Categorization by a three-state attractor neural network
David Domínguez, D. Bollé · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
The categorization properties of an attractor network of three-state neurons, which infers three-state concepts from examples, are studied. The evolution equations governing the parallel dynamics at zero temperature for the overlap between the state of the network and the examples, the state of the network, and the concepts, as well as the neuron activity, are derived in the limit of extreme dilution. The transition from the retrieval region to the categorization region occurring when the number of examples or their correlations are increased is discussed as a function of the zero-activity threshold of the neurons. In particular, the differences with models for binary concepts are highlighted.