Multifractal analysis of the coupling space of feedforward neural networks

Random input patterns induce a partition of the coupling space of feedforward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum f(alpha) can be calculated analytically using the replica trick. A phase transition in the multifractal spectrum corresponds to the crossover from percolating to nonpercolating cell sizes. instabilities of negative moments are related to the Vapnik-Chervonenkis (VC) dimension [Theor. Prob. Appl. 16, 264 (1971)].