the Synthesizing Diabetes dataset. Both alternative settings resulted in lower utility. Replacing the pre-trained decoders with data-specific decoders significantly increases data copying with lower PCT and DCR values. These findings indicate that pre-training enhances data diversity and mitigates the overfitting risk associated with data-specific decoding.

**Table 5: Effect of model components on Diabete fine-tune set A.**
| Pre-train Diffusion | Decoder | Pre-train Decoder | Acc | F1 | PCT | DCR |
| --- | --- | --- | --- | --- | --- | --- |
| $\checkmark$ | Type-specific | $\checkmark$ | 0.63 | 0.61 | 0.84 | 12.69 |
| $\times$ | Type-specific | $\checkmark$ | 0.60 | 0.58 | 0.80 | 2.80 |
| $\checkmark$ | Type-specific | $\times$ | 0.64 | 0.57 | 0.79 | 8.10 |
| $\checkmark$ | MLP | $\times$ | 0.61 | 0.57 | 0.36 | 4.15 |

## 5 Conclusion

In this paper, we introduced CTSyn, a pioneering framework within the realm of Generative Foundation Models (GFMs) for tabular data. Through extensive experimentation with real data, we demonstrated that CTSyn effectively leverages knowledge from diverse pre-trained tables to enhance synthetic data utility across various downstream datasets. To the best of our knowledge, our method is the first to consistently demonstrate a utility boost over real training data in downstream tasks, thereby paving the way for overcoming significant challenges in tabular data augmentation using deep generative models.

## Appendix A Broader Impact

A foundational table generator like CTSyn can significantly enhance various application domains, especially where real data is scarce, sensitive, or expensive to obtain, by providing high-quality synthetic tabular data. In healthcare, for example, CTSyn can generate synthetic patient records that maintain statistical fidelity to real data, enhancing the robustness and generalization ability of machine learning models by augmenting datasets with synthetic data.

CTSyn also facilitates data collaboration between parties, such as advertising companies and social media websites. Through conditional generation, CTSyn can augment one party’s dataset with essential columns for business analysis without violating privacy laws that prohibit linking individual data points across parties.

However, CTSyn’s performance relies heavily on clean, large-scale tabular datasets. The quality of generated data depends on the training data, and any biases or errors can be propagated. This risk can be mitigated by carefully curating high-quality datasets for different domains. Additionally, despite pre-training reducing memorization of downstream data, individuals included in the pre-training data still face privacy risks, complicating the safe gathering of large datasets. This can be mitigated by properly anonymizing or adding noise to public pre-training datasets to ensure privacy before they are used for pre-training.

## Appendix B Network Structures and Training

Number Auto-Encoder:

We use an auto-encoder to learn a latent space for quantiles uniformly distributed on Uniform(0,1). The encoder-decoder AE structure can be formally described as:

$$ $h_{0}=ReLU(FC_{1\to 1024}(x))$ $$

$$ $h_{1}=Tanh(FC_{1024\to 768}(h_{0}))\cdot 10$ $$

For the decoder:

$$ $d_{0}=ReLU(FC_{768\to 1024}(h_{1}))$ $$

$$ $d_{1}=FC_{1024\to 1}(d_{0})$ $$

For each epoch in pre-training, we sample $B=1024$ numbers from $\text{Uniform}(0,1)$, which match the range of transformed quantiles of numerical columns. Then the model is trained to reconstruct the input numbers with Mean-Squared Error(MSE) loss. Once pre-trained, the encoder part is used for projecting quantile-normalized values in all tables and tasks, to ensure consistency of embedding.

