Optimally adapted multi-state neural networks trained with noise

TL;DR

This paper extends the principle of adaptation to multi-state neural networks trained with noise, demonstrating enhanced storage capacity and retrieval performance through optimized thresholds and self-consistent parameters.

Contribution

It introduces a self-consistent adaptation method for multi-state neural networks trained with noise, improving storage capacity and retrieval quality.

Findings

Enhanced storage capacity with optimized thresholds

Explicit phase diagrams for Q=3 and Q=4 networks

Stable results against replica-symmetry-breaking fluctuations

Abstract

The principle of adaptation in a noisy retrieval environment is extended here to a diluted attractor neural network of Q-state neurons trained with noisy data. The network is adapted to an appropriate noisy training overlap and training activity which are determined self-consistently by the optimized retrieval attractor overlap and activity. The optimized storage capacity and the corresponding retriever overlap are considerably enhanced by an adequate threshold in the states. Explicit results for improved optimal performance and new retriever phase diagrams are obtained for Q=3 and Q=4, with coexisting phases over a wide range of thresholds. Most of the interesting results are stable to replica-symmetry-breaking fluctuations.