We define an extension of classical additive splines for multivariate

function approximation that we call hierarchical splines. We show that the

case of hierarchical, additive, piece-wise linear splines includes present-day

Deep Convolutional Learning Networks (DCLNs) with linear rectifiers and

pooling (sum or max). We discuss how these observations together with

i-theory may provide a framework for a general theory of deep networks.

http://hdl.handle.net/1721.1/100201