Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse communication graphs. To track opinion evolution, we map each message to an opinion score via sentiment analysis. We find that agents typically reach consensus and the disagreement between the agents decays exponentially. However, the limiting opinion departs from DeGroot's network-centrality-weighted forecast. The consensus between LLM agents turns out to be largely insensitive to initial conditions and instead depends strongly on the discussion subject and inherent biases. Nevertheless, transient dynamics align with classical graph theory and the convergence rate of opinions is closely related to the second-largest eigenvalue of the graph's combination matrix. Together, these findings can be useful for LLM-driven social-network simulations and the design of resource-efficient multi-agent LLM applications.

The increasing heterogeneity of multi-agent systems poses significant challenges for jointly training a global model across agents. At the same time, cooperative inference between agents has long been recognized as a powerful mechanism for distributed decision making over networks. Motivated by these observations, we propose a collaboration framework for distributed binary classification over multi-agent networks, where a set of independently trained agents, potentially differing in architecture, feature space, or modality, coordinate their actions during test time to form collective predictions. This coordination is achieved by exchanging local decision statistics through a distributed learning protocol. We develop a theoretical and experimental study of this independent training and cooperative inference paradigm, and examine its performance under different communication budgets and distributed learning rules. We establish classification error guarantees under sufficient, finite-round, and finite-precision communication, together with PAC-style generalization bounds. These results capture the influence of model heterogeneity, network topology, combination policy, and communication constraints on prediction accuracy. Taken together with the experimental results, they reveal both the price of independent training and the benefit of collective prediction for the proposed distributed decision making framework with models learned from data.

Non-Bayesian social learning (NBSL) is a framework in distributed inference that describes how agents in a network combine local observations and their neighbors’ beliefs to infer a hidden state. While the framework has been extensively analyzed in theory, its role as a model of belief formation in realistic multi-agent systems remains under-explored. In this work, we investigate whether NBSL can capture the belief dynamics of interacting large language model (LLM) agents. We design controlled experiments in which LLM agents revise their beliefs sequentially based on local evidence and exchanges with their neighbors. Then, we compare their belief trajectories to those predicted by NBSL. Our results provide the first empirical evaluations of NBSL on modern AI collectives, and show that LLM networks can exhibit belief evolution patterns that closely follow NBSL dynamics.

Distributed decision-making over graphs involves a group of agents that collaboratively work toward a common objective. In the social learning framework, the agents are tasked to infer an unknown state from a finite set by using a stream of local observations. The probability of decision errors for each agent asymptotically converges to zero at an exponential rate, characterized by the error exponent, which depends on the combination policy employed by the network. This work addresses the challenge of identifying optimal combination policies to maximize the error exponent for the true state while ensuring the errors for all other states converge to zero as well. We derive an upper bound on the achievable error exponent under the social learning rule, and then establish conditions for the combination policy to reach this upper bound. Moreover, we examine the performance loss scenarios when the combination policy is chosen inappropriately. From a geometric perspective, each combination policy induces a weighted nearest neighbor classifier where the weights correspond to the agents' Perron centralities. By implementing an optimized combination policy, we enhance the error exponent, leading to improved accuracy and efficiency in the distributed decision-making process.

Distributed decision-making over networks involves multiple agents collaborating to achieve a common goal. In the social learning process, where agents aim at inferring an unknown state from a stream of local observations, the probability of error in their decisions converges to zero exponentially in the asymptotic regime. The rate of this convergence, known as the error exponent, is influenced by the combination policy employed by the network. This work addresses the challenge of identifying the optimal combination policies to maximize the error exponent. We establish an upper bound on the achievable error exponents by the social learning rule and provide the conditions for the combination policy to reach this upper bound. By implementing the optimized policy, we enhance the error exponent, leading to improved accuracy and efficiency in the distributed decision-making process.

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. In this work, we examine the classification task with limited observations during the decision-making phase, which requires a non-asymptotic performance analysis. We establish a condition for consistent training and derive an upper bound on the probability of error for classification. The results clarify the dependence on the statistical properties of the data and the combination policy used over the graph. They also establish the exponential decay of the probability of error with respect to the number of unlabeled samples.

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We study the case where agents share information about only one hypothesis, namely, the trending topic, which can be randomly changing at every iteration. We show that agents can learn the true hypothesis even if they do not discuss it, at rates comparable to traditional social learning. We also show that using one's own belief as a prior for estimating the neighbors' non-transmitted beliefs might create opinion clusters that prevent learning with full confidence. This phenomenon occurs when a single hypothesis corresponding to the truth is exchanged exclusively during all times. Such a practice, however, avoids the complete rejection of the truth under any information exchange procedure -- something that could happen if priors were uniform.

Traditional social learning frameworks consider environments with a homogeneous state where each agent receives observations conditioned on the same hypothesis. In this work, we study the distributed hypothesis testing problem for graphs with a community structure, assuming that each cluster receives data conditioned on some different true state. This situation arises in many scenarios, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. We show that the adaptive social learning strategy is not only superior in nonstationary environments, but also allows each cluster to discover its own truth.

Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed hypothesis testing problem in a heterogeneous environment, where each agent can receive observations conditioned on their own personalized state of nature (or truth). We particularly focus on community structured networks, where each community admits their own true hypothesis. This scenario is common in various contexts, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. We show that the adaptive social learning strategy is a preferred choice for nonstationary environments, and allows each cluster to discover its own truth.

We consider a collaborative decision-making frame-work where heterogeneous agents receive streaming and partially informative observations. We consider two asynchronous scenarios that differ based on the agents' participation patterns and the fusion center's policies. By using hypothetical interventions on individual agents to conduct credit assignment, we attribute causal impact scores to each agent for the joint decision. By further employing these scores in a guided theoretical analysis, we compare the fusion center's two policies by evaluating their vulnerability to adversarial attacks, robustness against moderate deviations, and fairness.

