Intrinsic Stability Limits of Autoregressive Reasoning: Structural Consequences for Long-Horizon Execution

• URL: http://arxiv.org/abs/2602.06413v1
• Date: Fri, 06 Feb 2026 06:11:06 GMT
• Title: Intrinsic Stability Limits of Autoregressive Reasoning: Structural Consequences for Long-Horizon Execution
• Authors: Hsien-Jyh Liao,
• Abstract summary: Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their performance often deteriorates sharply in long-horizon tasks.<n>We propose that the fundamental constraint on long-horizon reasoning arises from process-level instability in autoregressive generation.<n>Our findings suggest new limitations on maintaining long-term coherence under purely autoregressive architectures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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