Aggregator and Decoders

For aggregator and decoders, we apply a Perceive Resampler [] that learns latent vector $\bm{v}\in\mathbb{R}^{d_{\text{agg}}}$ that iteratively cross-attend to embeddings of the row features $E\in\mathbb{R}^{(2D+1)\times d_{\text{LM}}}$. Applying the same formulation as in [], the learnable latent attend to both themselves and the input representation in each attention layer:

$$ $\bm{v}=\bm{v}+\text{MHA}(q=\bm{v},\text{kv}=[\bm{v};\bm{E}])$ $$

where $\text{MHA}(\cdot)$ is the multi-head attention operation with queries $q$ and keys/values kv. After each multi-head attention layer, a feedforward layer is applied to the latent representations.

For decoders, we apply one fully connected linear layer to downsize LM encoding of table metadata to the same dimension as $M_{\text{agg}}$. For numerical decoder, we apply one linear layer to map last layer representation to a 1 dimensional real number.

Both aggregator and decoders used a training batch size of 128, learning rate = $0.0005$, a cosine annealing schedule for learning rate and 1200 training epochs.

ResNet MLP

To model the reverse diffusion process, we use a Residual MLP architecture:

$$ $\text{ResMLPDiffusion}(x,t,y,\text{uncon_rate})=\text{OutputLinear}(\text{ ResMLPBlock}(\ldots(\text{ResMLPBlock}(x))))$ $$

Each ResMLPBlock consists of:

$$ $\text{ResMLPBlock}(x,t,y)=\text{SiLU}(\text{ResidualBlock}(x)$ $$

$$ $+\text{LinearBlock}(\text{TimestepEmbedding}(t))$ $$

$$ $+\text{LinearBlock}(y))$ $$

For the input, timestep, and conditional vector embeddings:

$$ $x=\text{SiLU}(\text{InputLinear}(x_{\text{in}}))$ $$

$$ $t_{\text{emb}}=\text{Linear}(\text{SiLU}(\text{Linear}(\text{SinTimeEmb}(t))))$ $$

$$ $y_{\text{emb}}=\text{SiLU}(\text{YLinear}(y))$ $$

The training setup includes both pre-training and fine-tuning phases. We use a batch size of 512 and 2500 timesteps. The Adam optimizer is employed with an initial learning rate of $5\times 10^{-4}$. The pre-training phase consists of 50000 epochs, while the fine-tuning phase is conducted for 10000 epochs.

## Appendix C Baselines Implementation

CTGAN: We use the official implementation at https://github.com/sdv-dev/CTGAN. We use embedding dimension =128, generator dimension=(256,256), discriminator dimension =(256,256), generator learning rate=0.0002, generator decay =0.000001, discriminator learning rate =0.0002, discriminator decay =0.000001, batch size=500, training epoch = 300, discriminator steps=1, pac size = 5.

CTGAN-Plus: We used the official implementation at: https://github.com/Team-TUD/CTAB-GAN-Plus. We used default parameters: class dimensions =(256, 256, 256, 256), random dimensions=100, 64 channels, l2scale=1e-5, batch size=500, training epoch = 150.

Autodiff: We use the official implementation at https://github.com/UCLA-Trustworthy-AI-Lab/AutoDiffusion with default hyperparameters.

TabDDPM: We used the official implementation at https://github.com/yandex-research/tab-ddpm. We used 2500 diffusion steps, 10000 training epochs, learning rate = 0.001, weight decay = 1e-05, batch size = 1024.

AIM: We use the code implementation at https://github.com/ryan112358/private-pgm, with default parameters: epsilon=3,delta=1e-9,max model size=80

PATE-CTGAN: We adapted the implementation posted at: https://github.com/opendp/smartnoise-sdk/blob/main/synth/snsynth, which combines the PATE [] learning framework with CTGAN. We use epsilon = 3, 5 iterations for student and teacher network, and the same value for other parameters which are shared with CTGAN.

