Supervised and Unsupervised protocols for hetero-associative neural networks

TL;DR

This paper develops a theoretical framework for Three-Directional Associative Memory models, analyzing their learning and retrieval capabilities under supervised and unsupervised protocols using statistical mechanics techniques.

Contribution

It introduces a novel analysis of hetero-associative neural networks with three-layer structures, extending Hebbian learning to new protocols and providing insights into their computational properties.

Findings

Derived self-consistency equations for learning thresholds and retrieval performance.

Validated theoretical predictions with numerical simulations on structured datasets.

Highlighted differences between supervised and unsupervised learning protocols.

Abstract

This paper introduces a learning framework for Three-Directional Associative Memory (TAM) models, extending the classical Hebbian paradigm to both supervised and unsupervised protocols within an hetero-associative setting. These neural networks consist of three interconnected layers of binary neurons interacting via generalized Hebbian synaptic couplings that allow learning, storage and retrieval of structured triplets of patterns. By relying upon glassy statistical mechanical techniques (mainly replica theory and Guerra interpolation), we analyze the emergent computational properties of these networks, at work with random (Rademacher) datasets and at the replica-symmetric level of description: we obtain a set of self-consistency equations for the order parameters that quantify the critical dataset sizes (i.e. their thresholds for learning) and describe the retrieval performance of these networks, highlighting the differences between supervised and unsupervised protocols. Numerical simulations validate our theoretical findings and demonstrate the robustness of the captured picture about TAMs also at work with structured datasets. In particular, this study provides insights into the cooperative interplay of layers, beyond that of the neurons within the layers, with potential implications for optimal design of artificial neural network architectures.