Alternative learning algorithms for feedforward neural networks

The efficiency of the back propagation algorithm to train feed forward multilayer neural networks has originated the erroneous belief among many neural networks users, that this is the only possible way to obtain the gradient of the error in this type of networks. The purpose of this paper is to show how alternative algorithms can be obtained within the framework of ordered partial derivatives. Two alternative forward-propagating algorithms are derived in this work which are mathematically equivalent to the BP algorithm. This systematic way of obtaining learning algorithms illustrated with this particular type of neural networks can also be used with other types such as recurrent neural networks