A Criterion for the Convergence of Learning with Spike Timing Dependent Plasticity

Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)

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Robert Legenstein, Wolfgang Maass


We investigate under what conditions a neuron can learn by experimen- tally supported rules for spike timing dependent plasticity (STDP) to pre- dict the arrival times of strong “teacher inputs” to the same neuron. It turns out that in contrast to the famous Perceptron Convergence Theo- rem, which predicts convergence of the perceptron learning rule for a simplified neuron model whenever a stable solution exists, no equally strong convergence guarantee can be given for spiking neurons with STDP. But we derive a criterion on the statistical dependency structure of input spike trains which characterizes exactly when learning with STDP will converge on average for a simple model of a spiking neuron. This criterion is reminiscent of the linear separability criterion of the Percep- tron Convergence Theorem, but it applies here to the rows of a correlation matrix related to the spike inputs. In addition we show through computer simulations for more realistic neuron models that the resulting analyti- cally predicted positive learning results not only hold for the common interpretation of STDP where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.