Probabilistic Circuits: A Tractable Framework for AI Reasoning

A recent cumulative habilitation thesis, identified as arXiv (2608.16565), introduces probabilistic circuits (PCs) as an effective and manageable framework for learning and reasoning amidst uncertainty in artificial intelligence. It posits probability as a fundamental language for AI, emphasizing its ties to logic and information theory, the straightforward nature of probabilistic reasoning through sum and product rules, the similarities between probabilistic inference and human thought processes, and its significance in optimal decision-making. Nonetheless, the NP-hard nature of probabilistic inference in most models presents considerable computational hurdles. PCs overcome these obstacles by implementing structural constraints that guarantee exact computations for various inference queries in polynomial time, including marginals, conditionals, and more complex tasks. This thesis is newly published on arXiv and is the first part of a series.