  We study news neural networks to approximate function of distributions in a
probability space. Two classes of neural networks based on quantile and moment
approximation are proposed to learn these functions and are theoretically
supported by universal approximation theorems. By mixing the quantile and
moment features in other new networks, we develop schemes that outperform
existing networks on numerical test cases involving univariate distributions.
For bivariate distributions, the moment neural network outperforms all other
networks.
