Author

Wei-Bing Deng

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Preprint Oct 2026

Fully Deterministic Shallow Neural Networks with Localized Activations. Part II: Condition Number Estimates

We prove positive definiteness and quantitative condition-number bounds for continuous Sobolev Gram matrices of deterministic shallow networks with Gaussian and tanh-difference activations. The prescribed feature families include the optimal Sobolev approximation constructions of Part I. On every fixed nonempty bounded...

R. Bi, Wei-Bing Deng · 0 citations

Preprint Oct 2026

Fully Deterministic Shallow Neural Networks with Localized Activations. Part I: Construction and Optimal Sobolev Approximation

We construct shallow neural networks with fixed Gaussian and tanh-difference activations on bounded Lipschitz domains $\Omega\subset\mathbb{R}^d$, $d\ge2$. For each $s>0$, explicit deterministic rules prescribe all hidden parameters independently of the target $u\in H^s(\Omega)$. At frequency resolution $M$, the $N_M\a...

R. Bi, Wei-Bing Deng · 0 citations