The three-state layered neural network with finite dilution

TL;DR

This paper analyzes a three-state layered neural network with finite dilution, exploring its dynamics, stationary states, and performance optimization, revealing how thresholds and noise affect its information processing capabilities.

Contribution

It provides an exactly solvable model extending previous work to include finite dilution and variable thresholds, with detailed phase diagrams and stability analysis.

Findings

Network develops instabilities at low thresholds

Performance improves with increasing threshold up to an optimal point

Robustness to synaptic noise is confirmed

Abstract

The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on a recurrent network. Detailed phase diagrams are obtained for the stationary states and for the time evolution of the retrieval overlap with a single pattern. It is shown that the network develops instabilities for low thresholds and that there is a gradual improvement in network performance with increasing threshold up to an optimal stage. The robustness to synaptic noise is checked and the effects of dilution and of variable threshold on the information content of the network are also established.