# Neural SDEs for Conditional Time Series Generation and the Signature-Wasserstein-1 metric

arXiv: https://arxiv.org/abs/2301.01315 · HTML: https://mlsanity.com/paper/2301.01315/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 3 Jan 2023.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [A Generalised Signature Method for Multivariate Time Series Feature Extraction](https://mlsanity.com/paper/2006.00873/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Brief Survey on the Approximation Theory for Sequence Modelling](https://mlsanity.com/paper/2302.13752/) (2023)

## Abstract (arXiv)

(Conditional) Generative Adversarial Networks (GANs) have found great success in recent years, due to their ability to approximate (conditional) distributions over extremely high dimensional spaces. However, they are highly unstable and computationally expensive to train, especially in the time series setting. Recently, it has been proposed the use of a key object in rough path theory, called the signature of a path, which is able to convert the min-max formulation given by the (conditional) GAN framework into a classical minimization problem. However, this method is extremely expensive in terms of memory cost, sometimes even becoming prohibitive. To overcome this, we propose the use of textitConditional Neural Stochastic Differential Equations, which have a constant memory cost as a function of depth, being more memory efficient than traditional deep learning architectures. We empirically test that this proposed model is more efficient than other classical approaches, both in terms of memory cost and computational time, and that it usually outperforms them in terms of performance.