Basin of attraction of the optimal perceptron with biased patterns
Andreas Engel, Th. Schnelle · Journal of Physics A Mathematical and General · 1991
For an extremely diluted neutral network model designed by the optimal Gardner rule that stores patterns with low level of activity the basin of attraction is studied analytically. The recursion relation for the overlap with a stored pattern is two-dimensional and yields a richer bifurcation scenario than in the case of patterns with symmetric statistics. The bias in the patterns gives rise to ferromagnetic attractors which compete with the patterns.