Separate but Equal: Equality in Belief Propagation for Single Cycle Graphs

Erel Cohen, Omer Lev, Roie Zivan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Belief propagation is a widely used incomplete optimization algorithm, whose main theoretical properties hold only under the assumptions that beliefs are not equal. Nevertheless, there is much evidence that equality between beliefs does occur. A method to overcome belief equality by using unary function-nodes is assumed to resolve the problem. We focus on Min-sum, the belief propagation version for solving constraint optimization problems. We prove that on a single cycle graph, belief equality can be avoided only when the algorithm converges to the optimal solution. In any other case, the unary function methods will not prevent equality, rendering some existing results in need of reassessment. We differentiate between belief equality, which includes equal beliefs in a single message, and assignment equality, that prevents a coherent selection of assignments to variables. We show the necessary and satisfying conditions for both.

Original languageEnglish
Title of host publicationAAAI-23 Technical Tracks 4
EditorsBrian Williams, Yiling Chen, Jennifer Neville
PublisherAAAI press
Number of pages8
ISBN (Electronic)9781577358800
StatePublished - 27 Jun 2023
Event37th AAAI Conference on Artificial Intelligence, AAAI 2023 - Washington, United States
Duration: 7 Feb 202314 Feb 2023

Publication series

NameProceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023


Conference37th AAAI Conference on Artificial Intelligence, AAAI 2023
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Artificial Intelligence

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