Convolutional Kernel Networks

TL;DR

This paper introduces a convolutional neural network that encodes invariance through a reproducing kernel, enabling simpler architectures that are easy to train and achieve competitive accuracy on standard visual recognition benchmarks.

Contribution

It presents a novel CNN approach that learns to approximate kernel feature maps, combining neural network flexibility with kernel-based invariance modeling.

Findings

Achieves competitive accuracy on MNIST, CIFAR-10, STL-10 datasets.

Simpler architectures with invariance outperform complex models.

Bridges neural networks and kernel methods for visual recognition.

Abstract

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.