We calculate the number, p = a N of random N-bit patterns that an optimal neural network can store allowing a given fraction f of bit errors and with the condition that each right bit is stabilised by a local field at least equal to a parameter K. For each value of a and K, there is a minimum fraction f", of wrong bits. We find a critical line, a , ( K ) with a,(O) = 2. The minimum fraction of wrong bits vanishes for a EC cyc( K ) a n d increases from zero for a > a,( K 1. The calculations are

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... one using a saddle-point method and the order parameters at the saddle point are assumed to be replica symmetric. This solution is locally stable in a finite region of the K,a plane including the line, a , ( K ) but there is a line above which the solution becomes unstable and replica symmetry must be broken.