Spike-based learning rules and stabilization of persistent neural activity

We analyze the conditions under which synaptic learning rules based on action potential timing can be approximated by learning rules based on firing 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-Hebbianplasticity can be approximated under certain conditions by a learning rule that depends on the time derivative of the postsynaptic firing rate. Such a learning rule acts to stabilize persistent neural activity patterns in recurrent neural networks.