Deep convolutional networks as shallow Gaussian processes
7th International Conference on Learning Representations, ICLR 2019
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Garriga-Alonso, A., Aitchison, L., & Rasmussen, C. (2018). Deep convolutional networks as shallow Gaussian processes. 7th International Conference on Learning Representations, ICLR 2019 https://doi.org/10.17863/CAM.42340
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.
This record's DOI: https://doi.org/10.17863/CAM.42340
This record's URL: https://www.repository.cam.ac.uk/handle/1810/295286
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