Unified analytic forms for Convolutional Neural Networks and Wavelet Filter Banks
This paper provides a unified analytic framework integrating expressions of several variants of convolutional neural networks and wavelet filter banks. The expressions are derived recursively, from dowstream to upstream layers, for the sequences of features returned at the nodes of a general form of network architecture. The inspiring framework for the derivation of these expressions is that of the so-called M-band convolution filter banks. In addition with the inter-layer inter-node expressions, activation sequences of convolutional neural networks also are mathematically described by suitable algebraic path representations.
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