# Sequential RC-TGAN: Generating Relational Time Series with Spectral Envelope Loss

arXiv: https://arxiv.org/abs/2606.31904 · HTML: https://mlsanity.com/paper/2606.31904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [REaLTabFormer: Generating Realistic Relational and Tabular Data using Transformers](https://mlsanity.com/paper/2302.02041/) (2023)
- [Tabular Transformers for Modeling Multivariate Time Series](https://mlsanity.com/paper/2011.01843/) (2020)
- [ClavaDDPM: Multi-relational Data Synthesis with Cluster-guided Diffusion Models](https://mlsanity.com/paper/2405.17724/) (2024)
- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [Row Conditional-TGAN for generating synthetic relational databases](https://mlsanity.com/paper/2211.07588/) (2022)
- [RelDiff: Relational Data Generative Modeling with Graph-Based Diffusion Models](https://mlsanity.com/paper/2506.00710/) (2025)
- [TIFO: Time-Invariant Frequency Operator for Stationarity-Aware Representation Learning in Time Series](https://mlsanity.com/paper/2602.17122/) (2026)

## Abstract (arXiv)

The generation of synthetic relational databases often involves modeling complex temporal dynamics, such as transaction logs or event sequences. A significant challenge in this domain is the handling of categorical time series (e.g., status codes), where standard encoding methods like one-hot encoding fail to capture intrinsic frequency-domain features such as seasonality and cyclicity. In this paper, we introduce Sequential RC-TGAN (Seq. RC-TGAN), a temporal extension of the RC-TGAN framework, equipped with a novel integrated loss function based on the textitSpectral Envelope Theory. This differentiable loss allows the generator to directly optimize the preservation of latent periodic structures via backpropagation. While spectral envelope theory is inherently designed for categorical sequences, we extend this frequency-domain regularization to continuous time series by employing a Variational Gaussian Mixture Model (VGM) discretization strategy. To establish a mathematically rigorous evaluation standard, we simulate categorical time series governed by a parameter α, with exactly known theoretical spectral envelopes. Integrating these dynamic sequences into the child tables of a relational database yields a robust ground-truth benchmark for evaluating the frequency-domain fidelity of our generative framework. Furthermore, we address the lack of robust evaluation standards for relational time series by proposing two new metrics: Spectral Density Divergence and Spectral Envelope Divergence. Experimental results on real-world datasets, as well as our simulated benchmarks, demonstrate that our end-to-end approach significantly outperforms state-of-the-art systems in reproducing cyclic patterns and long-term seasonality across both categorical and continuous features.