GReaT: We used the official implementation at [https://github.com/kathrinse/be_great/tree/main](https://github.com/kathrinse/be_great/tree/main). We used a batch size of 64 and save steps of 400000. We following the pre-training pipeline outlined in []. During pre-training, we began with a randomized distilgpt2 model. For each pre-training dataset, we iteratively loaded the latest model, fitted the model on the new dataset, and saved the model to be used for the next iteration. We used 50 epochs for the health model and 200 epochs for the out-of-domain model. For finetuning, we fitted the pre-trained model on only one dataset using 200 epochs. The dataset used in finetuning was the dataset we wished to emulate during synthesis. For reference, we also fitted a newly randomized model on the data alone to serve as a base metric. During generation, we synthesized the same number of samples as the finetune dataset.

## Appendix D Datasets

The link to datasets used is shown below:

NPHA: https://archive.ics.uci.edu/dataset/936/national+poll+on+healthy+aging+(npha)

Obesity: https://www.kaggle.com/code/mpwolke/obesity-levels-life-style

Diabetes: https://archi
ve.ics.uci.edu/dataset/34/diabetes

India Liver Patient : https://www.kaggle.com/datasets/uciml/indian-liver-patient-records?resource=download

Sick: [https://www.openml.org/search?type=data&sort=runs&id=38&status=active](https://www.openml.org/search?type=data&sort=runs&id=38&status=active)

## Appendix E Statistical Similarity Metrics

We compute additional statistical similarity metrics for marginal column distributions: Wasserstein distance for numerical columns and Jensen-Shannon divergence for categorical columns. The results are shown in table 6. We observed that CTSyn achieved lower ranking in these distance metrics compared with SoTA baselines such as TabDDPM, indicating closer distance to real column distributions.

