R\'{e}seaux d'Automates de Caianiello Revisit\'{e}

TL;DR

This paper revisits Caianiello neural networks, demonstrating how certain McCulloch-Pitts networks can be simulated by Caianiello networks, thereby reaffirming results on cycle lengths in neural network dynamics.

Contribution

It introduces a family of neural networks that can be simulated across different models, extending understanding of cycle lengths in Caianiello neural networks.

Findings

Neural networks of McCulloch-Pitts can be simulated by Caianiello networks.

Reaffirmation of exponential cycle lengths in Caianiello neural networks.

Extension of previous results on neural network cycle dynamics.

Abstract

We exhibit a family of neural networks of McCulloch and Pitts of size $2nk+2$ which can be simulated by a neural networks of Caianiello of size $2n+2$ and memory length $k$. This simulation allows us to find again one of the result of the following article: [Cycles exponentiels des r\'{e}seaux de Caianiello et compteurs en arithm\'{e}tique redondante, Technique et Science Informatiques Vol. 19, pages 985-1008] on the existence of neural networks of Caianiello of size $2n+2$ and memory length $k$ which describes a cycle of length $k \times 2^{nk}$.