Notes on Hierarchical Splines, DCLNs and i-theory

TitleNotes on Hierarchical Splines, DCLNs and i-theory
Publication TypeCBMM Memos
Year of Publication2015
AuthorsPoggio, T, Rosasco, L, Shashua, A, Cohen, N, Anselmi, F

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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