ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis
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arXiv:2609.15355v1 Announce Type: new Abstract: 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 co…
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- 2026-09-15 04:00 · arXiv stat.ML
ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis