Entropic Hetero-Associative Memory

TL;DR

This paper proposes three incremental methods to address the missing cue problem of the Entropic Associative Memory, and shows promise for storing, recognizing and retrieving very large sets of object with very limited computing resources.

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.

Figures (5)

• Figure 1: System Architecture. Source: pineda-imagery-eam-2023.
• Figure 2: Performance achieved in ten-fold cross validation by EAM for MNIST (left) and a subset of EMNIST Balanced (Table \ref{['tab:classes-HEMNIST']}) (right) using increasing percentages of the filling corpus. The parameters are set to their default values of $\iota=0$, $\kappa=0$ and $\xi=0$.
• Figure 3: Recognition precision, recall and accuracy setting the recognition parameters to their default value --$\iota=0$, $\kappa=0$ and $\xi=0$-- (top). Recognition performance using $\iota=0.05$, $\kappa=32$ and $\xi=0$ (bottom).
• Figure 4: Performance of the random method (top); the sample and test method (middle) and the sample and search method (bottom). From a digit of MNIST produce a letter of the EMNIST (left), and vice versa (right).
• Figure 5: Hetero-Associative recollection: letters from EMNIST retrieved using their associated digits of MNIST as cues (left) and digits from MNIST retrieved using their associated letters of EMNIST as cues (right). The top-row shows the initial cue, and the remaining rows show the objects produced by the $\beta$-retrieval operation using the sample and search, the sample and test, and the random methods, respectively.