Hierarchically correlated patterns in Potts neural networks
D. Bollé, Jozef Huyghebaert · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1995
The Q-state Potts neural network is extended to allow for storage and retrieval of hierarchically correlated patterns. A Markovian scheme is used for generating the patterns and their ancestors. Two learning rules are considered. The first one is a modified Hebbian learning rule involving a ferromagnetic term. The second one is derived from the pseudoinverse learning rule. Using replica-symmetric mean-field theory, the free energy and the fixed-point equations for the order parameters are derived for general Q and arbitrary temperature T. To compare the performance of both learning rules, the storage capacity and the retrieval quality are calculated for a Q=3 network at T=0 and different hierarchies of two generations.