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

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.

💡 Research Summary

The paper “Intrinsic Stability Limits of Autoregressive Reasoning: Structural Consequences for Long‑Horizon Execution” investigates why large language models (LLMs) often fail dramatically on tasks that require many reasoning steps, even when the underlying task is linear, unbranched, and free of semantic ambiguity. Existing explanations focus on task‑level difficulty—combinatorial explosion, long‑term credit assignment, or accumulating ambiguity—but the authors argue that these accounts are incomplete. They propose that the core limitation lies in the process of autoregressive generation itself: as the model repeatedly samples the next token, stochastic perturbations accumulate, eroding the model’s directional alignment toward the correct conclusion.

Theoretical contribution (Theorem A).
The authors formalize reasoning as a stochastic dynamical system. Let (Z_t) be the model’s internal latent state after (t) steps, and define decision advantage (\rho_t = P(G|Z_t) - P(\neg G|Z_t)), where (G) is the correct proposition. The autoregressive update is written (Z_{t+1}=f(Z_t)+\varepsilon_t), with (\varepsilon_t) capturing approximation error, sampling variance, and representation decay. Assuming the transition kernel (K(\cdot|Z_t)) contracts in total‑variation distance with coefficient (\eta<1), the authors prove that (\rho_t) decays exponentially: (\rho_t \le \rho_0 e^{-\gamma t}) where (\gamma=-\ln\eta>0). Consequently there exists a critical horizon (L^* = \frac{1}{\gamma}\ln(\rho_0/\tau)) beyond which the decision advantage falls below a reliability threshold (\tau). In plain terms, a single uninterrupted autoregressive chain cannot be extended arbitrarily; after a finite number of steps the model’s reasoning becomes effectively random (“hallucination”).

Structural implication: segmentation and DAGs.
The theorem suggests a natural remedy: break the long chain into shorter segments whose lengths stay below (L^*). Each segment can be thought of as an edge in a directed acyclic graph (DAG); the nodes correspond to “reset” or “compression” operations that purge accumulated uncertainty (e.g., external memory writes, state summarization, or explicit re‑initialization). By limiting each edge’s length, the exponential decay is reset, and the overall system can sustain arbitrarily many logical steps by traversing a graph of bounded‑size edges. This reframes many existing “System 2” techniques (Chain‑of‑Thought, Tree‑of‑Thought, Graph‑of‑Thought) as implicit implementations of such segmentation.

Empirical validation.
The authors test the theory in two settings: (1) synthetic linear tasks where the model must propagate numeric information across a sequence, and (2) TextWorld environments that require multi‑step planning and object manipulation. In both cases, performance (accuracy or success rate) remains high for short horizons, then drops sharply once the number of steps exceeds the predicted (L^*). When the authors introduce explicit segmentation—e.g., a 10‑step CoT followed by a memory write and reset—the performance cliff is mitigated, and the observed transition point aligns closely with the theoretical prediction.

Broader implications.

1. Long‑horizon stability is a distinct bottleneck from scaling laws or search complexity; simply increasing model size does not eliminate the exponential decay caused by stochastic updates.
2. Evaluation protocols that focus on short horizons mask the problem, potentially leading to over‑optimistic claims about LLM reasoning capabilities. New metrics that track decision advantage or information loss over time are needed.
3. Designing structured governance mechanisms (automatic segmentation, hierarchical memory, DAG‑based planning) becomes essential for future reasoning systems, especially in autonomous agents, program synthesis, and complex dialogue.
4. The contraction assumption, while idealized, captures a realistic phenomenon: each transformer layer introduces non‑zero variance, and the finite precision of hidden states prevents lossless accumulation of arbitrarily long histories.

Future directions include (i) quantifying the contraction coefficient for specific architectures, (ii) developing learning‑free or learned segmentation policies that adaptively decide when to reset, and (iii) exploring alternative generative paradigms (e.g., non‑autoregressive or hybrid models) that may avoid the cumulative noise problem altogether.

In summary, the paper provides a rigorous information‑theoretic and dynamical systems perspective on why autoregressive LLMs break down on long reasoning chains, demonstrates that the limitation is intrinsic to the generation process, and argues that stable long‑horizon reasoning demands explicit structural controls—effectively turning a linear chain into a graph of bounded‑size execution segments. This reframes the research agenda from pure scaling toward “structured governance” of reasoning dynamics.