activity
20192026
most citedEmbedding and Approximation Theorems for Echo State Networks

132 citations · 269 across the 11 of their papers we have counts for

collaborators

11 papers

cs.AI2026

Harbor Adapters and Harbor-Index: Infrastructure and a Curated Meta-Dataset for Large-Scale Agentic Evaluation

Lin Shi, Haowei Lin, Zixuan Zhu +123

Evaluating agents on the growing number of agentic benchmarks is challenging because they often require complex environments and agent integrations. We introduce Harbor Adapters, a…

cs.AI2026

MirrorCode: AI can rebuild entire programs from behavior alone

Tom Adamczewski, David Owen, David Rein +4

AI models are rapidly improving at autonomous coding, as shown by benchmark progress and one-off demonstrations such as AI implementing a C compiler. However, existing coding bench…

math.DS2025

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…

math.DS2025

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…

math.DS2022

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…

math.DS2021

(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…

math.DS2021★ 32 cited

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…

math.DS2021★ 3 cited

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…

math.DS2020★ 47 cited

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…

cs.LG2020★ 55 cited

Echo State Networks trained by Tikhonov least squares are L2(μ) approximators of ergodic dynamical systems

Allen G Hart, James L Hook, Jonathan H P Dawes

Echo State Networks (ESNs) are a class of single-layer recurrent neural networks with randomly generated internal weights, and a single layer of tuneable outer weights, which are u…

nlin.CD2019★ 132 cited

Embedding and Approximation Theorems for Echo State Networks

Allen G Hart, James L Hook, Jonathan H P Dawes

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series…