1996•Journal of Physics A Mathematical and GeneralOpen access

Optimal capacity of graded-response perceptrons: a replica-symmetry-breaking solution

D. Bollé, Rubem Erichsen

Abstract

Optimal capacities of perceptrons with graded input - output relations are studied within the first-step replica-symmetry-breaking Gardner approach. Input-data errors and a limited output precision are allowed. In particular, the role of non-monotonicity in the input - output relations on the breaking and on the overall performance is determined.

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Key concepts: Replica, Perceptron, Monotonic function, Symmetry breaking, Symmetry (geometry), Computer science, Mathematics, Statistical physics