**Table 6: Average Wasserstein Distance and Jansen-Shannon Distance between columns of real and synthetic tables. Lower ranks indicate better similarity.**
| Model | NPHA | Obesity | Diabetes | Liver | Sick | Avg Rank |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| WS | JS | WS | JS | WS | JS | WS | JS | WS | JS | WS | JS |  |
| Real | 0.48<br>(0.07) | 0.48<br>(0.07) | 0.57<br>(0.04) | 0.57<br>(0.04) | 0.48<br>(0.03) | 0.48<br>(0.03) | 0.55<br>(0.06) | 0.55<br>(0.06) | 0.40<br>(0.05) | 0.40<br>(0.05) | 7.20 | 7.20 |
| CTGAN | 0.48<br>(0.07) | 0.48<br>(0.07) | 0.57<br>(0.04) | 0.57<br>(0.04) | inf<br>(nan) | inf<br>(nan) | 0.53<br>(0.08) | 0.53<br>(0.08) | 0.42<br>(0.07) | 0.42<br>(0.07) | 5.30 | 5.30 |
| CTABGANPlus | 0.47<br>(0.07) | 0.47<br>(0.07) | 0.53<br>(0.05) | 0.53<br>(0.05) | 0.49<br>(0.03) | 0.49<br>(0.03) | 0.54<br>(0.06) | 0.54<br>(0.06) | 0.40<br>(0.04) | 0.40<br>(0.04) | 8.40 | 8.40 |
| Autodiff | 0.51<br>(0.05) | 0.51<br>(0.05) | 0.55<br>(0.04) | 0.55<br>(0.04) | 0.52<br>(0.06) | 0.52<br>(0.06) | 0.57<br>(0.09) | 0.57<br>(0.09) | 0.46<br>(0.06) | 0.46<br>(0.06) | 4.80 | 4.80 |
| TabDDPM | 0.50<br>(0.06) | 0.50<br>(0.06) | 0.57<br>(0.04) | 0.57<br>(0.04) | 0.48<br>(0.04) | 0.48<br>(0.04) | 0.54<br>(0.06) | 0.54<br>(0.06) | 0.42<br>(0.07) | 0.42<br>(0.07) | 5.40 | 5.40 |
| AIM | 0.54<br>(0.06) | 0.54<br>(0.06) | 0.57<br>(0.04) | 0.57<br>(0.04) | 0.48<br>(0.05) | 0.48<br>(0.05) | 0.54<br>(0.08) | 0.54<br>(0.08) | 0.47<br>(0.07) | 0.47<br>(0.07) | 4.80 | 4.80 |
| PATECTGAN | 0.50<br>(0.06) | 0.50<br>(0.06) | 0.56<br>(0.03) | 0.56<br>(0.03) | inf<br>(nan) | inf<br>(nan) | 0.51<br>(0.08) | 0.51<br>(0.08) | 0.44<br>(0.04) | 0.44<br>(0.04) | 6.10 | 6.10 |
| GReaT | 0.44<br>(0.11) | 0.44<br>(0.11) | 0.55<br>(0.03) | 0.55<br>(0.03) | 0.48<br>(0.01) | 0.48<br>(0.01) | 0.53<br>(0.07) | 0.53<br>(0.07) | 0.74<br>(0.01) | 0.74<br>(0.01) | 8.00 | 8.00 |
| GReaT (Finetuned) | 0.48<br>(0.08) | 0.48<br>(0.08) | 0.56<br>(0.04) | 0.56<br>(0.04) | 0.46<br>(0.02) | 0.46<br>(0.02) | 0.51<br>(0.08) | 0.51<br>(0.08) | 0.75<br>(0.01) | 0.75<br>(0.01) | 7.80 | 7.80 |
| CTSyn (Finetuned) | 0.45<br>(0.07) | 0.45<br>(0.07) | 0.58<br>(0.05) | 0.58<br>(0.05) | 0.49<br>(0.04) | 0.49<br>(0.04) | 0.56<br>(0.11) | 0.56<br>(0.11) | 0.39<br>(0.06) | 0.39<br>(0.06) | 6.20 | 6.20 |
| CTSyn (Cond Gen) | 0.51<br>(0.06) | 0.51<br>(0.06) | 0.58<br>(0.04) | 0.58<br>(0.04) | 0.44<br>(0.04) | 0.44<br>(0.06) | 0.53<br>(0.09) | 0.53<br>(0.09) | 0.40<br>(0.06) | 0.40<br>(0.06) | 6.60 | 6.60 |
| CTSyn (Cond Aug) | 0.52<br>(0.03) | 0.52<br>(0.02) | 0.55<br>(0.04) | 0.55<br>(0.02) | 0.43<br>(0.02) | 0.43<br>(0.03) | 0.63<br>(0.02) | 0.63<br>(0.02) | 0.38<br>(0.03) | 0.38<br>(0.02) | 7.40 | 7.40 |

## Appendix F Cross-Domain Dataset Results Performance

We further validates the effectiveness of our method by performin the same pre-training/fine-tuning pipeline tables across different domains. The datasets tested and their summary statistics are shown in table 7:

**Table 7: Summary statistics of cross-domain datasets.**
| Dataset | Rows | Categorical | Numerical | Domain |
| --- | --- | --- | --- | --- |
| [Abalone](https://archive.ics.uci.edu/dataset/1/abalone) | 4177 | 1 | 8 | Biology |
| [Churn Modeling](https://www.kaggle.com/datasets/shrutimechlearn/churn-modelling?resource=download) | 10000 | 3 | 8 | Finance |
| [Shoppers](https://www.kaggle.com/datasets/henrysue/online-shoppers-intention) | 12330 | 8 | 10 | Marketing |

We report the machine learning utility in table 8. We notice that CTSyn still consistently improve synthetic data generation with conditional generation, even for regression tasks.

