Understanding hierarchical neural network behaviour: a renormalization group approach
C.R. Willcox · Journal of Physics A Mathematical and General · 1991
A hierarchical neural network model, presented in an earlier paper (Wilcox, 1989), is analysed using a renormalization group (RG) approach. The RG method puts many of the previously found empirical results on a firm theoretical foundation. The functional dependence of the propagation of errors from one level of the hierarchical 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. This result along with individual cluster updating data is used to explain the content-addressability properties of the model.