Universality of shallow and deep neural networks on non-Euclidean spaces

ArXi:2602.23381v2 Announce Type: replace-cross We study shallow and deep neural networks whose inputs range over a general topological space. The model is built from a prescribed family of continuous feature maps and reduces to multilayer feedforward networks in the Euclidean case. We focus on the universal approximation property and establish general conditions under which such networks are dense in spaces of continuous vector-valued functions on arbitrary topological spaces and, in particular, locally convex spaces.