**Table 8: Machine learning utility of non-healthcare datasets.**
| Model | Abalone | Churn | Shoppers | Avg Rank |
| --- | --- | --- | --- | --- |
|  | $\text{Adjusted}R^{2}(\uparrow)$ | $F1(\uparrow)$ | $F1(\uparrow)$ |  |
| Real | 0.18 | 0.76 | 0.72 | 3.3 |
|  | (0.05) | (0.05) | (0.08) |  |
| CTGAN | -0.33 | 0.69 | 0.66 | 10 |
|  | (0.59) | (0.02) | (0.02) |  |
| CTABGANPlus | -0.09 | 0.70 | 0.66 | 9 |
|  | (0.17) | (0.02) | (0.05) |  |
| Autodiff | -1.26 | 0.68 | 0.63 | 11.3 |
|  | (1.53) | (0.14) | (0.13) |  |
| TabDDPM | 0.13 | 0.74 | 0.73 | 4.7 |
|  | (0.06) | (0.04) | (0.06) |  |
| AIM | -0.02 | 0.71 | 0.69 | 8 |
|  | (0.10) | (0.06) | (0.03) |  |
| PATECTGAN | -7.76 | 0.62 | 0.71 | 10.3 |
|  | (0.19) | (0.08) | (0.08) |  |
| GReaT | -0.28 | 0.72 | 0.71 | 7.7 |
|  | (0.13) | (0.05) | (0.04) |  |
| GReaT (Finetuned) | 0.15 | 0.75 | 0.73 | 3.7 |
|  | (0.13) | (0.05) | (0.03) |  |
| CTSyn (Finetuned) | 0.10 | 0.75 | 0.74 | 4 |
|  | (0.19) | (0.04) | (0.04) |  |
| CTSyn (Cond Gen) | 0.24 | 0.74 | 0.75 | 3 |
|  | (0.19) | (0.04) | (0.03) |  |
| CTSyn (Cond Aug) | 0.29 | 0.76 | 0.80 | 1 |
|  | (0.02) | (0.04) | (0.02) |  |

## Appendix G Conditional Generation As Classification

We further test the conditional generation ability of our model by incorporating latent embedding of a subset of row features in the conditions. For each sample $\bm{v_{i}}$, we now create the corresponding condition $y_{i}$ by concatenating the the table context embedding $e_{m}$ with feature subset embedding $\bm{v_{i}^{+}}=f(E_{i}^{+})$ and $\bm{v_{i}^{-}}=f(E_{i}^{-})$, where $E_{i}^{+}$ and $E_{i}^{-}$ are created by masking the embedding of target columns‘s value and feature columns value in $E_{i}$ with a fixed vector of -1. We train the model on the pooled pre-train dataset, and test on the holdout test sets. During inference, we perform conditional generation and use type-specific decoder to decode value of the target column from the generated latent vector. We treat such conditional generation as a classification task.

Table 9 compares the classification performance using regular classifiers vs using CTSyn to perform conditional generation. Our model achieved similar F1 score as state-of-the-art classifier across dataset. Note that while the baseline classifiers are trained in a data-specific manner, our model is pre-trained across datasets and perform all such classifications with the same model. This showcases the potential of generative foundation model in other tabular tasks such as prediction and imputation.

**Table 9: Classification F1 score with conditional generation and regular classifer models.**
| Model | Obesity | Diabetes | Sick | Liver 4 | NPHA |
| --- | --- | --- | --- | --- | --- |
| Decision Tree | 0.92 | 0.72 | 0.99 | 0.65 | 0.38 |
| Random Forest | 0.93 | 0.75 | 0.98 | 0.62 | 0.36 |
| XGBoost | 0.95 | 0.77 | 0.98 | 0.64 | 0.39 |
| CTSyn | 0.86 | 0.82 | 0.90 | 0.59 | 0.42 |

## Appendix H Computation Cost

The experiments are performed on a Amazon AWS EC2 g5.4xlarge instance with an A10G tensor core GPU, 24 GB GPU Memory, 64GB RAM. The pre-training time is 24.5 hours for aggregator and decoders and 4 hrs for conditional diffusion model. The average fine-tuning time of conditional diffusion model is 6 minutes.

