We analyze the conditions under which synaptic learning rules based on action potential timing can be approximated by learning rules based on ring rates. In particular, we consider a form of plasticity in which synapses depress when a presynaptic spike is followed by a postsynaptic spike, and potentiate with the opposite temporal ordering. Such differential anti-Hebbian plasticity can be approximated under certain conditions by a learning rule that depends on the time derivative of the postsynaptic ring rate. Such a learning rule acts to stabilize persistent neural activity patterns in recurrent neural networks
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