Deep Convolutional Networks as shallow Gaussian Processes

Abstract

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 [1, 2] for dense networks.

For a convolutional network (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 Gaussian processes with a comparable number of parameters.

Publication
Deep Convolutional Networks as shallow Gaussian Processes
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Adrià Garriga-Alonso
PhD student with Prof. Carl Rasmussen