In this paper, we consider a setting where heterogeneous agents with connectivity are performing inference using unlabeled streaming data. Observed data are only partially informative about the target variable of interest. In order to overcome the uncertainty, agents cooperate with each other by exchanging their local inferences with and through a fusion center. To evaluate how each agent influences the overall decision, we adopt a causal framework in order to distinguish the actual influence of agents from mere correlations within the decision-making process. Various scenarios reflecting different agent participation patterns and fusion center policies are investigated. We derive expressions to quantify the causal impact of each agent on the joint decision, which could be beneficial for anticipating and addressing atypical scenarios, such as adversarial attacks or system malfunctions. We validate our theoretical results with numerical simulations and a real-world application of multicamera crowd counting.

Social learning is a non-Bayesian framework for distributed hypothesis testing aimed at learning the true state of the environment. Traditionally, the agents are assumed to receive observations conditioned on the same true state, although it is also possible to examine the case of heterogeneous models across the graph. One important special case is when heterogeneity is caused by the presence of malicious agents whose goal is to move the agents towards a wrong hypothesis. In this work, we propose an algorithm that allows to discover the true state of every individual agent based on the sequence of their beliefs. In so doing, the methodology is also able to locate malicious behavior.

We study the asymptotic learning rates of belief vectors in a distributed hypothesis testing problem under linear and log-linear combination rules. We show that under both combination strategies, agents are able to learn the truth exponentially fast, with a faster rate under log-linear fusion. We examine the gap between the rates in terms of network connectivity and information diversity. We also provide closed-form expressions for special cases involving federated architectures and exchangeable networks.

We consider the problem of information aggregation in federated decision making, where a group of agents collaborate to infer the underlying state of nature without sharing their private data with the central processor or each other. We analyze the non-Bayesian social learning strategy in which agents incorporate their individual observations into their opinions (i.e., soft-decisions) with Bayes rule, and the central processor aggregates these opinions by arithmetic or geometric averaging. Building on our previous work, we establish that both pooling strategies result in asymptotic normality characterization of the system, which, for instance, can be utilized to derive approximate expressions for the error probability. We verify the theoretical findings with simulations and compare both strategies.

The adaptive social learning paradigm deals with the opinion formation process by a network of communicating agents in a dynamic environment. In this study, we show that a sequence of publicly exchanged beliefs allows users to discover rich information about the underlying model. In particular, it is shown that it is possible (i) to identify the influence of each individual agent to the objective of truth learning, (ii) to discover how well-informed each agent is, and (iii) to learn the underlying network topology.

The adaptive social learning paradigm helps model how networked agents are able to form opinions on a state of nature and track its drifts in a changing environment. In this framework, the agents repeatedly update their beliefs based on private observations and exchange the beliefs with their neighbors. In this work, it is shown how the sequence of publicly exchanged beliefs over time allows users to discover rich information about the underlying network topology and about the flow of information over the graph. In particular, it is shown that it is possible (i) to identify the influence of each individual agent to the objective of truth learning, (ii) to discover how well-informed each agent is, (iii) to quantify the pairwise influences between agents, and (iv) to learn the underlying network topology. The algorithm derived herein is also able to work under non-stationary environments where either the true state of nature or the graph topology are allowed to drift over time. We apply the proposed algorithm to different subnetworks of Twitter users, and identify the most influential and central agents by using their public tweets (posts).

This paper studies the non-asymptotic classification performance of the social machine learning strategy. This strategy involves an independent training phase followed by a cooperative inference phase to classify a growing number of samples. By considering instead a finite number of samples, we provide an upper bound for the probability of misclassification. This bound helps characterize the generalization ability of the social machine learning strategy, in terms of the statistical properties of the classification problem and the combination policy among the distributed classifiers. The analysis establishes the exponential decay of the probability of error with the number of samples when the training phase is consistent.

In non-Bayesian social learning, the agents of a network form their belief about a hypothesis of interest by performing individual Bayesian updates, which are then shared with their neighbors and aggregated according to a suitable pooling rule. This social learning scheme is called non-Bayesian because the pooling rule cannot be Bayesian owing to the limitations arising from the distributed learning setting. However, traditional non-Bayesian learning relies on using a local Bayesian update rule. In this work, we move away from this assumption and consider instead non-Bayesian learning with non-Bayesian updates. Taking as a benchmark the optimal centralized posterior, we show that this modified strategy can outperform traditional social learning and that, intriguingly, it can attain the same error exponent as the optimal scheme under two opposite scenarios: when the data are independent across the agents and when there are agents with highly dependent data.

This paper investigates causal influences between agents linked by a social graph and interacting over time. In particular, the work examines the dynamics of social learning models and distributed decision-making protocols, and derives expressions that reveal the causal relations between pairs of agents and explain the flow of influence over the network. The results turn out to be dependent on the graph topology and the level of information that each agent has about the inference problem they are trying to solve. Using these conclusions, the paper proposes an algorithm to rank the overall influence between agents to discover highly influential agents. It also provides a method to learn the necessary model parameters from raw observational data. The results and the proposed algorithm are illustrated by considering both synthetic data and real Twitter data.

Social learning algorithms provide a model for the formation and propagation of opinions over social networks. However, most studies focus on the case in which agents share their information synchronously over regular intervals. In this work, we analyze belief convergence and steady-state learning performance for both traditional and adaptive formulations of social learning under asynchronous behavior by the agents, where some of the agents may decide to abstain from sharing any information with the network at some time instants. We also show how to recover the underlying graph topology from observations of the asynchronous network behavior.