Fractional signature: A generalisation of the signature inspired by fractional calculus

José Manuel Corcuera and Rubén Jiménez

Statistics & Probability Letters, 2026, vol. 227, issue C

Abstract: 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.

Keywords: Fractional calculus; Machine learning; Signature (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spl.2025.110533

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