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.
Fourier multi-component and multi-layer neural networks: Unlocking high-frequency potential
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The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
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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.
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Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.