Hierarchically correlated patterns in Potts neural networks

q-state Potts-glass neural network based on pseudoinverse rule

We study the q -state Potts-glass neural network with the pseudoinverse (PI) rule. Its performance is investigated and compared with that of the counterpart network with the Hebbian rule instead. We find that there exists a critical point of q , i.e., q(cr)=14 , below which the storage capacity and the retrieval quality can be greatly improved by introducing the PI rule. We show that the dynamics of the neural networks constructed with the two learning rules respectively are quite different; but however, regardless of the learning rules, in the q-state Potts-glass neural networks with q≥3 there is a common novel dynamical phase in which the spurious memories are completely suppressed. This property has never been noticed in the symmetric feedback neural networks. Free from the spurious memories implies that the multistate Potts-glass neural networks would not be trapped in the metastable states, which is a favorable property for their applications.

Categorization in fully connected multistate neural network models

The categorization ability of fully connected neural network models, with either discrete or continuous Q-state units, is studied in this work in replica symmetric mean-field theory. Hierarchically correlated multistate patterns in a two level structure of ancestors and descendents (examples) are embedded in the network and the categorization task consists in recognizing the ancestors when the network is trained exclusively with their descendents. Explicit results for the dependence of the equilibrium properties of a Q=3-state model and a Q=infinity-state model are obtained in the form of phase diagrams and categorization curves. A strong improvement of the categorization ability is found when the network is trained with examples of low activity. The categorization ability is found to be robust to finite threshold and synaptic noise. The Almeida-Thouless lines that limit the validity of the replica-symmetric results, are also obtained.