[math] \newcommand\feature{x} [/math]

Consider a predictor map [math]h(\feature)[/math] which is piece-wise linear and consisting of [math]1000[/math] pieces. Assume we want to represent this map by an artificial neural network (ANN) using neurons with one hidden layer of neurons having a rectified linear unit (ReLU) activation function. The output layer consists of a single neuron with linear activation function.

How many neurons must the ANN contain at least ?