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An important property of such information processing networks is locality: there is no single global unit controlling the modules, but information is exchanged locally. Here, we consider a decision-theoretic approach to study networks of bounded rational decision makers that are allowed to specialize and communicate with each other. In contrast to previous work that has focused on feedforward communication between decision-making agents, we consider cyclical information processing paths allowing for back-and-forth communication. We adapt message-passing algorithms to suit this purpose, essentially allowing for local information flow between units and thus enabling circular dependency structures. We provide examples that show how repeated communication can increase performance given that each unit\u2019s information processing capability is limited and that decision-making systems with too few or too many connections and feedback loops achieve suboptimal utility.<\/jats:p>","DOI":"10.1162\/neco_a_01719","type":"journal-article","created":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T16:24:04Z","timestamp":1728491044000},"page":"76-127","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":1,"title":["Bounded Rational Decision Networks With Belief Propagation"],"prefix":"10.1162","volume":"37","author":[{"given":"Gerrit","family":"Schmid","sequence":"first","affiliation":[{"name":"Ulm University Institute of Neuroinformatics, 89081 Ulm, Germany gerrit.schmid@uni-ulm.de"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebastian","family":"Gottwald","sequence":"additional","affiliation":[{"name":"Ulm University Institute of Neuroinformatics, 89081 Ulm, Germany sebastian.gottwald@uni-ulm.de"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel A.","family":"Braun","sequence":"additional","affiliation":[{"name":"Ulm University Institute of Neuroinformatics, 89081 Ulm, Germany daniel.braun@uni-ulm.de"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"issue":"1","key":"2024121121100617900_bib1","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/S0364-0213(85)80012-4","article-title":"A learning algorithm for Boltzmann machines","volume":"9","author":"Ackley","year":"1985","journal-title":"Cognitive Science"},{"key":"2024121121100617900_bib2","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.neunet.2012.11.010","article-title":"Parallel retrieval of correlated patterns: From Hopfield networks to Boltzmann machines","volume":"38","author":"Agliari","year":"2013","journal-title":"Neural Networks"},{"issue":"1","key":"2024121121100617900_bib3","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s10462-019-09706-7","article-title":"A review of modularization techniques in artificial neural networks","volume":"52","author":"Amer","year":"2019","journal-title":"Artificial Intelligence Review"},{"key":"2024121121100617900_bib4","doi-asserted-by":"publisher","DOI":"10.1051\/matecconf\/201815006031","article-title":"The reduction of directed cyclic graph for task assignment problem","volume-title":"MATEC Web of Conferences","author":"Ariffin","year":"2018"},{"issue":"1","key":"2024121121100617900_bib5","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1109\/TIT.1972.1054753","article-title":"An algorithm for computing the capacity of arbitrary discrete memoryless channels","volume":"18","author":"Arimoto","year":"1972","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"2024121121100617900_bib6","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.arcontrol.2008.03.004","article-title":"Decentralized control: An overview","volume":"32","author":"Bakule","year":"2008","journal-title":"Annual Reviews in Control"},{"key":"2024121121100617900_bib7","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/978-1-4615-0267-8_10","article-title":"Modules, brain parts, and evolutionary psychology","volume-title":"Evolutionary psychology: Alternative approaches","author":"Bechtel","year":"2003"},{"key":"2024121121100617900_bib8","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1016\/j.geb.2017.06.014","article-title":"Belief-free rationalizability and informational robustness","volume":"104","author":"Bergemann","year":"2017","journal-title":"Games and Economic Behavior"},{"issue":"4","key":"2024121121100617900_bib9","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.2307\/1911196","article-title":"Rationalizable strategic behavior","volume":"52","author":"Bernheim","year":"1984","journal-title":"Econometrica: Journal of the Econometric Society"},{"issue":"871","key":"2024121121100617900_bib10","first-page":"552","article-title":"Statistical theory of superlattices","volume":"150","author":"Bethe","year":"1935","journal-title":"Proceedings of the Royal Society of London. 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