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

2025-04-20

AI Summary

This paper addresses the credibility degradation in multi-LLM collaborative networks for distributed data querying, caused by hallucination-induced inconsistencies. Methodologically, it introduces a novel modeling framework integrating dual-timescale stochastic dynamics with reputation-driven preferential attachment: (i) it combines dual-timescale random dynamical systems with mean-field approximation to characterize information diffusion evolution across the LLM network; and (ii) it designs a real-time reputation–based dynamic graph reconfiguration mechanism to adaptively amplify the influence of honest nodes. Theoretically, it proves the local asymptotic stability of the fully honest equilibrium. Empirically, on LLaMA-3.1-8B, the approach reduces hallucination rate by 37%, significantly improves overall answer credibility, and ensures stable convergence of the cost function.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

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.

Problem

• Modeling information diffusion in LLM networks with hallucination risks
• Ensuring stable equilibrium where LLMs remain truthful
• Mitigating hallucination via reputation-based network reconfiguration

Innovation

• Two-time-scale dynamical model for LLM networks
• Mean-field approximation for stable equilibrium
• Reputation-based preferential attachment mechanism