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.
Katznelson,An Introduction to Harmonic Analysis, 3rd ed
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The minimal number of dynamical degrees of freedom in regularised scalar field theory scales with area, governed by the count of distinct normal-mode frequencies below the ultraviolet cutoff.
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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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Area Scaling of Dynamical Degrees of Freedom in Regularised Scalar Field Theory
The minimal number of dynamical degrees of freedom in regularised scalar field theory scales with area, governed by the count of distinct normal-mode frequencies below the ultraviolet cutoff.