Hsien-Jyh Liao
Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their performance often deteriorates sharply in long-horizon tasks, exhibiting systematic breakdown beyond certain scales. Conventional explanations primarily attribute this phenomenon to task complexity, such as combinatorial search explosion or long-term credit assignment challenges. In this work, we argue that these explanations are incomplete: even in linear, unbranched tasks without semantic ambiguity, autoregressive execution is subject to an intrinsic stability limit. We propose that the fundamental constraint on long-horizon reasoning arises from process-level instability in autoregressive generation rather than solely from search or task complexity, reframing long-horizon reasoning as a problem of structural governance. We derive Theorem~A, showing that decision advantage in single-path autoregressive reasoning decays exponentially with execution length, imposing a fundamental bound on maintainable reasoning chains. This result implies a structural consequence: stable long-horizon reasoning requires discrete segmentation, naturally inducing graph-like execution structures such as directed acyclic graphs (DAGs). Empirical studies in both synthetic environments and real TextWorld tasks reveal observable performance cliffs consistent with theoretical predictions. Our findings provide a dynamical perspective on long-horizon reasoning failure and suggest new limitations on maintaining long-term coherence under purely autoregressive architectures. Furthermore, we highlight that short-horizon evaluation protocols may obscure structural instability, indicating a potential shift from scaling toward structured governance in future reasoning systems.