Current convolutional networks work with inefficient pixel-wise image representation, which does not provide almost any invariance. This leads to using very large training sets and massive augmentation. We propose to decompose intra-class variances into two degradation operators where one of them can be mathematically modelled by a superposition integral with a transformation of the coordinates. We propose to design hybrid network architectures that use both pixel-level and newly developed high-level invariant image representations such that the high-level representation will eliminate the influence of modelable degradations. The other intraclass variances will be tackled by deep learning on the pixel-level part of the network. We suppose to develop multi-branch parallel architectures as well as single-branch ones, that we obtain by generalization of group equivariant networks. This shall lead to a substantial reduction of the training set without sacrificing the recognition rate. The results of the project could define new standards in image-oriented network architectures.