M. Yoshioka et M. Shiino, PROPERTIES OF ASSOCIATIVE MEMORY ANALOG NEURAL NETWORKS WITH ASYMMETRIC SYNAPTIC COUPLINGS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(6), 1997, pp. 7401-7413
Using the self-consistent signal-to-noise analysis, we study fully con
nected analog neural networks having asymmetric synaptic couplings and
positive-valued nonmonotonic transfer functions. Asymmetric synaptic
couplings we assume are based on random patterns with bias a and given
by =(1/N)Sigma(mu){(xi(i)(mu)-a)(xi(j)(mu)-a)+(b/root N)(xi(i)(mu)-a)
+c(xi(j)(mu)-a)+(d/N)}, where N is the number of neurons. We find that
the synaptic interaction term of memorizing the postsynaptic activity
(b term) and that of the presynaptic activity (c term) respectively,
give rise to renormalized noise and a renormalized pattern-dependent b
ut neuron-independent component in the local field of neurons, with th
e latter making the network behavior sample dependent. An enhancement
of the storage capacity and the super retrieval phase due to the use o
f nonmonotonic transfer functions are shown to occur as a result of re
normalization of noise even in the presence of the asymmetric synaptic
couplings.