Categorization in fully connected multi-state neural network models

TL;DR

This paper investigates the categorization capabilities of fully connected multi-state neural networks using mean-field theory, revealing how training with low-activity examples enhances performance and robustness to noise.

Contribution

It provides explicit phase diagrams and categorization curves for multi-state neural networks, advancing understanding of their equilibrium properties and robustness.

Findings

Training with low-activity examples improves categorization.

Categorization ability is robust to noise and finite thresholds.

Explicit phase diagrams for Q=3 and Q=∞ models are derived.

Abstract

The categorization ability of fully connected neural network models, with either discrete or continuous Q-state units, is studied in this work in replica symmetric mean-field theory. Hierarchically correlated multi-state patterns in a two level structure of ancestors and descendents (examples) are embedded in the network and the categorization task consists in recognizing the ancestors when the network is trained exclusively with their descendents. Explicit results for the dependence of the equilibrium properties of a Q=3-state model and a $Q=\infty$-state model are obtained in the form of phase diagrams and categorization curves. A strong improvement of the categorization ability is found when the network is trained with examples of low activity. The categorization ability is found to be robust to finite threshold and synaptic noise. The Almeida-Thouless lines that limit the validity of the replica-symmetric results, are also obtained.