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Shu-Hao Jiao

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Preprint Sep 2026

Approximating Smooth Functionals with ReLU Networks

We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by ReLU neural networks. A key feature in deep learning for functional data is the varying importance of different coordinates/dimensions. Representing the functional input in a basis expansion, we...

Shu-Hao Jiao · 0 citations

#machine learning Preprint Sep 2026

ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis

We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural networks. Writing the functional input as $X(t)=\sum_{d\geq1}\xi_d\nu_d(t)$, we quantify the importance of coordinate $d$ through $w_ds_d$, where $s_d$ bounds the magnitude of th...

Shu-Hao Jiao · 0 citations