Testing Arithmetic Circuits

I will discuss Testing Arithmetic Circuits (TACs), which are new tractable probabilistic models that are universal function approximators like neural networks. A TAC represents a piecewise multilinear function and computes a marginal query on the newly introduced Testing Bayesian Network (TBN). The structure of a TAC is automatically compiled from a Bayesian network and its parameters are learned from labeled data using gradient descent. TACs can incorporate background knowledge that is encoded in the Bayesian network, whether conditional independence or domain constraints. Hence, the behavior of a TAC comes with some guarantees that are invariant to how it is trained from data. Moreover, a TAC is amenable to being interpretable since its nodes and parameters have precise meanings by virtue of being compiled from a Bayesian network. This recent work aims to fuse models (Bayesian networks) and functions (DNNs) with the goal of realizing their collective benefits.