1. A computer-implemented method of implementing learning in a computerized spiking neuron, the method being performed by one or more processors configured to execute computer program modules, the method comprising: operating the neuron in accordance with a learning process configured to be updated at one or more time intervals, the learning process update comprising: retrieving prior values of first and second traces associated, respectively, with first and second connections that are capable of providing spiking input into the neuron; determining a rate of change of: (i) the first trace based on (1) the prior value of the first trace and (2) a product of a neuron portion and a first connection portion; and (ii) the second trace based on (1) the prior value of the second trace and (2) a product of the neuron portion and a second connection portion; and determining an updated value of the first and second traces based on the respective rate of change; wherein: the prior values of the first and the second traces are associated with another update preceding the update, the first connection portion and the second connection portion are based on one or more spikes of a spiking input being provided, respectively, via the first and the second connections, the one or more spikes occurring within a time interval between the another update and the update; and the learning process is capable of causing the neuron to generate an output in accordance with the spiking input, the output being characterized by a performance measure configured such that the update is capable of reducing the measure.