New error function for single hidden layer feedforward neural networks

Feedforward neural networks (FNN) are most heavily used to identify the relation between a given set of input and desired output patterns. By the universal approximation theorem, it is clear that a single-hidden layer FNN is sufficient for the outputs to approximate the corresponding desired outputs arbitrarily close and so we consider a single-hidden layer FNN. In practice, we set up an error function so as to measure the performance of the FNN. As the error function is nonlinear, we define an iterative process, learning algorithm, to obtain the optimal choice of the connection weights and thus set up a numerical optimization problem. In this paper, we consider a new error function defined on the hidden layer We propose a new learning algorithm based on the least square methods converges rapidly. We discuss our method with the classic learning algorithms and the convergence for these algorithms.