Properties of associative memory analog neural networks with asymmetric synaptic couplings
Masahiko Yoshioka, Masatoshi Shiino · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
Using the self-consistent signal-to-noise analysis, we study fully connected 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 ${\mathrm{J}}_{\mathrm{ij}}$=(1/N)${\ensuremath{\sum}}_{\mathrm{\ensuremath{\mu}}}${(${\ensuremath{\xi}}_{\mathrm{i}}^{\mathrm{\ensuremath{\mu}}}$-a)(${\ensuremath{\xi}}_{\mathrm{j}}^{\mathrm{\ensuremath{\mu}}}$-a)+(b/$\sqrt{N}$)(${\ensuremath{\xi}}_{\mathrm{i}}^{\mathrm{\ensuremath{\mu}}}$-a)+c(${\ensuremath{\xi}}_{\mathrm{j}}^{\mathrm{\ensuremath{\mu}}}$-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 but neuron-independent component in the local field of neurons, with the latter making the network behavior sample dependent. An enhancement of the storage capacity and the super retrieval phase due to the use of nonmonotonic transfer functions are shown to occur as a result of renormalization of noise even in the presence of the asymmetric synaptic couplings.