Recently we introduced the concept of neural networks learning on Stiefel-Grassman manifold for MLP-like networks. Contributions of other authors have also appeared in the scientific literature about this topic. The aim of this paper is to present a general theory for it, and to illustrate how existing theories may be explained within the general framework proposed here. 1 1 Introduction In a multilayer-perceptron-like network formed by the interconnection of basic neurons, whose only adjustable part consists of weight-vectors, learning the optimal set of connection patterns may be interpreted as selecting the best directions among all possible ones in the space that the weight-vectors belong to (Fyfe, 1995). This interpretation is very useful, in that if a learning error criterion is defined over the weight-space, it measures how much interesting directions are, so that ultimately the rule with which network learns may be conceived as a searching procedure allowing to find out..