Multifractality in forgetful memories

Learning rules of a forgetful memory generate their synaptic efficacies through iterative procedures that operate on the input data, random patterns. We analyse invariant distributions of the synaptic couplings as they arise asymptotically and show that they exhibit fractal or multifractal properties. We also discuss their dependence upon the learning rule and the parameters specifying it, and indicate how the nature of the invariant distribution is related to the network performance.