Bayesian neural network unit priors and generalized Weibull-tail property

Mariia Vladimirova (Inria Grenoble Rhone-Alpes)*; Julyan Arbel (Inria Grenoble Rhone-Alpes); Stephane Girard (INRIA)


The connection between Bayesian neural networks and Gaussian processes gained a lot of attention in the last few years. Hidden units have been proven to follow a Gaussian process limit when the layer width tends to infinity. Recent work has suggested that finite Bayesian neural networks may outperform their infinite counterparts because they can flexibly adapt their internal representations. To establish solid ground for future research on finite-width neural networks, our goal is to study the prior induced on hidden units. Our main result is an accurate description of hidden units tails which shows that unit priors become heavier-tailed going deeper. This finding sheds light on the behavior of hidden units of finite Bayesian neural networks.