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

TL;DR

This work argues that long-horizon autoregressive reasoning suffers from an intrinsic process-level instability, not just task complexity. It formalizes a stability theorem (Theorem A) showing that the decision advantage along a single autoregressive trajectory decays exponentially with horizon, implying a finite stability horizon $L^*$ and necessitating segmentation into sub-edges to maintain coherence. The authors show that stable long-horizon reasoning naturally leads to graph-like topologies, such as DAGs, with stabilization nodes that consolidate state and control entropy. Empirically, synthetic tasks and TextWorld experiments reveal performance cliffs and demonstrate that structural governance—through segmentation and resets—mitigates instability, whileBranching-based search approaches incur exponential sample costs. The results advocate a shift from pure scaling to structural governance in designing future reasoning systems, with diagnostic indicators for monitoring stability and guidance for endogenous stabilization mechanisms.

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.

Figures (7)

• Figure 1: A process-level view of degradation in autoregressive reasoning. Even in linear tasks without branching search, a single long execution edge exhibits exponential decay of decision advantage due to accumulated uncertainty; in contrast, segmentation with resets suppresses accumulation, keeping each segment within a stable regime.
• Figure 2: Conceptual phase transition induced by intrinsic stability limits. Decision advantage decays exponentially and crosses the critical threshold at $L^*$.
• Figure 3: Track B: Exponential bottleneck transfer under structural segmentation. Median episodes-to-success (log scale) as a function of horizon length $L$ for unstructured (blue) and structured / landmark-based (orange) agents in the synthetic TW-HSF setting. The dashed curve shows the theoretical reference scale dominated by the longest effective segment length $h_{\max}$. Without structure, sample complexity grows exponentially in $L$, consistent with the $|\mathcal{A}|^{L}$ lower bound (Appendix A). Structural segmentation reconfigures the exponential scaling regime, shifting the dominant dependence from the full horizon $L$ to the longest sub-critical segment $h_{\max}$. Increasing landmark omission probability (not shown) increases $h_{\max}$ and restores the high-exponent scaling regime, confirming that structure functions primarily by constraining the uninterrupted autoregressive span rather than by providing additional semantic information.
• Figure 4: Structural trajectory comparison in Track A. Baseline execution exhibits early saturation due to oscillatory attractors, while structured execution maintains sustained exploration growth.
• Figure 5: Track A (Gemma 3 4B): Structural governance under paired-and-cached evaluation. Bars show mean $\pm$ std over paired trials. Structural resets increase exploration coverage and reduce oscillatory backtracking.

Theorems & Definitions (20)

• Definition 1: Decision Advantage
• Theorem 1: Process Collapse in Long-Horizon Autoregressive Reasoning
• Definition 2: TextWorld Hard Sparse Family, $\text{TW-HSF}_\varepsilon$
• Lemma 1: History Indistinguishability
• proof
• Corollary 1: Depth Unidentifiability
• Lemma 2: Near-Random Action Selection
• Lemma 3: Single-Episode Success Probability
• Theorem 2: Exponential Episode Complexity
• Corollary 2: Reduction via Landmarks