Training a perceptron by a bit sequence: Storage capacity

TL;DR

This paper investigates the storage capacity of a perceptron trained on a random bit sequence, revealing a reduced capacity due to correlations, supported by numerical and analytical analysis.

Contribution

It introduces a detailed analysis of perceptron storage capacity when trained on bit sequences, highlighting the impact of correlations and providing both numerical and theoretical insights.

Findings

Storage capacity decreases to alpha_c=1.70±0.02 due to correlations.

Numerical results align with signal-to-noise analysis of Hebbian weights.

Correlations between input and output bits affect perceptron performance.

Abstract

A perceptron is trained by a random bit sequence. In comparison to the corresponding classification problem, the storage capacity decreases to alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The numerical results are supported by a signal to noise analysis of Hebbian weights.