On-line Gibbs Learning. II. Application to Perceptron and multilayer networks

In the preceding paper (“On-line Gibbs Learning. I. General Theory”) we have presented the on-line Gibbs algorithm (OLGA) and studied analytically its asymptotic convergence. In this paper we apply OLGA to on-line supervised learning in several network architectures: a single-layer perceptron, two-layer committee machine, and a winner-takes-all (WTA) classifier. The behavior of OLGA for a single-layer perceptron is studied both analytically and numerically for a variety of rules: a realizable perceptron rule, a perceptron rule corrupted by output and input noise, and a rule generated by a committee machine. The two-layer committee machine is studied numerically for the cases of learning a realizable rule as well as a rule that is corrupted by output noise. The WTA network is studied numerically for the case of a realizable rule. The asymptotic results reported in this paper agree with the predictions of the general theory of OLGA presented in paper I. In all the studied cases, OLGA converges to a set of weights that minimizes the generalization error. When the learning rate is chosen as a power law with an optimal power, OLGA converges with a power law that is the same as that of batch learning.

Authors: J. W. Kim and H. Sompolinsky
Year of publication: 1998
Journal: Phys. Rev. E 58, 2348

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