This paper extends the fully recursive perceptron network (FRPN) model for vectorial inputs to include deep convolutional neural networks (CNNs) which can accept multi-dimensional inputs. A FRPN consists of a recursive layer, which, given a fixed input, iteratively computes an equilibrium state. The unfolding realized with this kind of iterative mechanism allows to simulate a deep neural network with any number of layers. The extension of the FRPN to CNN results in an architecture, which we call convolutional-FRPN (C-FRPN), where the convolutional layers are recursive. The method is evaluated on several image classification benchmarks. It is shown that the C-FRPN consistently outperforms standard CNNs having the same number of parameters. The gap in performance is particularly large for small networks, showing that the C-FRPN is a very powerful architecture, since it allows to obtain equivalent performance with fewer parameters when compared with deep CNNs.
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