Storage of correlated patterns in a perceptron

TL;DR

This paper analyzes how the storage capacity of a perceptron is affected by correlated Gaussian patterns, revealing that capacity can be less than 2 for similar patterns but remains at least 1 in general position, supported by simulations.

Contribution

It provides a new calculation of perceptron storage capacity for correlated patterns, extending previous results to include pattern correlations and confirming findings with simulations.

Findings

Storage capacity can be less than 2 for correlated patterns.

Capacity remains at least 1 for patterns in general position.

Numerical simulations confirm theoretical predictions.

Abstract

We calculate the storage capacity of a perceptron for correlated gaussian patterns. We find that the storage capacity $\alpha_c$ can be less than 2 if similar patterns are mapped onto different outputs and vice versa. As long as the patterns are in general position we obtain, in contrast to previous works, that $\alpha_c \geq 1$ in agreement with Cover's theorem. Numerical simulations confirm the results.