  Probabilistic circuits (PCs) have gained prominence in recent years as a
versatile framework for discussing probabilistic models that support tractable
queries and are yet expressive enough to model complex probability
distributions. Nevertheless, tractability comes at a cost: PCs are less
expressive than neural networks. In this paper we introduce probabilistic
neural circuits (PNCs), which strike a balance between PCs and neural nets in
terms of tractability and expressive power. Theoretically, we show that PNCs
can be interpreted as deep mixtures of Bayesian networks. Experimentally, we
demonstrate that PNCs constitute powerful function approximators.
