Theoretical analysis of co-existing periodic orbits in sparse binary neural networks

Abstract

A sparse binary neural network is a discrete-time recurrent neural network characterized by local binary connections and signum-type neuron models. The dynamics is described by an autonomous difference equation of binary state variables. Depending on the parameters, the network generates various periodic orbits of binary vectors. Multiple periodic orbits can co-exist and the network exhibits one of them depending on initial condition. Real/potential applications of the periodic orbits include control signals of switching circuits and basic signals for time-series approximation. The network is well suited for theoretical analysis and simple hardware implementation. This paper considers shift-type periodic orbits in the networks. As the main theoretical results, we clarify the number, period, and stability of the periodic orbits for key parameters. As a first step to the applications in the future, we present an FPGA-based hardware prototype and confirm typical periodic orbits experimentally.