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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.21522 |
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| _version_ | 1866908601297141760 |
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| author | Hart, Allen G |
| author_facet | Hart, Allen G |
| contents | We prove that a generic reservoir system admits a generalized synchronization that is a topological embedding of the input system's attractor. We also prove that for sufficiently high reservoir dimension (given by Nash's embedding theorem) there exists an isometric embedding generalized synchronization. The isometric embedding can be constructed explicitly when the reservoir system and source dynamics are linear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic and Isometric Embeddings in Reservoir Computers Hart, Allen G Dynamical Systems We prove that a generic reservoir system admits a generalized synchronization that is a topological embedding of the input system's attractor. We also prove that for sufficiently high reservoir dimension (given by Nash's embedding theorem) there exists an isometric embedding generalized synchronization. The isometric embedding can be constructed explicitly when the reservoir system and source dynamics are linear. |
| title | Generic and Isometric Embeddings in Reservoir Computers |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2508.21522 |