# On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics

arXiv: https://arxiv.org/abs/2201.00384 · HTML: https://mlsanity.com/paper/2201.00384/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 2 Jan 2022.

## Builds on (most cited first, 13 of 13)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Deep Learning for Time-Series Analysis](https://mlsanity.com/paper/1701.01887/) (2017)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [Deep neural networks, generic universal interpolation, and controlled ODEs](https://mlsanity.com/paper/1908.07838/) (2019)
- [Discrete-time signatures and randomness in reservoir computing](https://mlsanity.com/paper/2010.14615/) (2020)

## Built on by (most cited first, 3 of 3)

- [Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detection](https://mlsanity.com/paper/2407.11873/) (2024)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Random Controlled Differential Equations](https://mlsanity.com/paper/2512.23670/) (2025)

## Abstract (arXiv)

Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory and leverages the so-called Signature Transform. This algorithm enjoys strong theoretical guarantees but is hard to scale to high-dimensional data. In this paper, we study a recently derived random projection variant called Randomized Signature, obtained using the Johnson-Lindenstrauss Lemma. We provide an in-depth experimental evaluation of the effectiveness of the Randomized Signature approach, in an attempt to showcase the advantages of this reservoir to the community. Specifically, we find that this method is preferable to the truncated Signature approach and alternative deep learning techniques in terms of model complexity, training time, accuracy, robustness, and data hungriness.