Function approximation on non-Euclidean spaces

This paper presents a family of layered feed-forward networks that is able to uniformly approximate functions on any metric space, and also on a wide variety of non-metric spaces. Non-Euclidean input spaces are frequently encountered in practice, while usual approximation schemes are guaranteed to work only on Euclidean metric spaces. Theoretical foundations are provided, as well as practical algorithms and illustrative examples. This tool potentially constitutes a significant extension of the common notion of 'universal approximation capability'.