ALTERNATIVE ENERGY FUNCTIONS FOR OPTIMIZING NEURAL NETWORKS
Andrew H. Gee and Richard W. Prager
When feedback neural networks are used to solve combinatorial optimization problems, their dynamics perform some sort of descent on a continuous energy function related to the objective of the discrete problem. For any particular discrete problem, there are generally a number of suitable continuous energy functions, and the performance of the network can be expected to depend heavily on the choice of such a function. In this paper, alternative energy functions are employed to modify the dynamics of the network in a predictable manner, and progress is made towards identifying which are well suited to the underlying discrete problems. This is based on a revealing study of a large database of solved problems, in which the optimal solutions are decomposed along the eigenvectors of the network's connection matrix. It is demonstrated that there is a strong correlation between the mean and variance of this decomposition and the ability of the network to find good solutions. A consequence of this is that there may be some problems which neural networks are not well adapted to solve, irrespective of the manner in which the problems are mapped onto the network for solution.
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