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.
Optimal Stable Nonlinear Approximation
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A fixed-width, shared-activation deep network architecture is constructed so that every intermediate readout approximates the target function at a geometrically decaying rate proportional to depth.
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Layer-wise Geometric Approximation Rates for Deep Networks
A fixed-width, shared-activation deep network architecture is constructed so that every intermediate readout approximates the target function at a geometrically decaying rate proportional to depth.