文章背景与核心概要

结构化推理任务要求模型做出并修正相互依赖的决策，以达到全局一致的解决方案。传统的自回归模型在进行序列决策时无法修正早期的选择，而掩码扩散模型则通常需要复杂的解码方案。为了克服这些局限，本文引入了流式推理模型（Flow Reasoning Models, FRMs），这是一个全新的框架，它通过一个简单的循环精炼机制，将连续流适配到离散的结构化输出上。

通过将流模型自身过去的输出作为自条件（self-conditioning），FRMs 将单次去噪转化为迭代式的解决方案精炼。这使得模型能够并行地做出和修正决策，高效地协调各个解之间的相互依赖关系。然而，由于一步训练预测和递归生成的推理状态之间存在暴露偏差（exposure bias），传统的自条件机制在更大的循环深度下会变得不可靠。为此，本文提出了固定点强迫（Fixed-Point Forcing, FPF）技术，它在保持标准流匹配目标的同时，利用模型自身推理动态所产生的状态来训练 FRMs。实验表明，FRMs 在数独极难版（Sudoku-Extreme）、斑马谜题（Zebra）和唯一迷宫（Maze-Unique）上分别实现了 \(99.5\%\)、\(100.0\%\) 和 \(99.9\%\) 的极高解题率，并且在计算效率上显著优于现有的专业推理基线。

Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners

Summary

Structured reasoning requires making and revising interdependent decisions to achieve globally consistent solutions. Traditional autoregressive models commit sequentially without the ability to revise earlier choices, while masked diffusion models often demand complex decoding schemes. This paper introduces Flow Reasoning Models (FRMs), a novel framework that adapts continuous flows over discrete structured outputs using a simple recurrent refinement mechanism. By employing Fixed-Point Forcing (FPF) to resolve exposure bias, FRMs achieve exceptional solve rates (99.5% on Sudoku-Extreme, 100.0% on Zebra, and 99.9% on Maze-Unique) while requiring significantly fewer inference FLOPs compared to existing specialized reasoning baselines.

Metadata & Document Information

Abstract

结构化推理要求做出并修正相互依赖的决策，以达成全局一致的解。现有的架构在这一任务上面临诸多挑战：自回归模型按顺序进行决策且无法修正早期的选择，而掩码扩散模型通常需要精心设计的解码方案来协调相互依赖的预测。

Structured reasoning requires making and revising interdependent decisions to reach a globally consistent solution. Existing architectures struggle with this: autoregressive models commit sequentially and cannot revise earlier decisions, while masked diffusion models often require careful decoding schemes to coordinate interdependent predictions.

我们引入了流式推理模型（Flow Reasoning Models, FRMs），这是一个用于结构化推理的新颖框架，它通过一个简单的循环精炼机制，将连续流适配到离散的结构化输出上。通过将流模型自身过去的输出作为自条件，我们将单次去噪转化为迭代式的解精炼。这使 FRMs 能够并行地做出和修正决策，高效地协调解决方案中相互依赖的选择。

We introduce Flow Reasoning Models (FRMs), a novel framework for structured reasoning that adapts continuous flows over discrete structured outputs with a simple recurrent refinement mechanism. By self-conditioning a flow model on its own past outputs, we turn one-shot denoising into iterative solution refinement. This lets FRMs make and revise decisions in parallel, efficiently coordinating interdependent choices across solutions.

然而，由于一步训练预测和递归生成的推理状态之间存在暴露偏差，传统的自条件机制在更大的循环深度下会变得不可靠。我们通过固定点强迫（Fixed-Point Forcing, FPF）来解决这种不匹配问题，该方法在保持标准流匹配目标的同时，使用由模型自身推理动态产生的状态来训练 FRMs。

Yet conventional self-conditioning becomes unreliable at greater recurrent depth due to exposure bias between one-step training predictions and recursively generated inference states. We address this mismatch with Fixed-Point Forcing (FPF), which trains FRMs on states produced by their own inference dynamics while preserving the standard flow-matching objective.

FRMs 在 Sudoku-Extreme（数独极难版）、Zebra（斑马谜题）和 Maze-Unique（唯一迷宫）上分别实现了 \(99.5\%\)、\(100.0\%\) 和 \(99.9\%\) 的解题率。在 Sudoku-Extreme 上，FRMs 达到了比所评估的掩码扩散和专业推理基线更高的峰值准确率，同时保持了极高的计算效率，以少 \(44\times\) 的推理浮点运算数（FLOPs）匹配了次优方法 \(98.7\%\) 的峰值解题率。

FRMs achieve solve rates of \(99.5\%\), \(100.0\%\), and \(99.9\%\) on Sudoku-Extreme, Zebra, and Maze-Unique, respectively. On Sudoku-Extreme, FRMs achieve higher peak accuracy than the evaluated masked-diffusion and specialized reasoning baselines while remaining highly compute-efficient, matching the next-best method's \(98.7\%\) peak solve rate with \(44\times\) fewer inference FLOPs.

Associated Resources & References

• 代码、数据与媒体整合： 可通过 alphaXiv、CatalyzeX Code Finder、DagsHub、Hugging Face Spaces 以及 ScienceCast 获取。

  • Code, Data & Media Integration: Available via alphaXiv, CatalyzeX Code Finder, DagsHub, Hugging Face Spaces, and ScienceCast.

• 外部引用： 已在 Google Scholar、Semantic Scholar 和 NASA ADS 中建立索引。

  • External Citations: Indexed on Google Scholar, Semantic Scholar, and NASA ADS.

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