Invariant recognition in Potts glass neural networks

The authors show that a Potts glass neural network can be used for invariant recognition. Each neuron is modelled as a q state Potts variable and p Potts configurations are stored in the network. The learning rule is a generalized Hebb rule, so that all pq! permutations of the patterns are stabilized simultaneously. They analyse the model for an extensive number of patterns and present results of numerical simulations to confirm the analytical results and to illustrate the relaxation to equilibrium. The model is applied to the recognition of isomorphic graphs. Finally they show how to generalize the model, such that its stable states are patterns, were the permutational symmetry is broken in a hierarchical manner.