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

TL;DR

This paper reveals an intrinsic stability limit in autoregressive reasoning, showing that long-horizon reasoning inherently faces structural instability, which can be mitigated by adopting graph-like execution structures.

Contribution

It introduces a theoretical framework demonstrating the exponential decay of decision advantage in autoregressive reasoning and highlights the necessity of structured segmentation for stability.

Findings

Decision advantage decays exponentially with execution length

Stable long-horizon reasoning requires segmentation into graph-like structures

Empirical results confirm theoretical predictions of performance cliffs

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.