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.

通过用一种新型卷积神经网络（CNN）来编码不变性的再生核，本文解决了视觉识别中旨在设计对特定变换具有不变性的图像表示的问题， 其中与传统方法不同的是，我们的网络学习在训练数据上逼近核特征映射，从而带来了多个优势，包括获得具有不变性的简单神经网络体系结构，实现与更复杂CNNs相似的准确度，以及抵抗过拟合等。

卷积核网络