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I-theory on depth vs width: hierarchical function composition
(Center for Brains, Minds and Machines (CBMM), 2015-12-29)
Deep learning networks with convolution, pooling and subsampling are a special case of hierar- chical architectures, which can be represented by trees (such as binary trees). Hierarchical as well as shallow networks can ...
Notes on Hierarchical Splines, DCLNs and i-theory
(Center for Brains, Minds and Machines (CBMM), 2015-09-29)
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 ...