推理越长越容易出错，工具调用才是解决之道。
The Deterministic Horizon: When Extended Reasoning Fails and Tool Delegation Becomes Necessary
- 发现解码器注意力存在信息瓶颈，限制了推理深度。
- 在19到31步后，纯神经推理准确率跌破50%。
- 适合研究大模型推理极限与工具增强的读者。
扩展式思维链推理在确定性状态追踪任务中表现下降，不仅因偏好偏差，更源于解码器仅注意力机制的信息理论容量限制。本文提出：（1）注意力瓶颈分析，证明状态追踪容量受头数、头维度和上下文长度制约，但总容量非主要约束；（2）上下文依赖的误差模型，误差指数含深度相关的二次项；（3）状态空间交集度量（State-Space Jaccard）用于评估状态漂移；（4）确定性极限 $d^* \\[19, 31]$（当 $α=0.5$ 时），标志着无辅助推理准确率降至50%的深度。在十二个模型、八个任务领域（包括 SWE-Bench、WebArena、SQL-Multi）中，集成工具的推理准确率达76%-94%，而神经思维链仅17%-42%（在 PermutationProbe 上）。对最优长度轨迹微调带来的提升不足3个百分点，支持架构上限的存在。
原文摘要 · Abstract (English)
Extended chain-of-thought reasoning can degrade performance on deterministic state-tracking tasks, not solely because of preference biases but, on the evidence we present, because of information-theoretic limits in the capacity of decoder-only attention. We present: (1) an Attention Bottleneck analysis providing evidence that total state-tracking capacity in bits is bounded in terms of head count, head dimension, and context length under stated modeling assumptions, and that total capacity is not the binding constraint; (2) a context-dependent error model with a depth-dependent quadratic term in the error exponent; (3) the State-Space Jaccard metric measuring state drift; and (4) a Deterministic Horizon $d^* \in [19, 31]$ (at $α= 0.5$) marking the depth at which unaided accuracy crosses 50%. Across twelve models and eight task domains (including SWE-Bench, WebArena, and SQL-Multi), tool-integrated reasoning reaches 76-94% accuracy versus 17-42% for neural chain-of-thought on PermutationProbe. Fine-tuning on optimal-length traces yields $<$3 percentage-point improvement, supporting an architectural ceiling.
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