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.

中文翻译：

---

在 CNN 架构中嵌入 FRPN

本文扩展了矢量输入的完全递归感知器网络 (FRPN) 模型，以包括可以接受多维输入的深度卷积神经网络 (CNN)。FRPN 由递归层组成，在给定固定输入的情况下，递归层迭代计算平衡状态。用这种迭代机制实现的展开允许模拟具有任意层数的深度神经网络。将 FRPN 扩展到 CNN 产生了一种我们称之为卷积 FRPN (C-FRPN) 的架构，其中卷积层是递归的。该方法在多个图像分类基准上进行评估。结果表明，C-FRPN 始终优于具有相同参数数量的标准 CNN。对于小型网络，性能差距特别大，