1. J. Hanson, M. Raginsky, and E.D. Sontag. Learning recurrent neural net models of nonlinear systems. Proc. of Machine Learning Research, 144:1-11, 2021. [PDF] Keyword(s): machine learning, empirical risk minimization, recurrent neural networks, dynamical systems, continuous time, system identification, statistical learning theory, generalization bounds. Abstract:

   This paper considers the following learning problem: given sample pairs of input and output signals generated by an unknown nonlinear system (which is not assumed to be causal or time-invariant), one wishes to find a continuous-time recurrent neural net, with activation function tanh, that approximately reproduces the underlying i/o behavior with high confidence. Leveraging earlier work concerned with matching derivatives up to a finite order of the input and output signals the problem is reformulated in familiar system-theoretic language and quantitative guarantees on the sup-norm risk of the learned model are derived, in terms of the number of neurons, the sample size, the number of derivatives being matched, and the regularity properties of the inputs, the outputs, and the unknown i/o map.

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