Mixed states on neural network with structural learning

TL;DR

This paper analyzes the properties of mixed states in a sparsely encoded associative memory model with structural learning, revealing their capacity and threshold behaviors, and implications for transform-invariant recognition.

Contribution

It introduces a detailed analysis of mixed states in a structural learning model, highlighting their capacity divergence and coexistence with memory patterns at the sparse limit.

Findings

Storage capacity of mixed states diverges at the sparse limit

Memory and mixed states thresholds are nearly equal

Mixed states can coexist with memory patterns at the sparse limit

Abstract

We investigated the properties of mixed states in a sparsely encoded associative memory model with a structural learning method. When mixed states are made of s memory patterns, s types of mixed states, which become equilibrium states of the model, can be generated. To investigate the properties of s types of the mixed states, we analyzed them using the statistical mechanical method. We found that the storage capacity of the memory pattern and the storage capacity of only a particular mixed state diverge at the sparse limit. We also found that the threshold value needed to recall the memory pattern is nearly equal to the threshold value needed to recall the particular mixed state. This means that the memory pattern and the particular mixed state can be made to easily coexist at the sparse limit. The properties of the model obtained by the analysis are also useful for constructing a transform-invariant recognition model.