A fast new algorithm for training feedforward neural networks

A fast algorithm is presented for training multilayer perceptrons as an alternative to the backpropagation algorithm. The number of iterations required by the new algorithm to converge is less than 20% of what is required by the backpropagation algorithm. Also, it is less affected by the choice of initial weights and setup parameters. The algorithm uses a modified form of the backpropagation algorithm to minimize the mean-squared error between the desired and actual outputs with respect to the inputs to the nonlinearities. This is in contrast to the standard algorithm which minimizes the mean-squared error with respect to the weights. Error signals, generated by the modified backpropagation algorithm, are used to estimate the inputs to the nonlinearities, which along with the input vectors to the respective nodes, are used to produce an updated set of weights through a system of linear equations at each node. These systems of linear equations are solved using a Kalman filter at each layer