转录本管理Transformer：具有两个启用弹出的转录本的单调多智能体崩溃与普适性
Transcript-Managed Transformers: Monotone Multi-Agent Collapse and Universality with Two Pop-Enabled Transcripts
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中文总结 AI 辅助
该研究针对固定有限精度因果Transformer的转录本管理，提出转录本管理转换器模型，证明两个启用弹出的转录本足以实现普适性，明确不同通道数对应的语言层次及相关模拟特性。
中文摘要 AI 辅助
我们研究固定有限精度因果Transformer的转录本管理。转录本被划分为具有受限块的通道，每次转换会查询固定的可见后缀，并可追加一个块，同时保持模型、权重和token协议不变。操作$P_c:=\text{PopContext}(c)$会删除通道$c$上的最新块并暴露其前一个块。我们用转录本管理转换器$\text{TMT}_k$对该层建模：它包含一个有限控制器、$k$个通道，以及在调用者驱动的状态映射下的每轮动作（停留、推送和弹出），固定可见窗口编码为有限符号。无弹出的受限转录本管理转换器$\text{RTMT}_k$是标准的仅追加层，对于每个固定的$k$，它恰好实现确定的有限状态转换。在追加、路由和复制可见块的单调协议下，对于每个固定的有限智能体群体，该结论同样成立。允许$\text{Pop}$操作$\text{\textbackslash}\text{lbrace}P_c\text{\textbackslash}\text{\textbar}_{c=1}^k\text{\textbackslash}\text{rbrace}$可恢复弹出功能。按最新优先，启用弹出的通道是一个栈；编译为Hopcroft–Ullman表示后，经典层次结构成立：$k=1$时对应确定上下文无关语言（$\text{DCFL}$），$k\backslashge2$时对应递归可枚举语言（$\text{RE}$）。协调的单通道智能体匹配一个控制器与$k$个通道，因此无论是单个智能体还是两个智能体中的两个启用弹出的转录本，都足以实现普适性。文中还说明了模拟成本，以及对固定块大小和可见半径的不变性。这些界限固定了精度、字母表、块、可见性、控制器状态和群体；扩展精确上下文、隐藏块访问、可写存储和无界$\text{Spawn}$会增加更多状态。
英文摘要
We study transcript management for fixed, finite-precision causal Transformers. A transcript is partitioned into channels of bounded blocks. Each transition consults a fixed visible suffix and may append one block, leaving the model, weights, and token protocol unchanged. The operation $P_c:=\PopContext(c)$ deletes the newest block on channel $c$ and exposes its predecessor. We model the layer by the Transcript-Managed Transducer $\TMTn{k}$: one finite controller, $k$ channels, and per-round actions from stay, push, and pop under a caller-driven status map. Fixed visible windows encode as finite symbols. The pop-free Restricted Transcript-Managed Transducer $\RTMTn{k}$ is the standard append-only layer and, for every fixed $k$, realizes exactly the deterministic finite-state transductions. The same holds for every fixed finite agent population under a monotone protocol that appends, routes, and copies visible blocks. Admitting $\{P_c\}_{c=1}^k$ restores pop. Newest-first, a pop-enabled channel is a stack; compiling to the Hopcroft--Ullman presentation transfers the classical hierarchy: $\DCFL$ for $k=1$ and $\RE$ for every $k\ge2$. Orchestrated one-channel agents match one controller with $k$ channels, so two pop-enabled transcripts---in one agent or two---suffice for universality. Simulation costs and invariance to fixed block size and visible radius are stated. The bounds fix precision, alphabets, blocks, visibility, controller state, and population; growing exact context, hidden-block access, writable stores, and unbounded \textbf{Spawn} add further state.
