A characterization of neural network performances based on Fokker-Planck statistical models

The authors examine the connection between training period and detection performance by showing that a network can be described by a Fokker-Planck statistical model. Closed-form expressions are derived for the weight probabilities under suitable assumptions on the weight adaptivity and the noise process. Output node statistics are determined by computing the conditional output density as a function of the input statistics and averaging over the weight probabilities for a specific training time. It is shown that the training period is dominated by the time required to stabilize the bias weight. This weight is analogous to an adaptive threshold and is related directly to the network false alarm probability. A second issue addressed is the steady-state performance of the network. Explicit expressions are derived for the false alarm and detection probabilities. The authors show that the network implements a classical mini-max best