AI 中文总结
本文提出控制理论框架，将仅解码器语言模型建模为多索引、多速率系统，并通过随机混合系统统一生成与智能体工具交互的多相动力学，同时给出任务级误差过程的界。
AI 中文摘要
大型语言模型（LLMs）越来越多地被部署为自主决策与规划循环中的计算引擎，然而其系统与控制处理仍受到架构简化、索引混淆以及工具交互的非正式描述所阻碍。本文提出一种将仅解码器语言模型视为多索引、多速率系统的控制理论表述，并为控制智能体工具交互的多相动力学奠定随机混合系统框架的基础。我们通过三个层级耦合的演化索引来形式化该架构：（i）跨层深度的变压器块超快前馈级联，其中层归一化被建模为球面投影，且键-值缓存被证明通过因果前缀不变性实现精确的内部状态实现；（ii）在令牌生成步骤上的非受控随机差分递推，其中有限上下文截断诱导出时间齐次马尔可夫链；（iii）控制令牌生成与工具执行模式之间转换的自主模式切换机制，其中工具调用在轨迹到达切换流形时被触发，随后通过外部状态跳变映射将外部观测附加到上下文字符串中。通过定义在连续可评估声明上的提示依赖评估器，我们获得任务级误差过程，其无故障历史与预期误差增长在条件故障危险与误差漂移假设下可被界定。
英文摘要
Large language models (LLMs) are increasingly deployed as computational engines in autonomous decision-making and planning loops, yet their systems and control treatment remains hindered by architectural simplifications, index conflations, and informal descriptions of tool interactions. This paper presents a control-theoretic formulation of decoder-only language models as multi-index, multi-rate systems, and sets the stage for a stochastic hybrid systems framework to govern the multi-phase dynamics of agentic tool interaction. We formalize the architecture across three hierarchically coupled evolution indices: (i) an ultrafast feedforward cascade of transformer blocks across layer depth, where layer normalization is cast as a spherical projection and key--value caching is proven to be an exact internal state realization via causal prefix invariance; (ii) an uncontrolled stochastic difference recursion over token generation steps, where finite context truncation induces a time-homogeneous Markov chain; and (iii) an autonomous mode-switching mechanism governing transitions between token generation and tool execution regimes, where tool invocations are triggered upon trajectory arrival at switching manifolds, followed by exogenous state jump maps that augment the context string with external observations. By defining a prompt-dependent evaluator over successive evaluable claims, we obtain a task-level error process whose fault-free histories and expected error growth admit bounds under conditional fault-hazard and error-drift assumptions.
