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 ${\alpha }_c$ 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 ${\alpha }_c\ge 1$ in agreement with Cover's theorem. Numerical simulations confirm the results.

9 pages LaTeX ioplppt style, figures included using epsf

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