Categorization by a three-state attractor neural network

TL;DR

This paper investigates a three-state attractor neural network's ability to categorize concepts from examples, analyzing its dynamics and phase transitions under various conditions.

Contribution

It introduces a detailed analysis of the network's dynamics at zero temperature, revealing how increasing examples or correlations induce a transition from retrieval to categorization.

Findings

Transition from retrieval to categorization with more examples or higher correlations

Effective categorization when pattern activity is low and threshold is appropriately set

Dynamics analyzed in the limit of extreme dilution

Abstract

The categorization properties of an attractor network of three-state neurons which infers three-state concepts from examples are studied. The evolution equations governing the parallel dynamics at zero temperature for the overlap between the state of the network and the examples, the state of the network and the concepts as well as the neuron activity are discussed in the limit of extreme dilution. A transition from a retrieval region to a categorization region is found when the number of examples or their correlations are increased. If the pattern activity is small enough, the examples (concepts) are very well retrieved (categorized) for an appropriate choice of the zero-activity threshold of the neurons.