Detailed balance in large language model-driven agents
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917137911644160 |
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| author | Song, Zhuo-Yang Cao, Qing-Hong Luo, Ming-xing Zhu, Hua Xing |
| author_facet | Song, Zhuo-Yang Cao, Qing-Hong Luo, Ming-xing Zhu, Hua Xing |
| contents | Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10047 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Detailed balance in large language model-driven agents Song, Zhuo-Yang Cao, Qing-Hong Luo, Ming-xing Zhu, Hua Xing Machine Learning Statistical Mechanics Artificial Intelligence Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable. |
| title | Detailed balance in large language model-driven agents |
| topic | Machine Learning Statistical Mechanics Artificial Intelligence Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2512.10047 |