%0 Generic %1 garrigaalonso2018convolutional %A Garriga-Alonso, Adrià %A Aitchison, Laurence %A Rasmussen, Carl Edward %D 2018 %K CNN GP and %T Deep Convolutional Networks as shallow Gaussian Processes %U http://arxiv.org/abs/1808.05587 %X 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.

@misc{garrigaalonso2018convolutional, 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 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.}, added-at = {2018-12-09T00:37:49.000+0100}, author = {Garriga-Alonso, Adrià and Aitchison, Laurence and Rasmussen, Carl Edward}, biburl = {https://www.bibsonomy.org/bibtex/2e3ddc7c06705f200df3eb67539ed6b6e/zezhou}, description = {1808.05587.pdf}, interhash = {4331896f17dee7b3d7e6b2bdca9c2266}, intrahash = {e3ddc7c06705f200df3eb67539ed6b6e}, keywords = {CNN GP and}, note = {cite arxiv:1808.05587}, timestamp = {2018-12-09T00:37:49.000+0100}, title = {Deep Convolutional Networks as shallow Gaussian Processes}, url = {http://arxiv.org/abs/1808.05587}, year = 2018 }