A Hopfield network implementation of the Viterbi algorithm for hidden Markov models

Treating the Viterbi algorithm as a form of combinatorial optimization, the authors show how it can be implemented on a Hopfield network. The implementation uses a framework which ensures that the network can achieve valid solutions for a much larger class of combinatorial optimization problems than previously considered. This class includes dynamic programming problems of the type represented by the Viterbi algorithm. The aim here is to present in detail the actual mapping required to implement the Viterbi algorithm on the Hopfield network, together with an analysis and justification of it. Finally, to confirm the theory, results are presented which show that the Hopfield network achieves the same solution as a standard dynamic-programming-based Viterbi algorithm for a recognition task based on a pretrained 10-state hidden Markov model