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Infinite-dimensional reservoir computing
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DOI：10.1016/j.neunet.2024.106486.png)
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Abstract
En 中文
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 recurrent neural network-based learning algorithm with provable convergence guarantees that do not suffer from the curse of dimensionality when learning input/output systems in the class of generalized Barron functionals and measuring the error in a mean-squared sense.
Keywords:
Recurrent neural network
Reservoir computing
Echo state network
ESN
Extreme learning machine
ELM
Recurrent linear network
Machine learning
Barron functional
Recurrent barron functional
Universality
Finite memory functional
Approximation bound
Convolutional filter
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