Microscopic Equations in Rough Energy Landscape for Neural Networks

Part of Advances in Neural Information Processing Systems 9 (NIPS 1996)

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K. Y. Michael Wong


We consider the microscopic equations for learning problems in neural networks. The aligning fields of an example are obtained from the cavity fields, which are the fields if that example were absent in the learning process. In a rough energy landscape, we assume that the density of the local minima obey an exponential distribution, yielding macroscopic properties agreeing with the first step replica symmetry breaking solution. Iterating the microscopic equations provide a learning algorithm, which results in a higher stability than conventional algorithms.