do this in a hierarchical way through a number of layers in a network and what I'm going to argue is that deep net do this in a very particular kind of way using a spline approximation so show of hands how many people here know about splines okay so there's two key parts to a spline approximation the first is a partition of the input space or the domain so if X is just a one-dimensional input variable then we have a partition Omega in this case we're splitting the domain up into four different regions we're now the second important thing is