2023/04/02 by Lukas Gonon, Gonon, Lukas, Lyudmila Grigoryeva +3
Computer Science · Engineering · #Advanced Memory and Neural Computing #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM #Neural Networks and Reservoir Computing #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2304.00490
openalex publication_date 2023/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to a dynamic context. This new class is characterized by the readouts with a certain integral representation built on infinite-dimensional state-space systems. It is shown that this class is very rich and possesses useful features and universal approximation properties. The reservoir architectures used for the approximation and estimation of elements in the new class are randomly generated echo state networks with either linear or ReLU activation functions. Their readouts are built using randomly generated neural networks in which only the output layer is trained (extreme learning machines or random feature neural networks). The results in the paper yield a fully implementable recurrent neural network-based learning algorithm with provable convergence guarantees that do not suffer from the curse of dimensionality.