On stochastic dynamics of supervised learning

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Abstract
Recently Hansen et al. (1993) derived a Fokker-Planck equation (FPE) for the learning dynamics of neural networks, which differs from a previously given version by Radons et al. (1993). It is shown that the discrepancies are due to different implicit assumptions for the distribution of time intervals between the discrete learning events. Both approximations are therefore equally justified from a general point of view. The long-time properties, however, are independent of this distribution and are in general more accurately described in the original FPE of Radons et al. Especially, mean and variance of the synaptic parameter distributions are exact only in the latter approach.