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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2407.01250 |
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- This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate nonlinear systems -- that satisfy a Lipschitz property and forget past inputs fast enough -- in metric-entropy-optimal manner. As the sets of sequence-to-sequence mappings realized by the dynamical systems we consider are significantly more massive than function classes generally analyzed in approximation theory, a refined metric-entropy characterization is needed, namely in terms of order, type, and generalized dimension. We compute these quantities for the classes of exponentially- and polynomially Lipschitz fading-memory systems and show that RNNs can achieve them.