Decision-making with the Boltzmann machine

The Boltzmann machine is used to perform global optimization for multimodal objective functions using the principles of simulated annealing. The authors consider its utility as a spurious-free content-addressable memory and provide bounds on its performance in the context. They show how to exploit the machine's ability to escape local minima, in order to use it, at a constant temperature, for unambiguous associative pattern-retrieval in noisy environments. An association rule, which creates a sphere of influence around each stored pattern, is used along with the machine's dynamics to match the machine's noisy input with one of the prestored patterns. The authors propose the use of the incremental Hebbian rule as a learning scheme for the Boltzmann-machine-based content-addressable memory. They described the Hamming distance from a stored pattern using a birth-and-death Markov chain and find bounds on the retrieval probabilities. The bounds allow an assessment of the machine's efficiency as a content-addressable memory. The results apply to the Boltzmann machine and to the asynchronous net of binary threshold elements (Hopfield model). They provide the network designer with worst-case and best-case bounds for the network's performance and allow polynomial-time tradeoff studies of design parameters.