Mixed state on a sparsely encoded associative memory model

TL;DR

This paper analyzes symmetric mixed states in a sparsely encoded associative memory model, revealing that the OR mixed state's storage capacity diverges in the sparse limit and relating findings to neural data.

Contribution

It introduces and analyzes three types of mixed states in a sparsely encoded associative memory model, highlighting the OR state's divergent capacity and optimal threshold alignment.

Findings

OR mixed state's storage capacity diverges in the sparse limit

Optimal thresholds for pattern and OR mixed states coincide in the sparse limit

The OR mixed state is a reasonable representative in the sparse encoding regime

Abstract

In the present paper, we analyze symmetric mixed states corresponding to the so-called concept formation on a sparsely encoded associative memory model with 0-1 neurons. Three types of mixed states, OR, AND and a majority decision mixed state are described as typical examples. Each element of the OR mixed state is composed of corresponding memory pattern elements by means of the OR-operation. The other two types are similarly defined. By analyzing their stabilities through the SCSNA and the computer simulation, we found that the storage capacity of the OR mixed state diverges in the sparse limit, but that the other states do not diverge. In addition, we found that the optimal threshold values, which maximize the storage capacity, for the memory pattern and the OR mixed state coincide with each other in the spare limit. Thus, we conclude that the OR mixed state is a reasonable representative of the mixed state in the spare limit. Finally, the paper examines the relationship between our results and recently reported physiological findings regarding face-responsive neurons in the inferior temporal cortex.