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1. Oscillatory and excitable dynamics in an opinion model with group opinions

   https://doi.org/10.1103/PhysRevE.112.024303  

   Sampson, Corbit R; Restrepo, Juan G; Porter, Mason A (August 2025, Physical Review E)

   In traditional models of opinion dynamics, each agent in a network has an opinion and changes in opinions arise from pairwise (i.e., dyadic) interactions between agents. However, in many situations, groups of individuals possess a collective opinion that can differ from the opinions of their constituent individuals. In this paper, we study the effects of group opinions on opinion dynamics. We formulate a hypergraph model in which both individual agents and groups of three agents have opinions, and we examine how opinions evolve through both dyadic interactions and group memberships. We find for some parameter values that the presence of group opinions can lead to oscillatory and excitable opinion dynamics. In the oscillatory regime, the mean opinion of the agents in a network has self-sustained oscillations. In the excitable regime, finite-size effects create large but short-lived opinion swings (as in social fads). We develop a mean-field approximation of our model and obtain good agreement with direct numerical simulations. We also show—both numerically and via our mean-field description—that oscillatory dynamics occur only when the numbers of dyadic and polyadic interactions of the agents are not completely correlated. Our results illustrate how polyadic structures, such as groups of agents, can have important effects on collective opinion dynamics. 

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2. Multidimensional attributes expose Heider balance dynamics to measurements

   https://doi.org/10.1038/s41598-023-42390-w  

   Linczuk, Joanna; Górski, Piotr J.; Szymanski, Boleslaw K.; Hołyst, Janusz A. (September 2023, Scientific Reports)

   Abstract Most of studied social interactions arise from dyadic relations. An exception is Heider Balance Theory that postulates the existence of triad dynamics, which however has been elusive to observe. Here, we discover a sufficient condition for the Heider dynamics observability: assigning the edge signs according to multiple opinions of connected agents. Using longitudinal records of university student mutual contacts and opinions, we create a coevolving network on which we introduce models of student interactions. These models account for: multiple topics of individual student opinions, influence of such opinions on dyadic relations, and influence of triadic relations on opinions. We show that the triadic influence is empirically measurable for static and dynamic observables when signs of edges are defined by multidimensional differences between opinions on all topics. Yet, when these signs are defined by a difference between opinions on each topic separately, the triadic interactions’ influence is indistinguishable from noise. 

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3. Local non-Bayesian social learning with stubborn agents

   https://doi.org/10.1109/TCNS.2022.3154679  

   Vial, Daniel; Subramanian, Vijay G. (February 2022, IEEE Transactions on Control of Network Systems)

   Altafini, Claudio; Como, Giacomo; Hendrickx, Julien M.; Olshevsky, Alexander; Tahbez-Salehi, Alireza (Ed.)

   We study a social learning model in which agents iteratively update their beliefs about the true state of the world using private signals and the beliefs of other agents in a non-Bayesian manner. Some agents are stubborn, meaning they attempt to convince others of an erroneous true state (modeling fake news). We show that while agents learn the true state on short timescales, they "forget" it and believe the erroneous state to be true on longer timescales. Using these results, we devise strategies for seeding stubborn agents so as to disrupt learning, which outperform intuitive heuristics and give novel insights regarding vulnerabilities in social learning. 

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4. Sample Complexity of Linear Regression Models for Opinion Formation in Networks

   https://doi.org/10.1609/aaai.v39i13.33531  

   Liu, Haolin; Rajaraman, Rajmohan; Sundaram, Ravi; Vullikanti, Anil Kumar; Wasim, Omer; Xu, Haifeng (April 2025, Proceedings of the AAAI Conference on Artificial Intelligence)

   Consider public health officials aiming to spread awareness about a new vaccine in a community interconnected by a social network. How can they distribute information with minimal resources, so as to avoid polarization and ensure community-wide convergence of opinion? To tackle such challenges, we initiate the study of sample complexity of opinion formation in networks. Our framework is built on the recognized opinion formation game, where we regard each agent’s opinion as a data-derived model, unlike previous works that treat opinions as data-independent scalars. The opinion model for every agent is initially learned from its local samples and evolves game-theoretically as all agents communicate with neighbors and revise their models towards an equilibrium. Our focus is on the sample complexity needed to ensure that the opinions converge to an equilibrium such that every agent’s final model has low generalization error. Our paper has two main technical results. First, we present a novel polynomial time optimization framework to quantify the total sample complexity for arbitrary networks, when the underlying learning problem is (generalized) linear regression. Second, we leverage this optimization to study the network gain which measures the improvement of sample complexity when learning over a network compared to that in isolation. Towards this end, we derive network gain bounds for various network classes including cliques, star graphs, and random regular graphs. Additionally, our framework provides a method to study sample distribution within the network, suggesting that it is sufficient to allocate samples inversely to the degree. Empirical results on both synthetic and real-world networks strongly support our theoretical findings. 

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5. Learning Trust Over Directed Graphs in Multiagent Systems

   Akgun, Orhan Eren; Dayı, Arif Kerem; Gil, Stephanie; Nedic, Angelia (June 2023, Proceedings of Machine Learning Research)

   Matni, N.; Morari, M.; Pappas, G. J. (Ed.)

   We address the problem of learning the legitimacy of other agents in a multiagent network when an unknown subset is comprised of malicious actors. We specifically derive results for the case of directed graphs and where stochastic side information, or observations of trust, is available. We refer to this as “learning trust” since agents must identify which neighbors in the network are reliable, and we derive a learning protocol to achieve this. We also provide analytical results showing that under this protocol i) agents can learn the legitimacy of all other agents almost surely, and ii) the opinions of the agents converge in mean to the true legitimacy of all other agents in the network. Lastly, we provide numerical studies showing that our convergence results hold for various network topologies and variations in the number of malicious agents. 

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