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A novel algorithm named Spike-LMS is described that adapts the synaptic weights of an artificial spiking neuron to produce a desired response. The derivation of Spike-LMS follows from the derivation of the least-mean squares (LMS) algorithm used in adaptive filter theory. Spike-LMS works directly in the domain of spike trains, and therefore makes no assumptions about any particular neural encoding method. This algorithm is able to identify the synaptic weights of a spiking neuron given the pre-synaptic and post-synaptic spike trains.