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## Peer Reviews

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: Please address the weaknesses above.
soundness: 3
strengths: 1. While there have been prior works employing auto-encoders + latent diffusion models towards tabular data synthesis (e.g. https://arxiv.org/abs/2310.09656), prior works dealing with heterogenous table synthesis have been limited.
2. The authors provide good comparison against baselines on a good range of datasets -- for fidelity, privacy and ML utility of generated data.
summary: The authors propose CTSyn, specifically targeting generating heterogeneous tables. The author propose to do this by first using a cross table VAE, which can embed tables with different types of rows and projects them in a common latent space. Subsequently, they employ a DDPM based diffusion model (With classifier free guidance via a pre-trained LM) to generate samples for different types of tables. They also show the benefits of pre-training on a large number of diverse tables -- so as to serve as a starting point for different downstream tasks. The authors present results on multiple downstream tabular datasets with classification and regression tasks - and compare with multiple baselines -- with regard to fidelity, ML utility, and privacy.
weaknesses: 1. While a common latent space across tables provides a strategy to work on heterogeneous tables, it certainly limits the ability to interpret what the embeddings in the space mean - and the authors have not studied this aspect (to clarify, this is different from the privacy plots)
2. The pre-trained LM to emit embeddings for rows - individually for each column type, while preserving tabular structure - raises questions about scalability to enterprise tables - which have thousands of columns associated with each table (and can become even bigger due to joins, lineage additions, etc). Since this directly impacts the dimension (Eq 1, Page 4) - it can have an impact on the representative power when reduced to a common low dimensional space (with tables with much smaller number of columns)
3. Many tables often have short form/ abbreviated or cryptic tabular headers - where the tokenizer of the pre-trained LM can suffer - the authors can potentially add a study on this.

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 3
questions: 1. As part of the ablation study, I am also interested in seeing the results of experiments with only the column name condition applied.
2. While reviewing the provided code in the supplementary material, I encountered issues running vae.sh smoothly. Would it be possible to provide an updated .sh script that can reliably reproduce the main experimental results or specify the exact package versions used? Thank you for your help in ensuring reproducibility.
soundness: 3
strengths: A strength of this work is the successful application of a straightforward approach to map embedding vectors of categorical variables back to their original space. Although simple, this method effectively demonstrates that returning to the original categorical space can be achieved without complex transformations, providing a useful baseline for handling categorical data embeddings.
summary: This paper introduces CTSyn, a foundational model designed to generate heterogeneous tabular data. CTSyn leverages an autoencoder that consolidates diverse tables into a unified latent space and reconstructs data based on the provided table schema embedding, allowing it to adapt dynamically to various table formats. Through large-scale pre-training, CTSyn outperforms existing data synthesizers and demonstrates superior performance compared to real data in low-data scenarios.
weaknesses: A limitation of this work is that it primarily proposes a method for handling individual variables within a framework similar to LSGM [1] that trains a diffusion model in latent space. As such, the approach lacks substantial novelty and may have limited impact, given that it focuses on variable handling within an established generative model framework rather than introducing fundamentally new techniques.

Minors. Typos in line 129 (specific) and 266 (The)

[1] Vahdat, Arash, Karsten Kreis, and Jan Kautz. "Score-based generative modeling in latent space." Advances in neural information processing systems 34 (2021): 11287-11302.

