How can an animal learn from experience? How can it train sensors, such as the auditory or tactile system, based on other sensory input such as the visual system? Supervised spike-timing-dependent plasticity (supervised STDP) is a possible answer. Supervised STDP trains one modality using input from another one as “supervisor.” Quite complex time-dependent relationships between the senses can be learned. Here we prove that under very general conditions, supervised STDP converges to a stable configuration of synaptic weights leading to a reconstruction of primary sensory input.