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Recent research shows that for training with $\ell_2$ loss, convolutional neural networks (CNNs) whose width (number of channels in convolutional layers) goes to infinity correspond to regression with respect to the CNN Gaussian Process kernel (CNN-GP) if only the last layer is trained, and correspond to regression with respect to the Convolutional Neural Tangent Kernel (CNTK) if all layers are trained.
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Sanjeev Arora, Simon S Du, Wei Hu, Zhiyuan Li, Ruslan Salakhutdinov, and Ruosong Wang · 2019
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Invariance reduces variance: Understanding data augmentation in deep learning and beyond
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Bayesian deep convolutional networks with many channels are gaussian processes
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