Size and depth of monotone neural networks: interpolation and approximation Dan Mikulincer Massachusetts Institute of Technology Daniel Reichman Worcester Polytechnic Institute

Monotone functions and data sets arise in a variety of applications. We study the interpolation problem for monotone data sets: The input is a monotone data set with n points, and the goal is to find a size and depth efficient monotone neural network with non negative parameters and threshold units that interpolates the data set. We show that there are monotone data sets that cannot be interpolated by a monotone network of depth 2. On the other hand, we prove that for every monotone data set with n points in R