Probabilistic Circuits (PCs) [1, 2] are considered to be the lingua franca for Tractable Probabilistic
Models (TPMs) as they offer a uniﬁed framework to abstract from a wide variety of TPM circuit
representations, such as arithmetic circuits (ACs) [3], sum-product networks (SPNs) [4], and prob-
abilistic sentential decision diagrams (PSDDs) [5]. PCs are a successful combination of classic
probabilistic graphical models (PGMs) and neural networks (NNs). Moreover, by enforcing various
structural properties, PCs permit efﬁcient and exact computation of a large family of probabilistic
inference queries [6, 7, 8]. The ability to answer these queries leads to successful applications in
areas such as model compression [9] and model bias detection [10, 11]. At the same time, PCs are
analogous to NNs since their evaluation is also carried out using computation graphs. By exploiting
the parallel computation power of GPUs, dedicated implementations [2, 12] can train a complex PC
Tractable Regularization of Probabilistic Circuits