---

confidence: 4
contribution: 2
initial_rating: 6
presentation: 3
questions: 1. Why are `free text` and `date-time` containing tables dropped (line 280)? Does this have to do with the inability of the existing pipeline to encode linearly increasing data (e.g., dates / times) or was there some other reasoning?
2.  How was PE generated to be employed with different tables? Although the motivation of column order invariance is clear in the tabular data generation context, what is the intuition behind treating column embeddings and positional encoding as substitutes, i.e., could they not have complementary strengths (e.g., could PEs be designed in a way to encode information not captured in column embeddings, table metadata embedding?) due to which the model might benefit from usage of both PE, col. embeddings in conjunction with metadata embeddings?
3. How does the proposed CTSyn method perform in the context of missing column values in the training / fine-tuning tables? Has this investigation been conducted?
4. What is the intuition behind the result in Table 2a where F1 scores achieved by a classifier trained on CTSyn data outperforms the performance of a classifier trained on real data?
soundness: 3
strengths: - The paper is well-written and the proposed technique is detailed clearly. 
- The results clearly demonstrate the prowess of CTSyn in terms of matching the training data at least as captured by column-wise statistical metrics (Table 2). 
- Figure 2 and Table 3 demonstrate the ability of CTSyn to maintain privacy of training data (compared to other non differentially-private synthetic tabular data generators) while still learning useful representations. This demonstrates that the model is capable of balancing learning rich / accurate representations of the tabular data without replicating training data.
summary: Authors propose Cross Table Synthesizer (CTSyn), a tabular data generation pipeline that leverages diffusion models and variational autoencoders to encode and generate data from diverse types of tables. Specifically, CTSyn comprises a pre-processing step where the table meta-data, table column names and column values are all embedded using Language Models (and quantile transformer in the case of continuous column values) into a common embedding space. Each table row is then represented using the meta-data, column-name and column-value embedding vectors. This sequence of embeddings is supplied to a $\beta$-variational autoencoder ($\beta$-VAE) for embedding multiple diverse types of tables in a common embedding space. Finally, a diffusion model is trained (conditioned upon the latent representation output from the encoder in the $\beta$-VAE) to generate synthetic table data. Results demonstrate that synthetic data generated by the proposed technique achieves good statistical similarity (evaluated using column-wise metrics) to real data. Further, results also demonstrate that the representation learned by CTSyn is statistically similar to the training data while not exactly replicating the training data. Overall, the experimental comparison to baselines and research questions investigated demonstrate the prowess of the proposed synthetic tabular data generation technique.
weaknesses: - The training process employing a diffusion model requires costly pre-training and fine-tuning hence scaling the modeling pipeline to large tables (e.g., 100s of columns, millions of rows) may be challenging.

- One crucial facet of the paper that is lacking clarification is a description of the meta-data for the various tables employed. 

- Further, as the current model is termed as a foundation model for tabular data generation, it is crucial to demonstrate its effectiveness on noisy training / fine-tuning tabular data. The noise-free nature of datasets (at least during fine-tuning) cannot be guaranteed and an investigation of the robustness of the proposed technique to noisy training data is necessary but not presented.

---

confidence: 5
contribution: 2
initial_rating: 6
presentation: 4
questions: - The statement *"synthesizers cannot add information not included in the original training data"* may not fully capture the recent advances in synthetic data generation that utilize pre-trained LLMs for transfer learning. Specifically, methods like TabTab and LaTable, which are pre-trained on extensive tabular datasets, leverage LLMs' vast prior knowledge, extending the potential of data generation beyond what’s strictly in the training dataset. This aligns with approaches like GReaT, which explicitly incorporate pre-trained LLMs to enable effective transfer learning across tabular domains. To further clarify the novelty of CTSyn, it would be helpful if the authors addressed these points, including a comparison to methods that already exploit LLM-based architectures for tabular data synthesis. Additionally, on Line 099, the authors mention that existing methods struggle to capture "intrinsic structural properties of tables" and continuous values when using LLMs. Could the authors provide more context on this limitation? Recent studies indicate that fine-tuning can improve LLM performance for modeling continuous values, potentially overcoming some of these structural challenges [1]. 

 - CTSyn employs quantile transformation for handling numerical values, but it’s unclear why this choice was made over alternative scaling methods, such as min-max or standard normalization. Quantile transformation can improve handling of skewed distributions but might also introduce artifacts in certain cases. Could the authors elaborate on the rationale behind selecting quantile transformation? 

