Short-term synaptic depression: implications for learning

We investigate the implications of the recently observed short term synaptic depression (STD) occurring for rapid pre-synaptic ¯ring, for the properties of the working memory states in a recurrent network of spiking neurons. To this end, starting from the phenomenological model proposed by Tsodyks and Markram, we calculate an `exact' analytical expression for the time evolution of all the moments of the variable expressing the amount of synaptic resources involved in each spike transmission. Using this result, we develop an 'extended ' mean ¯eld theory, and perform simulations. We argue that the frequency adaptation under stimulation brings about a smooth dependence of the frequencies of the stable ¯xed points for the collective states of the network on the average level of synaptic potentiation.