Entropic Hetero-Associative Memory

TL;DR

This paper extends entropic associative memory to hetero-associative cases, enabling the storage and retrieval of paired objects across different domains or modalities using a 4D relation, with methods to handle missing cues.

Contribution

It introduces a novel hetero-associative memory model that preserves entropic properties and proposes three methods to retrieve associated objects without cues.

Findings

Successfully associated digits with letters from MNIST and EMNIST datasets.

Demonstrated retrieval performance with limited computational resources.

Showed effectiveness of three retrieval methods in handling missing cues.

Abstract

The Entropic Associative Memory holds objects in a 2D relation or ``memory plane'' using a finite table as the medium. Memory objects are stored by reinforcing simultaneously the cells used by the cue, implementing a form of Hebb's learning rule. Stored objects are ``overlapped'' on the medium, hence the memory is indeterminate and has an entropy value at each state. The retrieval operation constructs an object from the cue and such indeterminate content. In this paper we present the extension to the hetero-associative case in which these properties are preserved. Pairs of hetero-associated objects, possibly of different domain and/or modalities, are held in a 4D relation. The memory retrieval operation selects a largely indeterminate 2D memory plane that is specific to the input cue; however, there is no cue left to retrieve an object from such latter plane. We propose three incremental methods to address such missing cue problem, which we call random, sample and test, and search and test. The model is assessed with composite recollections consisting of manuscripts digits and letters selected from the MNIST and the EMNIST corpora, respectively, such that cue digits retrieve their associated letters and vice versa. We show the memory performance and illustrate the memory retrieval operation using all three methods. The system shows promise for storing, recognizing and retrieving very large sets of object with very limited computing resources.