Global universal approximation of functional input maps on weighted spaces

arXiv:2306.03303v3 Announce Type: replace-cross
Abstract: We introduce so-called functional input neural networks defined on a possibly infinite dimensional weighted space with values also in a possibly infinite dimensional output space. To this end, we use an additive family to map the input weighted space to the hidden layer, on which a non-linear scalar activation function is applied to each neuron, and finally return the output via some linear readouts. Relying on Stone-Weierstrass theorems on weighted spaces, we can prove a …

abstract approximation arxiv cs.lg family functional global hidden layer map maps math.fa math.pr networks neural networks q-fin.mf space spaces stat.ml type universal values