The local minima-free condition of feedforward neural networks forouter-supervised learning

摘要

In this paper, the local minima-free conditions of thenouter-supervised feedforward neural networks (FNN) based on batch-stylenlearning are studied by means of the embedded subspace method. It isnproven that only if the rendition that the number of the hidden neuronsnis not less than that of the training samples, which is sufficient butnnot necessary, is satisfied, the network will necessarily converge tonthe global minima with null cost, and that the condition that the rangenspace of the outer-supervised signal matrix is included in the rangenspace of the hidden output matrix Is sufficient and necessary conditionnfor the local minima-free in the error surface. In addition, under thencondition of the number of the hidden neurons being less than that ofnthe training samples and greater than the number of the output neurons,nit is demonstrated that there will also only exist the global minimanwith null cost in the error surface if the first layer weights arenadequately selected