We introduce repriorisation, a data-dependent reparameterisation which transforms a Bayesian neural network (BNN) posterior to a distribution whose KL divergence to the BNN prior vanishes as layer widths grow. The repriorisation map acts directly on parameters, and its analytic simplicity complements the known neural network Gaussian process (NNGP) behaviour of wide BNNs in function space. Exploiting the repriorisation, we develop a Markov chain Monte Carlo (MCMC) posterior sampling algorithm which mixes faster the wider the BNN. This contrasts with the typically poor performance of MCMC in high dimensions. We observe up to 50x higher effective sample size relative to no reparametrisation for both fully-connected and residual networks. Improvements are achieved at all widths, with the margin between reparametrised and standard BNNs growing with layer width.

本研究提出了一种名为'prior重定向'的方法，通过将贝叶斯神经网络后验变换为一种与BNN先验KL散度消失的分布，使用prior重定向，可以开发出更快的MCMC后验抽样算法，相较于未采用重参数化的标准BNN，我们观测到全连接和残差网络的有效样本量最高可提高50倍。

宽泛的贝叶斯神经网络具有简单的权重后验分布：理论和加速采样