132 citations · 269 across the 11 of their papers we have counts for
7 papers · 1 filter
Can LLMs Write Mathematics Papers? A Case Study in Reservoir Computing
Allen G Hart
As AI capabilities continue to grow exponentially on economically relevant human expert tasks, with task completion horizons doubling every 7 months according to the Model Evaluati…
Generic and Isometric Embeddings in Reservoir Computers
Allen G Hart
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 h…
Generalised Synchronisations, Embeddings, and Approximations for Continuous Time Reservoir Computers
Allen G Hart
We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation between between th…
(Thesis) Reservoir Computing With Dynamical Systems
Allen G Hart
A reservoir computer is a special type of neural network, where most of the weights are randomly fixed and only a subset are trained. In this thesis we prove results about reservoi…
Learning strange attractors with reservoir systems
Lyudmila Grigoryeva, Allen Hart, Juan-Pablo Ortega
This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space rep…
Using Echo State Networks to Approximate Value Functions for Control
Allen G. Hart, Kevin R. Olding, A. M. G. Cox +2
An Echo State Network (ESN) is a type of single-layer recurrent neural network with randomly-chosen internal weights and a trainable output layer. We prove under mild conditions th…
Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem
Lyudmila Grigoryeva, Allen Hart, Juan-Pablo Ortega
This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields contin…