AI 中文总结
该研究揭示了多智能体LLM命名博弈中，解码温度作为架构依赖控制参数，通过不同听者机制调控共识形成的微观动力学，得出了双速率动力学的解析有序条件。
AI 中文摘要
由大语言模型（LLM）智能体组成的去中心化群体可自发就共享约定达成共识，但其内部随机性塑造宏观有序性的微观机制尚未被探索。我们研究了一种极简的LLM命名博弈，其中听者的决策是解码温度为T的单令牌LLM调用，替代了确定性命名博弈中的库存检查。每次交互分解为库存内和库存外两个通道，条件概率分别为π(T)≡P（是|w∈P_j）和φ(T)≡P（是|w∉P_j），二者的平衡控制着有序-无序漂移。针对双速率动力学的平均场理论得出了一个解析有序条件，将随机命名博弈的共识阈值推广到(π,φ)平面上的临界线。在三种开放权重架构中，共识总能达成，但通过三种不同的听者机制实现：宽容型（重绘噪声主导）、近确定型和保守型（遗漏崩溃主导）。t_conv∼N^β中的有效有限尺寸指数β(T)随温度变化，而t_c∼e^(αT)中的温度敏感性α在不同架构间从约0.67到约0不等。因此，解码温度成为去中心化LLM群体的架构依赖控制参数，可通过统计物理工具定量表征。
英文摘要
Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature $T$, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates $π(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $ϕ(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the $(π,ϕ)$ plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent $β(T)$ in $t_{\rm conv}\!\sim\!N^β$ shifts with temperature, and the temperature-sensitivity $α$ in $t_c\!\sim\!e^{αT}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.
Comments8 pages, 8 figures, 1 table, 1 appendix
