Advances in Neural Information Processing Systems (NIPS) 11, pp. 125-131 M.S. Kearns, S. A. Solla, and D. A. Cohn, eds.,Cambridge, MA, MIT Press, 1999.

Spike-based compared to rate-based Hebbian learning

R. Kempter, W. Gerstner, and J. L. van Hemmen

A correlation-based learning rule at the spike level is formulated, mathematically analyzed, and compared to learning in a firing-rate description. A differential equation for the learning dynamics is derived under the assumption that the time scales of learning and spiking can be separated. For a linear Poissonian neuron model which receives time-dependent stochastic input we show that spike correlations on a millisecond time scale play indeed a role. Correlations between input and output spikes tend to stabilize structure formation, provided that the form of the learning window is in accordance with Hebb's principle. Conditions for an intrinsic normalization of the average synaptic weight are discussed.