Feed-forward chains of recurrent attractor neural networks with finite dilution near saturation

TL;DR

This paper extends the analysis of a neural network model to include finite dilution of recurrent interactions, revealing how dilution affects phase transitions and network performance in layered attractor networks.

Contribution

It introduces a finite dilution extension to the replica analysis of a dual neural network model, exploring effects on phase transitions and network performance.

Findings

Finite dilution suppresses some phase transitions.

Long chains maintain good performance with finite dilution.

Balance between inter-layer and intra-layer interactions is crucial.

Abstract

A stationary state replica analysis for a dual neural network model that interpolates between a fully recurrent symmetric attractor network and a strictly feed-forward layered network, studied by Coolen and Viana, is extended in this work to account for finite dilution of the recurrent Hebbian interactions between binary Ising units within each layer. Gradual dilution is found to suppress part of the phase transitions that arise from the competition between recurrent and feed-forward operation modes of the network. Despite that, a long chain of layers still exhibits a relatively good performance under finite dilution for a balanced ratio between inter-layer and intra-layer interactions.