Storage of correlated patterns in a perceptron

Abstract

We calculate the storage capacity of a perceptron for correlated gaussian patterns. We find that the storage capacity $α_c$ 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 $α_c \geq 1$ in agreement with Cover's theorem. Numerical simulations confirm the results.