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A Compositional Atlas for Algebraic Circuits
Benjie Wang, Denis Deratani Mauá, Guy Van den Broeck +1
Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing cons…
Restructuring Tractable Probabilistic Circuits
Honghua Zhang, Benjie Wang, Marcelo Arenas +1
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation…
Probabilistic Circuits for Cumulative Distribution Functions
Oliver Broadrick, William Cao, Benjie Wang +2
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, sup…
Where is the signal in tokenization space?
Renato Lui Geh, Honghua Zhang, Kareem Ahmed +2
Large Language Models (LLMs) are typically shipped with tokenizers that deterministically encode text into so-called canonical token sequences, to which the LLMs assign probability…
On the Relationship Between Monotone and Squared Probabilistic Circuits
Benjie Wang, Guy Van den Broeck
Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where…
A Circus of Circuits: Connections Between Decision Diagrams, Circuits, and Automata
Antoine Amarilli, Marcelo Arenas, YooJung Choi +3
This document is an introduction to two related formalisms to define Boolean functions: binary decision diagrams, and Boolean circuits. It presents these formalisms and several of…