# A Primer on the Signature Method in Machine Learning

arXiv: https://arxiv.org/abs/1603.03788 · HTML: https://mlsanity.com/paper/1603.03788/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2016.

## Built on by (most cited first, 30 of 104)

- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)
- [Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference](https://mlsanity.com/paper/2402.18512/) (2024)
- [Signature Methods in Machine Learning](https://mlsanity.com/paper/2206.14674/) (2022)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data](https://mlsanity.com/paper/2105.04211/) (2021)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [SVC-onGoing: Signature Verification Competition](https://mlsanity.com/paper/2108.06090/) (2021)
- [SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series](https://mlsanity.com/paper/2406.17890/) (2024)
- [Approximate Bayesian Computation with Path Signatures](https://mlsanity.com/paper/2106.12555/) (2021)
- [New directions in the applications of rough path theory](https://mlsanity.com/paper/2302.04586/) (2023)
- [Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition](https://mlsanity.com/paper/2110.13008/) (2021)
- [Lead-lag detection and network clustering for multivariate time series with an application to the US equity market](https://mlsanity.com/paper/2201.08283/) (2022)
- [Applications of Signature Methods to Market Anomaly Detection](https://mlsanity.com/paper/2201.02441/) (2022)
- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [ICDAR 2021 Competition on On-Line Signature Verification](https://mlsanity.com/paper/2106.00739/) (2021)
- [Path Development Network with Finite-dimensional Lie Group Representation](https://mlsanity.com/paper/2204.00740/) (2022)
- [The Signature Kernel](https://mlsanity.com/paper/2305.04625/) (2023)
- [BR-NS: an Archive-less Approach to Novelty Search](https://mlsanity.com/paper/2104.03936/) (2021)
- [Feature Engineering with Regularity Structures](https://mlsanity.com/paper/2108.05879/) (2021)
- [Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs](https://mlsanity.com/paper/2206.14284/) (2022)
- [SigFormer: Signature Transformers for Deep Hedging](https://mlsanity.com/paper/2310.13369/) (2023)
- [Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis](https://mlsanity.com/paper/2105.12778/) (2021)
- [pySigLib -- Fast Signature-Based Computations on CPU and GPU](https://mlsanity.com/paper/2509.10613/) (2025)
- [The Volterra signature](https://mlsanity.com/paper/2603.04525/) (2026)
- [G-Signatures: Global Graph Propagation With Randomized Signatures](https://mlsanity.com/paper/2302.08811/) (2023)
- [Randomized Signature Methods in Optimal Portfolio Selection](https://mlsanity.com/paper/2312.16448/) (2023)
- [Dynamical Regimes of Multimodal Diffusion Models](https://mlsanity.com/paper/2602.04780/) (2026)
- [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)

## Abstract (arXiv)

We provide an introduction to the signature method, focusing on its theoretical properties and machine learning applications. Our presentation is divided into two parts. In the first part, we present the definition and fundamental properties of the signature of a path. The signature is a sequence of numbers associated with a path that captures many of its important analytic and geometric properties. As a sequence of numbers, the signature serves as a compact description (dimension reduction) of a path. In presenting its theoretical properties, we assume only familiarity with classical real analysis and integration, and supplement theory with straightforward examples. We also mention several advanced topics, including the role of the signature in rough path theory. In the second part, we present practical applications of the signature to the area of machine learning. The signature method is a non-parametric way of transforming data into a set of features that can be used in machine learning tasks. In this method, data are converted into multi-dimensional paths, by means of embedding algorithms, of which the signature is then computed. We describe this pipeline in detail, making a link with the properties of the signature presented in the first part. We furthermore review some of the developments of the signature method in machine learning and, as an illustrative example, present a detailed application of the method to handwritten digit classification.