Upward Pass Semantics in Arithmetic Circuit Inference
Cory J. Butz, Jhonatan S. Oliveira, André dos Santos, Anna Norris, Kadence Meredith · 2023
An Arithmetic Circuit (AC) is a deep learning probabilistic model that is compiled by eliminating every variable in a given Bayesian Network (BN). We introduce a special case of AC, called a p-AC, in which every node is a 1, marginal, or conditional of the joint distribution defined by the given BN. This is accomplished by using wait-sets to restrict the elimination ordering used. We show both theoretical and practical advantages of p-ACs over ACs, including that there is no increase in network size. Lastly, we observe and analyze an interesting graphical relationship between semantics in deep learning inference and causal analysis.