Decomposing Tensor Spaces via Path Signatures
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929618793005056 |
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| author | Améndola, Carlos Galuppi, Francesco Ortiz, Ángel David Ríos Santarsiero, Pierpaola Seynnaeve, Tim |
| author_facet | Améndola, Carlos Galuppi, Francesco Ortiz, Ángel David Ríos Santarsiero, Pierpaola Seynnaeve, Tim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decomposing Tensor Spaces via Path Signatures Améndola, Carlos Galuppi, Francesco Ortiz, Ángel David Ríos Santarsiero, Pierpaola Seynnaeve, Tim Representation Theory Algebraic Geometry Probability 60L10, 60L70, 05E10, 15A72, 14N07 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. |
| title | Decomposing Tensor Spaces via Path Signatures |
| topic | Representation Theory Algebraic Geometry Probability 60L10, 60L70, 05E10, 15A72, 14N07 |
| url | https://arxiv.org/abs/2308.11571 |