Lower Bounds for Tractable Arithmetic Circuits

Explore a 43-minute lecture on lower bounds for tractable arithmetic circuits presented by Alexis de Colnet from TU Wien at the Simons Institute. Delve into the world of arithmetic circuits (AC) and their role in probabilistic models. Examine the complexity-theoretic assumptions that render many operations in probabilistic reasoning intractable when distributions are represented as AC. Discover how structural restrictions like decomposability, determinism, and smoothness enable efficient polynomial-time algorithms, albeit at the cost of dramatically increased circuit size. Learn techniques for proving lower bounds on the size of tractable AC, understanding the variations based on structural restrictions. Gain insights through an example application demonstrating a function that can only be represented by large structured-decomposable AC. Enhance your understanding of probabilistic circuits and logic in this comprehensive exploration of tractable arithmetic circuits and their limitations.