Work

Decomposing tensor spaces via path signatures

Year: 2024

Type: article

Abstract: The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. We show that the parametrization of this variety induces a natural decomposition of the tensor space via representation theory, and connect this to the study of path invariants. We also reveal certain constraints that apply to the rank and symmetry of a signature tensor.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2024.107807

Authors: Carlos Améndola, Francesco Galuppi, Ángel David Ríos Ortiz, Pierpaola Santarsiero, Tim Seynnaeve

Institutions: Technische Universität Berlin, University of Warsaw, University of Bologna, KU Leuven

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,330