- Eq. 1 introduces the sequence $\mathbf{E}$, representing tokenized and embedded table values, but the meta embedding $e_m$ is excluded. Since $e_m$ likely contains crucial table-specific metadata, incorporating it directly into $\mathbf{E}$ might strengthen the alignment between table content and contextual information

-  Table 2 presents a *column-wise comparison* of synthetic and real data, which provides some indication of CTSyn’s data fidelity. However, this approach does not fully address the challenges of synthetic data generation, particularly regarding joint modeling of column relationships and complex dependencies. For synthetic data to be *realistic*, it must ideally preserve not just marginal distributions but also higher-order dependencies and potential causal relationships between columns. Could the authors consider additional evaluation metrics, such as multivariate measures or metrics assessing the preservation of conditional distributions, to more rigorously demonstrate CTSyn’s capability for joint data modeling? 

- In Fig. 2, the authors show that synthetic data generated by CTSyn outperforms real data in certain tasks, which is a quite surprising result in my view. How can authors elaborate on that? Please provide detailed explanation of the experiment settings here. 

- What is the final parameter size for the CTSyn model?


[1] Akhtar, Mubashara, Abhilash Shankarampeta, Vivek Gupta, Arpit Patil, Oana Cocarascu, and Elena Simperl. "Exploring the numerical reasoning capabilities of language models: A comprehensive analysis on tabular data." arXiv preprint arXiv:2311.02216 (2023).
soundness: 3
strengths: - Relevance. CTSyn focuses on the important area of generating high-quality tabular data, which is essential for improving machine learning models. Synthetic data can help when real data is limited or sensitive, such as in healthcare and finance.

- Novel Architecture Design. The model features a new design that combines a cross-table variational autoencoder with a conditional diffusion model. This approach effectively maintains data quality and flexibility across different types of tables, significantly enhancing the capabilities of previous methods in this field.

- Solid Baseline and Dataset Choice. CTSyn compares its performance with SOTA models and uses large, diverse datasets from the real world.
summary: The paper presents CTSyn, a generative model designed for synthesizing tabular data by unifying diverse datasets into a single latent space.
The proposed architecture combines a cross-table variational autoencoder model with a conditional diffusion model to generate flexible synthetic data for various domains. Extensive pre-training across real-world datasets enables CTSyn to outperform existing models in data diversity and fidelity, also enhancing downstream machine learning tasks, especially in low-data regimes, even *surprisingly* surpassing real data.
weaknesses: - CTSyn cannot handle datasets where columns include free text (e.g., in medical records with text entries), limiting its application to purely structured numerical or categorical data. 

- The evaluation lacks certain robustness tests for synthetic data quality, such as a discriminator test to assess whether a surrogate model can distinguish between real and synthetic data, or metrics like "distance to closest record" for authenticity. Additionally, the experimental setup for machine learning utility (e.g., cross-validation specifics) needs more transparency and detail to fully validate CTSyn's claims of enhancing downstream tasks.

- A more comprehensive ablation study is needed to assess the impact of each component in CTSyn’s architecture, such as the specific roles of the cross-table variational autoencoder and the conditional diffusion model in enhancing data fidelity and adaptability. Including these would offer clearer insights into model design choices.

Meta-review: This paper applies a diffusion-based approach to map diverse tables into a unified latent space and dynamically reconstruct table values based on the provided table schema embedding. While simple, this method effectively demonstrates that reconstructing the original categorical space can be achieved without complex transformations, offering a useful baseline for handling categorical data embeddings.

The work primarily proposes a method for handling individual variables within a framework similar to LSGM, which trains a diffusion model in latent space. Consequently, the approach lacks substantial novelty and may have limited impact, as it focuses on variable handling within an existing generative model framework rather than introducing fundamentally new techniques. Another limitation is the computational cost associated with the diffusion model's training process, which requires pre-training and fine-tuning. This could make scaling the modeling pipeline to large tables (e.g., hundreds of columns and millions of rows) challenging.

Decision: Accept (Poster)