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.
Nonlinear approximation and (deep) ReLU networks.Constructive Approximation, 55: 127–172
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RG-inspired lattice models for piecewise GLMs provide explicit interpretable partitions and a replica-analysis-derived scaling law for regularization that allows increasing complexity without expected rise in generalization loss.
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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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A renormalization-group inspired lattice-based framework for piecewise generalized linear models
RG-inspired lattice models for piecewise GLMs provide explicit interpretable partitions and a replica-analysis-derived scaling law for regularization that allows increasing complexity without expected rise in generalization loss.