Deep neural networks (DNN) and Gaussian processes (GP) are two powerful
models with several theoretical connections relating them, but the relationship
between their training methods is not well understood. In this paper, we show
that certain Gaussian posterior approximations for Bayesian DNNs are equivalent
to GP posteriors. This enables us to relate solutions and iterations of a
deep-learning algorithm to GP inference. As a result, we can obtain a GP kernel
and a nonlinear feature map while training a DNN. Surprisingly, the resulting
kernel is the neural tangent kernel. We show kernels obtained on real datasets
and demonstrate the use of the GP marginal likelihood to tune hyperparameters
of DNNs. Our work aims to facilitate further research on combining DNNs and GPs
in practical settings.

本文研究神经网络和高斯过程之间的关系，证明了贝叶斯神经网络的高斯后验近似等同于高斯过程的后验。在训练神经网络时，利用高斯过程的边缘似然函数来调整神经网络的超参数，得到的核函数是神经切向核。我们的工作旨在促进进一步将神经网络和高斯过程在实际应用中相结合的研究。