Generic and Isometric Embeddings in Reservoir Computers
Allen G Hart
Published: 2025/8/29
Abstract
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 is linear.