%0 Generic %D 2015 %T Notes on Hierarchical Splines, DCLNs and i-theory %A Tomaso Poggio %A Lorenzo Rosasco %A Amnon Shashua %A Nadav Cohen %A F. Anselmi %X

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.

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