We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike "deep kernels", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass through the original CNN with only one filter per layer. The kernel equivalent to a 32-layer ResNet obtains 0.84% classification error on MNIST, a new record for GPs with a comparable number of parameters.
@article{arxiv.1808.05587,
title = {Deep Convolutional Networks as shallow Gaussian Processes},
author = {Adrià Garriga-Alonso and Carl Edward Rasmussen and Laurence Aitchison},
journal= {arXiv preprint arXiv:1808.05587},
year = {2019}
}