Richard Kempter, Wulfram Gerstner, J. 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. Corre(cid:173) lations 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 nor(cid:173) malization of the average synaptic weight are discussed.