Inference in deep Bayesian neural networks is only fully understood in the infinite-width limit, where the posterior flexibility afforded by increased depth washes out and the posterior predictive collapses to a shallow Gaussian process. Here, we interpret finite deep linear Bayesian neural networks as data-dependent scale mixtures of Gaussian process predictors across output channels. We leverage this observation to study representation learning in these networks, allowing us to connect limiting results obtained in previous studies within a unified framework. In total, these results advance our analytical understanding of how depth affects inference in a simple class of Bayesian neural networks.

翻译：深海贝叶斯神经网络的推论只有在无限宽度限制下才能完全理解, 深度升高提供的后方灵活度被冲走, 后方预测崩溃到浅高斯进程。 在这里, 我们将有限的深线贝叶斯神经网络解释为高斯过程预测器在产出渠道之间的数据依赖级混合物。 我们利用这一观察来研究这些网络的代表性学习, 使我们能够在统一框架内连接先前研究获得的有限结果。 总之, 这些结果增进了我们对于深度如何影响一个简单的贝叶斯神经网络类别中的推论的分析理解。