# The iisignature library: efficient calculation of iterated-integral signatures and log signatures

arXiv: https://arxiv.org/abs/1802.08252 · HTML: https://mlsanity.com/paper/1802.08252/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2018.

## Built on by (most cited first, 30 of 40)

- [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)
- [Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching](https://mlsanity.com/paper/2405.20799/) (2024)
- [Lecture notes on rough paths and applications to machine learning](https://mlsanity.com/paper/2404.06583/) (2024)
- [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)
- [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)
- [Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework](https://mlsanity.com/paper/2307.13147/) (2023)
- [Sparse Signature Coefficient Recovery via Kernels](https://mlsanity.com/paper/2412.08579/) (2024)
- [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)
- [Deep Signature FBSDE Algorithm](https://mlsanity.com/paper/2108.10504/) (2021)
- [Novelty Detection on Radio Astronomy Data using Signatures](https://mlsanity.com/paper/2402.14892/) (2024)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [Hedging with memory: shallow and deep learning with signatures](https://mlsanity.com/paper/2508.02759/) (2025)
- [A Neural RDE-based model for solving path-dependent PDEs](https://mlsanity.com/paper/2306.01123/) (2023)
- [Sig-Networks Toolkit: Signature Networks for Longitudinal Language Modelling](https://mlsanity.com/paper/2312.03523/) (2023)
- [Signature Kernel Scoring Rule: A Spatio-Temporal Diagnostic for Probabilistic Weather Forecasting](https://mlsanity.com/paper/2510.19110/) (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)
- [Learning with Signatures](https://mlsanity.com/paper/2204.07953/) (2022)
- [Log-PDE Methods for Rough Signature Kernels](https://mlsanity.com/paper/2404.02926/) (2024)
- [Fractional signature: a generalisation of the signature inspired by fractional calculus](https://mlsanity.com/paper/2407.17446/) (2024)
- [Deep Signature: Characterization of Large-Scale Molecular Dynamics](https://mlsanity.com/paper/2410.02847/) (2024)
- [SigBERT: Combining Narrative Medical Reports and Rough Path Signature Theory for Survival Risk Estimation in Oncology](https://mlsanity.com/paper/2507.22941/) (2025)

## Abstract (arXiv)

Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine learning. We present algorithms for efficiently calculating these signatures, and benchmark their performance. We release the methods as a Python package.