Error propagation in fractal neural networks

A fractal tree neural network comprised of binary-state neurons grouped into clusters provides a hierarchical model which can be analyzed by a renormalization group approach. Training and updating algorithms are presented along with numerical simulation results. The functional dependence of the propagation of errors from one level of the tree to the next is derived and is shown to exhibit a phase transition. When the probability of entering errors at a given level exceeds some critical value, the error propagation is unbounded and will extend throughout the entire network, whereas below the critical value, the errors remain localized and hence are contained