# Fractional signature: a generalisation of the signature inspired by fractional calculus

arXiv: https://arxiv.org/abs/2407.17446 · HTML: https://mlsanity.com/paper/2407.17446/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 3 of 3)

- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Signature Methods in Machine Learning](https://mlsanity.com/paper/2206.14674/) (2022)

## Abstract (arXiv)

In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the signature, inspired by the previous one, but more convenient to use in machine learning. Finally, we test this last signature in a toy application to the problem of handwritten digit recognition, where significant improvements in accuracy rates are observed compared to those of the original signature.