Transcript-Managed Transformers: Monotone Multi-Agent Collapse and Universality with Two Pop-Enabled Transcripts

Abstract: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.

14 pages, 2 tables, 0 figures. Theoretical results on transcript management for fixed-precision Transformers: monotone multi-agent collapse to finite-state transducers, and universality with two pop-enabled transcript channels

Machine Learning (cs.LG); Formal Languages and Automata Theory (cs.FL); Multiagent Systems (cs.MA)

arXiv:2607.29496 [cs.LG]

(or arXiv:2607.29496v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.29496 arXiv-issued DOI via DataCite (pending registration)