(eng): A great deal of attention has been paid to alternative techniques to data augmentation in the literature. Their goal is to make convolutional neural networks (CNNs) invariant or at least robust to various transformations. In this paper, we present an ensemble model combining a classic CNN with an invariant CNN\nwhere both were trained without any augmentation. The goal is to preserve the performance of the classic CNN on nondeformed images (where it is supposed to classify more accurately) and the performance of the invariant CNN on deformed images (where it is the other way around). The combination is controlled by another network which outputs a coefficient that determines the fusion rule of the two networks. The auxiliary network is trained to output the coefficient depending on the intensity of the image deformation. In the experiments, we focus on rotation as a simple and most frequently studied case of transformation. In addition, we present a network invariant to rotation that is fed with the Radon transform of the input images. The performance of this network is tested on rotated MNIST and is further used in the ensemble whose performance is demonstrated on the CIFAR10- dataset.