This talk discusses the role of logical reasoning in statistical machine learning. While their unification has been a long-standing and crucial open problem, automated reasoning and machine learning are still disparate fields within artificial intelligence. I will describe recent progress towards their synthesis in three facets.
I start with a very practical question: how can we enforce logical constraints on the output of deep neural networks to incorporate symbolic knowledge? Second, I explain how circuits developed for tractable logical reasoning can be turned into statistical models. When brought to bear on a variety of machine learning tasks, including discrete density estimation and simple image classification, these probabilistic and logistic circuits yield state-of-the-art results. In a third facet, I argue for high-level representations of uncertainty, such as probabilistic programs, probabilistic databases, and statistical relational models. These pose unique challenges for inference that can only be overcome by high-level reasoning about their first-order structure to exploit symmetry and exchangeability.