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We introduce a weight update formula that is expressed only in terms offiring rates and their derivatives and that results in changes consistent withthose associated with spike-timing dependent plasticity (STDP) rules andbiological observations, even though the explicit timing of spikes is notneeded. The new rule changes a synaptic weight in proportion to the product ofthe presynaptic firing rate and the temporal rate of change of activity on thepostsynaptic side. These quantities are interesting for studying theoreticalexplanation for synaptic changes from a machine learning perspective. Inparticular, if neural dynamics moved neural activity towards reducing someobjective function, then this STDP rule would correspond to stochastic gradientdescent on that objective function.

STDP as presynaptic activity times rate of change of postsynaptic activity