  An important goal in visual recognition is to devise image representations
that are invariant to particular transformations. In this paper, we address
this goal with a new type of convolutional neural network (CNN) whose
invariance is encoded by a reproducing kernel. Unlike traditional approaches
where neural networks are learned either to represent data or for solving a
classification task, our network learns to approximate the kernel feature map
on training data. Such an approach enjoys several benefits over classical ones.
First, by teaching CNNs to be invariant, we obtain simple network architectures
that achieve a similar accuracy to more complex ones, while being easy to train
and robust to overfitting. Second, we bridge a gap between the neural network
literature and kernels, which are natural tools to model invariance. We
evaluate our methodology on visual recognition tasks where CNNs have proven to
perform well, e.g., digit recognition with the MNIST dataset, and the more
challenging CIFAR-10 and STL-10 datasets, where our accuracy is competitive
with the state of the art.
