Sorting by Hopfield net

Abstract
In a manner similar to T.T. Hopfield and D.W. Tank's implementation of the traveling salesman problem on a Hopfield net (Bio. Cybern. vol. 52, p.141-52, 1985), a Hopfield net is programmed to sort a list of arbitrary positive numbers. A detailed derivation of the mathematical constraints is presented, from the general four-axis energy equations to the numerical simulations. Excellent results were obtained from the simulations for sorts on lists containing 4 to 10 evenly spaced integers. It was found that increasing the list size n or the spacing f caused the network to become increasingly sensitive to the two parameters C and D, but near-optimal values for these were found. Sorting is probably a considerably more practical use of neural nets than solving the traveling salesman problem since sorts are used extensively throughout many applications.

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