Title: The Deterministic Horizon: When Extended Reasoning Fails and Tool Delegation Becomes Necessary

Abstract: Performance on deterministic state-tracking tasks suffers under extended chain-of-thought reasoning, a decline driven not by preference biases but by the inherent information-theoretic constraints of decoder-only attention mechanisms. This study establishes four key findings: first, an Attention Bottleneck Theorem, supported by a complementary achievability construction, which limits state-tracking capacity to $O(H \cdot \log(L/H) \cdot \sqrt{d_h})$; second, a context-dependent error model that demonstrates super-exponential accuracy decay; third, the State-Space Jaccard metric, designed to differentiate capability failures from preference issues; and fourth, the identification of a Deterministic Horizon ($d^* \in [19, 31]$), marking the threshold where tool delegation becomes essential.

Evaluations across 12 models and 8 task domains—including SWE-Bench, WebArena, and SQL-Multi—reveal that tool-integrated reasoning consistently surpasses neural chain-of-thought. On the primary model suite, hybrid approaches achieve 86-94% accuracy, compared to just 24-42% for pure neural methods. Furthermore, fine-tuning on optimal-length traces yields less than a 5% improvement, confirming an architectural ceiling. The high cross-model correlation ($r = 0.81$-$0.91$) suggests these failures are rooted in architecture rather than specific training regimes. These findings offer principled guidance for determining when pure neural reasoning should be replaced by hybrid approaches in agentic systems.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC