1. A system configured to implement an update for a computerized spiking neuron capable of producing an outcome consistent with (i) an input spiking signal, and (ii) a learning task, the system comprising: one or more processors configured to execute computer program modules to cause the one or more processors to: determine a present value of an eligibility trace, the eligibility trace comprising a time history of one or more spikes of the input spiking signal, the time history including information associated with individual ones of the one or more spikes occurring at a time period prior to the present time; determine a rate of change of the eligibility trace at the present time based on (i) the present value of the eligibility trace; and (ii) a product of a neuron portion and connection portion; and effectuate the update based on the rate of change of the eligibility trace; wherein: the neuron portion is characterized by a present neuron state; and the update is configured to transition the present neuron state towards a target state, the target state being associated with producing the outcome.