Bayesian Neural Network Priors Revisited

Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using SGD. We find that convolutional neural network (CNN) weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. Building these observations into priors leads to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.