Juncai He

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20242026

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math.NA2026

Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain $L^{p}$ Ridge Integral Spaces for ReLU $^{k}$ Networks

Juncai He, Zitong Tian

We develop the $L^{p}$ space and approximation theory for shallow neural networks with $ReLU^{k}$ activations. The central object is the Radon-domain $L^{p}$ space $\mathcal{R}L…

math.NA2026

Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates

Juncai He, Xinliang Liu, Zitong Tian

This paper studies the numerical approximation of divergence-free vector fields by linearized shallow neural networks, also referred to as random feature models or finite neuron sp…

Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain Lp Ridge Integral Spaces for ReLUk Networks

Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates

Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain $L^{p}$ Ridge Integral Spaces for ReLU $^{k}$ Networks