Neural networks and image pyramids share many similarities, as we have shown in previous papers. In this paper we explore the usage of neural network learning algorithms for image pyramids. In particular, learning algorithms for principal component extraction have some interesting properties for pyramids. These algorithms are consistent with Linskers principle of maximum information preservation. We will review several algorithms for principal component extraction and show how they can be used in regular, gray-level pyramids. The usage of constraint autoassociative back-propagation networks yields a new type of pyramid, where not all cells perform the same reduction function. Several applications for this new type of pyramid are outlined.