| Abstract: |
| In this talk, an innovative approach and the result of the approximability of shallow neural networks on Korobov spaces will be presented. Then, the generalization analysis of shallow neural networks for classification on Korobov Space will be discussed.
The talk is organized as follows. In the beginning, a dimensional independent rate of approximating functions from the Korobov space by ReLU shallow neural networks will be established. Following the first main result, a generalization error will be emphasized. A specific example will be given to justify the novelty and sufficiency of the main results. In addition, with the approximation error we get, we study the learning rates of the excess misclassification error according to the convex $\eta$-norm loss function $\phi(v)=(1 - v)_{+}^{\eta}$, $\eta\geq1$. The error under Tsybakov noise conditions is also discussed. |
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