Logo image
Back
Decision-making with the Boltzmann Machine
Conference proceeding

Decision-making with the Boltzmann Machine

Moshe Kam and Roger Cheng
1989 American Control Conference, pp 902-907
Jun 1989
DOI: https://doi.org/10.23919/ACC.1989.4790318

Abstract

Association rules Convergence Decision making Decoding Machine learning Neural networks Neurons Polynomials State-space methods Tellurium
The Boltzmann Machine has been introduced as a means to perform global optimization for multimodal objective functions using the principles of simulated annealing. In this paper we consider its utility as a spurious-free content-addressable memory and provide bounds on its performance in this context: a) We 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 pre-stored patterns. Spurious fixed points, whose regions of attraction are not recognized by the rule, are skipped, due to the Machine's finite probability to escape from any state. b) We propose the use of the incremental Hebbian rule as a learning scheme for the Boltzmann-Machine-based content addressable memory. This learning rule is different from the probability-distribution-matching learning rules which are used at present for the Machine's weights in the global-minimizer application. We interpret the incremental Hebbian rule as a steepest-descent algorithm, maximizing the probability of pattern stabilization during learning. C) We describe the Hamming distance from a stored pattern using a birth-and-death Markov chain, and find bounds on the retrieval probabilities. Our bounds allow an assessment of the Machine's efficiency as a content-addressable memory.

Metrics

24 Record Views
2 citations in Scopus

Details

Logo image