A Complexity Map of Probabilistic Reasoning for Neurosymbolic Classification Techniques

Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. Informed multi-label classification is a sub-field of neurosymbolic AI which studies how to leverage prior knowledge to improve neural classification systems. Recently, a family of neurosymbolic techniques for informed classification based on probabilistic reasoning has gained significant traction. Unfortunately, depending on the language used to represent prior knowledge, solving certain probabilistic reasoning problems can become prohibitively hard when the number of classes increases. Therefore, the asymptotic complexity of probabilistic reasoning is of cardinal importance to assess the scalability of such techniques. In this paper, we develop a unified formalism for four probabilistic reasoning problems. Then, we compile several known and new tractability results into a single complexity map of probabilistic reasoning. We build on top of this complexity map to characterize the domains of scalability of several techniques. We hope this work will help neurosymbolic AI practitioners navigate the scalability landscape of probabilistic neurosymbolic techniques.