**N**ext Friday, 13 March at 1:30p.m., Julyan Arbel, researcher at Inria Grenoble will give a All about that Bayes talk at CMLA, ENS Paris-Saclay (building D’Alembert, room Condorcet, Cachan, RER stop Bagneux) on

**Understanding Priors in Bayesian Neural Networks at the Unit Level**

We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L², “weight decay”, regularization. Our results characterize a more intricate regularization effect at the level of the unit activations. Our main result establishes that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. We show that first layer units are Gaussian, second layer units are sub-exponential, and units in deeper layers are characterized by sub-Weibull distributions. Our results provide new theoretical insight on deep Bayesian neural networks, which we corroborate with simulation experiments.