Exponential storage and retrieval in hierarchical neural networks
C R Wilcox · Journal of Physics A Mathematical and General · 1989
A hierarchical neural network model capable of storing and retrieving an exponential number of states is introduced. Formulated on a spin glass analogy, the network spins (neurons) are organised into a multitier cluster hierarchy such that, for an N-spin system, the number of stored states grows exponentially with N. Relaxation occurs at zero temperature by what is essentially a tunnelling process and can be implemented using either a bottom-up or top-down updating procedure. As a result of the encoding prescription, the stored states are highly correlated and can be embedded within an ultrametric topology. The information capacity is determined, as well as the model's ability to content-address its stored memory patterns. Numerical simulations illustrating the operation and effectiveness of various hierarchical systems are also presented.