A shared mixed-activation network of width 2dN+d+2 yields layer-wise L^p approximation rates bounded by the modulus of continuity at geometric scale N^{-ℓ}, reducing to (2d+1)N^{-ℓ} for 1-Lipschitz targets.
Multigrade neural network approximation
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Geometric Layer-wise Approximation Rates for Deep Networks
A shared mixed-activation network of width 2dN+d+2 yields layer-wise L^p approximation rates bounded by the modulus of continuity at geometric scale N^{-ℓ}, reducing to (2d+1)N^{-ℓ} for 1-Lipschitz targets.