Phase transitions in AI-human interaction networks: statistics, computation, and probabilistic modeling

In recent years, Large Language Models (LLMs) have revolutionized Natural Language Processing with their ability to generate human-like texts. However, a fundamental challenge remains in understanding the underlying mechanisms driving their emergent behaviors, particularly the randomness in their outputs. This paper investigates the application of spin glass theory as a mathematical framework to quantify the uncertainty of LLMs. Moreover, we analyze how the interaction between the noise in LLMs and from social networks shape emergent collective behaviors of the system. By making connections between LLMs and spin glass models, we gain insights into the high-dimensional optimization landscapes of LLMs, the uncertainty in their outputs, and the role of noise in their learning process. We focus on LLMs' ability to replicate human-written flitzes, a form of flirtatious poems unique to Dartmouth College, used to invite peers or a potentially romantic partner to social events. Given flitzes' playful tone, personal references, and role in complex social networks, they represent a uniquely creative form of language, making them ideal for exploring how the temperature parameter in LLMs affects the creativity and verisimilitude of AI-generated content. To better understand where temperature affects model behavior, we look for temperature-based phase transitions through statistical analysis, computational methods, and simulation of our spin glass model. Our findings demonstrate that temperature not only governs randomness in LLM output, but also mediates deeper transitions in linguistic structure, perceived quality, and human-machine alignment. By connecting statistical physics with language generation, we provide a novel framework for understanding emergent behavior in LLMs and their interaction with complex social networks.