Understanding neural networks with reproducing kernel Banach spaces

Characterizing the function spaces corresponding to neural networks can provide a way understand their properties. In this paper we discuss how theory of reproducing kernel Banach be used tackle challenge. particular, prove representer theorem for wide class that admit suitable integral representation and include one hidden layer possibly infinite width. Further, show that, ReLU activation functions, norm in space characterized terms inverse Radon transform bounded real measure, with given by total variation measure. Our analysis simplifies extends recent results [45], [36], [37].