12. A non-transitory computer-readable storage medium apparatus, said storage medium comprising a plurality of instructions to adjust a learning parameter associated with a computerized spiking neuron configured to produce an output spike signal consistent with (i) an input spike signal, and (ii) a learning task, the instructions configured to, when executed: construct a time derivative representation of a trace of a neuron state, based at least in part on said input spike signal and a state parameter; obtain a realization of said trace, based at least in part on an integration of said time derivative representation; and determine an adjustment of said learning parameter, based at least in part on said trace; wherein: said adjustment is configured to transition said neuron state towards a target state, said target state associated with said production of said output spike signal by said neuron; and said state parameter q is configured to characterize a time evolution of said neuron state in accordance with a state evolution process characterized by: a response mode and a transition mode, said response mode is associated with generation of a neuronal response; a state transition term V describing changes of neuronal state in said transition mode; a state transition term R describing changes of state set in said response mode; and a state transition term G describing changes of state set due to said input spike signal.
14. The apparatus of claim 12 , wherein said input spike signal comprises a plurality of spikes, and said state transition term G is configured to describe changes of said state parameter due to an integral effect of said plurality of spikes; and said output spike signal comprises at least said neuronal response.