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cs.LG2024
Metric-Entropy Limits on the Approximation of Nonlinear Dynamical Systems
Yang Pan, Clemens Hutter, Helmut Bölcskei
This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate non…
math.FA2024★ 2 cited
Entropy of Compact Operators with Applications to Landau-Pollak-Slepian Theory and Sobolev Spaces
Thomas Allard, Helmut Bölcskei
We derive a precise general relation between the entropy of a compact operator and its eigenvalues. It is then shown how this result along with the underlying philosophy can be app…
math.FA2024★ 1 cited
Metric Entropy of Analytic Function Classes via Ellipsoidal Methods
Thomas Allard, Helmut Bölcskei
We present a systematic methodology for characterizing the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. The approach does not rely on th…