To CoT 还是 To Loop？思维链与循环 Transformer 的形式化比较
To CoT or To Loop? A Formal Comparison Between Chain-of-Thought and Looped Transformers
AI总结：
本文形式化比较思维链与循环 Transformer，证明前者擅长组合结构的近似推断，后者擅长并行计算，为推理范式选择提供实用指导。
摘要：
思维链（Chain-of-Thought, CoT）和循环 Transformer（Looped Transformers）已被证明在经验上能提升推理任务的性能，并在理论上通过递归增加计算步骤数来增强表达能力。然而，它们各自的能力对比仍未被充分理解。本文对它们各自的优势与局限性进行了形式化分析。我们证明，循环 Transformer 能高效地模拟确定性任务的并行计算，我们将此形式化为对有向无环图的求值。相反，采用随机解码的思维链在组合结构的近似推断上表现出色，即自归约问题。这些区分表明，对于哪些任务，深度驱动的递归更为合适，从而为在推理范式之间进行选择提供了实用线索。
英文摘要：
Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their comparative capabilities are still not well understood. In this paper, we provide a formal analysis of their respective strengths and limitations. We show that Looped Transformers can efficiently simulate parallel computations for deterministic tasks, which we formalize as evaluation over directed acyclic graphs. In contrast, CoT with stochastic decoding excels at approximate inference for compositional structures, namely self-reducible problems. These separations suggest the tasks for which depth-driven recursion is more suitable, thereby offering practical cues for choosing between reasoning paradigms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
