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A global universality of two-layer neural networks with ReLU activations
In the present study, we investigate a universality of neural networks, which concerns a density of the set of two-layer neural networks in a function spaces.
Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions
In this paper, we specify what functions induce the bounded composition operators on a reproducing kernel Hilbert space (RKHS) associated with an analytic positive definite function defined on $\mathbf{R}^d$.
The global optimum of shallow neural network is attained by ridgelet transform
We prove that the global minimum of the backpropagation (BP) training problem of neural networks with an arbitrary nonlinear activation is given by the ridgelet transform.
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