Comparative study of spurious-state distribution in analogue neural networks and the Boltzmann machine

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Abstract
The authors conducted a comparative study of the density distribution of metastable states in analogue neural networks and the Boltzmann machine by evaluating number densities of the attractors of the networks as functions of storage capacity, analogue gain or temperature and pattern overlap. The analysis is based on the fact that the Boltzmann machine and the analogue neural network can be described by the Thouless-Anderson-Palmer equations with and without the Onsager reaction term, respectively. They found the remarkable result that the spurious-state density around spin glass equilibrium states is much larger for the Boltzmann machine than for the analogue neural network for a reasonably wide range of analogue gain or temperature, which leads to an expectation that the analogue neural network should possess a much better potential for memory retrieval than the Boltzmann machine.