The cerebellum aids the learning of fast, coordinated movements. According to
current consensus, erroneously active parallel fibre synapses are depressed by complex spikes
signalling movement errors. However, this theory cannot solve the credit assignment problem of
processing a global movement evaluation into multiple cell-specific error signals. We identify a
possible implementation of an algorithm solving this problem, whereby spontaneous complex
spikes perturb ongoing movements, create eligibility traces and signal error changes guiding
plasticity. Error changes are extracted by adaptively cancelling the average error. This framework,
stochastic gradient descent with estimated global errors (SGDEGE), predicts synaptic plasticity
rules that apparently contradict the current consensus but were supported by plasticity
experiments in slices from mice under conditions designed to be physiological, highlighting the
sensitivity of plasticity studies to experimental conditions. We analyse the algorithm’s convergence
and capacity. Finally, we suggest SGDEGE may also operate in the basal ganglia.