Microscopic Equations in Rough Energy Landscape for Neural Networks
K. Y. Michael Wong · 1996
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 metastable states 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. 1 INTRODUCTION Most neural networks learn iteratively by gradient descent. As a result, closed expressions for the final network state after learning are rarely known. This precludes further analysis of their properties, and insights into the design of learning algorithms. To complicate the situation, metastable states are often present in the energy landscape of the learning space so that, depending on the initial co...