@article {1439, title = {Notes on Hierarchical Splines, DCLNs and i-theory}, year = {2015}, abstract = {

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.

}, author = {Tomaso Poggio and Lorenzo Rosasco and Amnon Shashua and Nadav Cohen and F. Anselmi} }