# Embedding and learning with signatures

arXiv: https://arxiv.org/abs/1911.13211 · HTML: https://mlsanity.com/paper/1911.13211/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2019.

## Built on by (most cited first, 29 of 29)

- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [Generative modeling for time series via Schr"odinger bridge](https://mlsanity.com/paper/2304.05093/) (2023)
- [Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching](https://mlsanity.com/paper/2405.20799/) (2024)
- [SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series](https://mlsanity.com/paper/2406.17890/) (2024)
- [BR-NS: an Archive-less Approach to Novelty Search](https://mlsanity.com/paper/2104.03936/) (2021)
- [Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs](https://mlsanity.com/paper/2206.14284/) (2022)
- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)
- [Conditional Loss and Deep Euler Scheme for Time Series Generation](https://mlsanity.com/paper/2102.05313/) (2021)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [On the Generalization and Approximation Capacities of Neural Controlled Differential Equations](https://mlsanity.com/paper/2305.16791/) (2023)
- [Path Signatures for Diversity in Probabilistic Trajectory Optimisation](https://mlsanity.com/paper/2308.04071/) (2023)
- [SigGate: Enhancing Recurrent Neural Networks with Signature-Based Gating Mechanisms](https://mlsanity.com/paper/2502.09318/) (2025)
- [Signature Maximum Mean Discrepancy Two-Sample Statistical Tests](https://mlsanity.com/paper/2506.01718/) (2025)
- [System identification using Bayesian neural networks with nonparametric noise models](https://mlsanity.com/paper/2104.12119/) (2021)
- [Path Signature Area-Based Causal Discovery in Coupled Time Series](https://mlsanity.com/paper/2110.12288/) (2021)
- [Signature Isolation Forest](https://mlsanity.com/paper/2403.04405/) (2024)
- [Clustering Digital Assets Using Path Signatures: Application to Portfolio Construction](https://mlsanity.com/paper/2410.23297/) (2024)
- [Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs](https://mlsanity.com/paper/2412.03271/) (2024)
- [VWAP Execution with Signature-Enhanced Transformers: A Multi-Asset Learning Approach](https://mlsanity.com/paper/2503.02680/) (2025)
- [Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting](https://mlsanity.com/paper/2510.12337/) (2025)
- [Local regression on path spaces with signature metrics](https://mlsanity.com/paper/2510.16728/) (2025)
- [Path Signatures Enable Model-Free Mapping of RNA Modifications](https://mlsanity.com/paper/2511.08855/) (2025)
- [Path Signatures for Seizure Forecasting](https://mlsanity.com/paper/2308.09312/) (2023)
- [Path Signatures and Graph Neural Networks for Slow Earthquake Analysis: Better Together?](https://mlsanity.com/paper/2402.03558/) (2024)
- [Scalable Signature-Based Distribution Regression via Reference Sets](https://mlsanity.com/paper/2410.09196/) (2024)
- [Online Handwritten Signature Verification Based on Temporal-Spatial Graph Attention Transformer](https://mlsanity.com/paper/2510.19321/) (2025)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)
- [A Heisenberg Lift Descriptor for Order Sensitive Online Handwriting Recognition](https://mlsanity.com/paper/2609.17565/) (2026)

## Abstract (arXiv)

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered. Its basic principle is to represent multidimensional paths by a graded feature set of their iterated integrals, called the signature. This approach relies critically on an embedding principle, which consists in representing discretely sampled data as paths, i.e., functions from [0,1] to ℝd. After a survey of machine learning methodologies for signatures, the influence of embeddings on prediction accuracy is investigated with an in-depth study of three recent and challenging datasets. It is shown that a specific embedding, called lead-lag, is systematically the strongest performer across all datasets and algorithms considered. Moreover, an empirical study reveals that computing signatures over the whole path domain does not lead to a loss of local information. It is concluded that, with a good embedding, combining signatures with other simple algorithms achieves results competitive with state-of-the-art, domain-specific approaches.