  In this paper we propose a conceptual framework for higher-order artificial
neural networks. The idea of higher-order networks arises naturally when a
model is required to learn some group of transformations, every element of
which is well-approximated by a traditional feedforward network. Thus the group
as a whole can be represented as a hyper network. One of typical examples of
such groups is spatial transformations. We show that the proposed framework,
which we call HyperNets, is able to deal with at least two basic spatial
transformations of images: rotation and affine transformation. We show that
HyperNets are able not only to generalize rotation and affine transformation,
but also to compensate the rotation of images bringing them into canonical
forms.
