Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
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Fourier residual networks achieve spectral convergence for piecewise continuous functions with discontinuities in the function or derivatives, without needing periodicity or continuity.
Develops dual-space characterizations, Hölder embeddings via interpolation, and Schrödinger PDE applications for spectral Barron spaces defined by Fourier decay.
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Time-Frequency Analysis for Neural Networks
Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
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Fourier Residual Networks Achieve Spectral Accuracy for Discontinuous Functions
Fourier residual networks achieve spectral convergence for piecewise continuous functions with discontinuities in the function or derivatives, without needing periodicity or continuity.
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Functional analysis and partial differential equations in spectral Barron spaces
Develops dual-space characterizations, Hölder embeddings via interpolation, and Schrödinger PDE applications for spectral Barron spaces defined by Fourier decay.