Convolutional Deep Kernel Machines
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Keywords: Gaussian process, infinite-width neural network, NNGP, Bayesian deep learning
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TL;DR: We develop a convolutional version of the recently introduced deep kernel machine algorithm, using a novel inducing point scheme and NN inspired techniques to obtain a practical algorithm for CIFAR-10 size datasets.
Abstract: Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (“A theory of representation learning gives a deep generalisation of kernel methods”, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the “deep kernel machine” (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99\% test accuracy on MNIST, 72\% on CIFAR-100, and 92.7\% on CIFAR-10, which is SOTA for kernel methods.
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Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Submission Number: 5645
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