Information Diffusion and Preferential Attachment in a Network of Large Language Models
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| Format: | Preprint |
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2025
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| _version_ | 1866908328357003264 |
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| author | Jain, Adit Krishnamurthy, Vikram Zhang, Yiming |
| author_facet | Jain, Adit Krishnamurthy, Vikram Zhang, Yiming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information Diffusion and Preferential Attachment in a Network of Large Language Models Jain, Adit Krishnamurthy, Vikram Zhang, Yiming Social and Information Networks Systems and Control 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. |
| title | Information Diffusion and Preferential Attachment in a Network of Large Language Models |
| topic | Social and Information Networks Systems and Control |
| url | https://arxiv.org/abs/2504.14438 |