Information Diffusion and Preferential Attachment in a Network of Large Language Models

TL;DR

This work addresses information diffusion in a centrally controlled network of LLMs prone to hallucinations by formulating a mean-field two-time-scale model, where fast diffusion dynamics interact with slow network reconfiguration. It develops a singular perturbation approach to approximate the coupled system, and proposes a reputation-based readjustment (trust-based preferential attachment) algorithm to rewire the network in favor of truthful nodes. Key theoretical contributions include a local asymptotic stability result for the all-truthful equilibrium, and concentration bounds establishing the validity of the mean-field approximation; these are complemented by empirical validation on LLaMA-3.1 8B showing improved convergence and token-efficient control via SPSA-based optimization. The framework provides a scalable, privacy-preserving mechanism to reduce hallucinations in distributed LLM inference and offers principled guidance for designing adaptive LLM networks in practice.

Abstract

This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for the centrally administered network, where opinions evolve faster while the network's degree distribution changes more slowly. Using a mean-field approximation, we establish conditions for a locally asymptotically stable equilibrium where all LLMs remain truthful. We provide approximation guarantees for the mean-field approximation and a singularly perturbed approximation of the two-time-scale system. To mitigate hallucination and improve the influence of truthful nodes, we propose a reputation-based preferential attachment mechanism that reconfigures the network based on LLMs' evaluations of their neighbors. Numerical experiments on an open-source LLM (LLaMA-3.1-8B) validate the efficacy of our preferential attachment mechanism and demonstrate the optimization of a cost function for the two-time-scale system.

Figures (4)

• Figure 1: System Model of a Single LLM: At each time step $k$, each LLM receives a composite input consisting of a private observation from the true state $x$, answers from the previous round of the LLM and its neighbors, and the system prompt (which acts as the control). The LLM outputs either an estimate of the state or "does not know". If the private information is non-informative, the LLM can either say it does not know or can make up a state estimate.
• Figure 2: Algorithm \ref{['alg:trustrankbasedreadjustment']} can readjust the network to ensure a faster convergence to stable equilibrium near $(1,0,0)$ compared to other static preferential attachment-based network initializations.
• Figure 3: Final value of $\boldsymbol{\rho}_T$ and token cost under varying the control $u$ (soft token thresholds) across 20 questions (5 trials each). $\boldsymbol{\rho}_T$ peaks around control $u=20$ and $\boldsymbol{\rho}_H$ peaks around control $u=35$, then plateus, while token cost rises steadily. This highlights the need for optimized control to balance cost and hallucination reduction.
• Figure 4: Gradient descent can be used to optimize the cost function associated with a network of LLMs. The blue line indicates the cost function being optimized using a set of $10$ question and answer (QA) pair set. The orange line indicates the cost function on a separate $10$ QA pair set. The cost decreases and stabilizes, indicating effective convergence. This confirms that the optimized $u$ successfully optimizes the trade-off defined in \ref{['eq:costfunction']}.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2: krishnamurthy_partially_2016
• Theorem 3: khalil2002nonlinear
• Proposition 1
• proof