We consider the problem of on-line gradient descent learning for general two-layer neural networks. An analytic solution is pre(cid:173) sented and used to investigate the role of the learning rate in con(cid:173) trolling the evolution and convergence of the learning process. Learning in layered neural networks refers to the modification of internal parameters {J} which specify the strength of the interneuron couplings, so as to bring the map fJ implemented by the network as close as possible to a desired map 1. The degree of success is monitored through the generalization error, a measure of the dissimilarity between fJ and 1. Consider maps from an N-dimensional input space e onto a scalar (, as arise in the formulation of classification and regression tasks.

We consider the problem of online gradient descent learning for general two-layer neural networks. An analytic solution is presented and used to investigate the role of the learning rate in controlling the evolution and convergence of the learning process. Two-layer networks with an arbitrary number of hidden units have been shown to be universal approximators [1] for such N-to-one dimensional maps. We investigate the emergence of generalization ability in an online learning scenario [2], in which the couplings are modified after the presentation of each example so as to minimize the corresponding error. The resulting changes in {J} are described as a dynamical evolution; the number of examples plays the role of time.

We consider the problem of online gradient descent learning for general two-layer neural networks. An analytic solution is presented and used to investigate the role of the learning rate in controlling the evolution and convergence of the learning process. Two-layer networks with an arbitrary number of hidden units have been shown to be universal approximators [1] for such N-to-one dimensional maps. We investigate the emergence of generalization ability in an online learning scenario [2], in which the couplings are modified after the presentation of each example so as to minimize the corresponding error. The resulting changes in {J} are described as a dynamical evolution; the number of examples plays the role of time.

Sollat CONNECT, The Niels Bohr Institute Blegdamsdvej 17 Copenhagen 2100, Denmark Abstract We consider the problem of online gradient descent learning for general two-layer neural networks. An analytic solution is presented andused to investigate the role of the learning rate in controlling theevolution and convergence of the learning process. Two-layer networks with an arbitrary number of hidden units have been shown to be universal approximators [1] for such N-to-one dimensional maps. We investigate the emergence of generalization ability in an online learning scenario [2], in which the couplings are modified after the presentation of each example so as to minimize the corresponding error. The resulting changes in {J} are described as a dynamical evolution; the number of examples plays the role of time.