Robustness of retrieval properties against imbalance between long-term potentiation and depression of spike-timing-dependent plasticity

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Spike-timing-dependent plasticity (STDP) has recently been shown in some physiological studies. STDP depends on the precise temporal relationship of pre- and post-synaptic spikes. Many authors have indicated that a precise balance between long-term potentiation (LTP) and long-term depression (LTD) of STDP is significant for a stable learning. However, a situation in which the balance is maintained precisely is inconceivable in the brain. Using a method of the statistical neurodynamics, we show robust retrieval properties of spatio-temporal patterns in an associative memory model against the imbalance between LTP and LTD. When the fluctuation of LTD is assumed to obey a Gaussian distribution with mean 0 and variance δ², the storage capacity takes a finite value even at large δ. This means that the balance between LTP and LTD of STDP need not to be maintained precisely, but must be maintained on average. Furthermore, we found that a basin of attraction becomes smaller as δ increases while an initial critical overlap remains unchanged.