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文章背景与核心概要

尽管测试期计算（test-time compute）可以显著提升大型语言模型（LLM）的推理性能，但关于额外计算资源“如何”以及“何时”发挥作用的底层机制，目前仍缺乏充分的理解。为此，本文引入了分歧-收敛推理（Divergent-Convergent Reasoning, DCR），这是一种结构化的双阶段基元，它将发散探索阶段（生成多个候选解决方案）与收敛对账阶段相结合。

作者展示了三大核心发现：1. 少数派报告放大：即使在正确输出处于少数的场景下——传统多数投票完全失效的情况——单步对账也能可靠地恢复出正确答案；2. 递归 DCR：一种自回归对账系统，能够迭代分析分歧并动态分配计算资源，在比固定计算基线平均节省约 27% 计算量的同时，实现了卓越的准确率（在 AIME 2024 上达到 93.3%，在 AIME 2025 上达到 92.0%）；3. 结构化离散度指标：提出了一种无需训练的离散度指标，证明了探索输出之间的高度分歧与对账带来的更大准确率提升呈正相关，这表明系统的分歧可以被系统性地利用，而非仅仅被视为噪声。

Divergent-Convergent Reasoning: Scaling Test-Time Compute through Structured Solution Synthesis

Divergent-Convergent Reasoning: Scaling Test-Time Compute through Structured Solution Synthesis

Authors: Bo Wen, Yuhao Chen, Erhan Bilal, Carla Agurto Rios, Chen Wang, Junchen Jiang
Published: August 15, 2026
Primary Subject: Artificial Intelligence (cs.AI)
arXiv ID: 2608.15303 [cs.AI]
DOI: 10.48550/arXiv.2608.15303

Authors: Bo Wen, Yuhao Chen, Erhan Bilal, Carla Agurto Rios, Chen Wang, Junchen Jiang
Published: August 15, 2026
Primary Subject: Artificial Intelligence (cs.AI)
arXiv ID: 2608.15303 [cs.AI]
DOI: 10.48550/arXiv.2608.15303

📌 Summary

📌 Summary

虽然测试期计算可以大幅改善大语言模型（LLM）的推理性能，但关于额外计算在“如何”以及“何时”起作用的机制，人们依然知之甚少。本文介绍了分歧-收敛推理（Divergent-Convergent Reasoning, DCR），这是一种结构化的双阶段基元，将发散探索阶段（生成多个候选解）与收敛对账阶段结合起来。

While test-time compute can substantially improve Large Language Model (LLM) reasoning performance, the mechanics of how and when additional compute helps remain poorly understood. This paper introduces Divergent-Convergent Reasoning (DCR), a structured two-phase primitive that combines a divergent exploration phase (generating multiple candidate solutions) with a convergent reconciliation phase.

作者展示了三个核心发现： 1. 少数派报告放大：即使正确输出属于少数派——即传统多数投票完全失效的场景——单步对账也能可靠地恢复出正确答案。 2. 递归 DCR：一种自回归对账系统，能够迭代分析分歧并动态分配计算资源。与固定计算基线相比，它在平均节省约 27% 计算量的同时，实现了更高的准确率（在 AIME 2024 上达到 93.3%，在 AIME 2025 上达到 92.0%）。 3. 结构化离散度指标：一个无需训练的离散度指标证明，探索输出之间的高分歧与对账带来的更大准确率提升呈正相关，这表明系统分歧可以被系统性地加以利用，而不应被视为单纯的噪声。

The authors demonstrate three core findings: 1. Minority Report Amplification: Even a single reconciliation step can reliably recover correct answers when correct outputs are in the minority—a scenario where traditional majority voting completely fails. 2. Recursive DCR: An autoregressive reconciliation system that iteratively analyzes disagreements and allocates compute dynamically. It achieves superior accuracy (reaching 93.3% on AIME 2024 and 92.0% on AIME 2025) while using roughly 27% less compute on average compared to fixed-compute baselines. 3. Structured Dispersion Metric: A training-free dispersion metric proves that high disagreement among exploration outputs correlates with larger accuracy gains from reconciliation, showing that system disagreement can be systematically exploited rather than treated as noise.

🔬 Core Results & Findings

🔬 Core Results & Findings

1. 单步对账的力量

传统的扩展方法严重依赖多数投票，该方法假设正确答案是频率最高的输出。然而，DCR 表明，即使正确答案是少数探索输出的一部分，结构化对账也能够识别并验证它们。

1. The Power of Single-Step Reconciliation

Traditional scaling methods rely heavily on majority voting, which assumes the correct answer is the most frequent output. However, DCR shows that structured reconciliation can identify and validate correct answers even when they are part of the minority exploration outputs.

2. 递归 DCR 与计算效率

递归 DCR 没有在所有问题上应用统一、固定的测试期计算量，而是充当自适应资源分配器： * 迭代分析解之间的分歧。 * 仅在必要的地方分配计算资源。 * 性能基准： * AIME 2024： 93.3% 准确率 * AIME 2025： 92.0% 准确率 * 效率： 比统一扩展基准平均少用 27% 的计算量，证明了精细的资源分配优于暴力计算扩展。

2. Recursive DCR & Compute Efficiency

Instead of applying a uniform, fixed amount of test-time compute across all problems, Recursive DCR acts as an adaptive resource allocator: * Iteratively analyzes solution disagreements. * Allocates compute only where necessary. * Performance benchmarks: * AIME 2024: 93.3% Accuracy * AIME 2025: 92.0% Accuracy * Efficiency: Uses 27% less compute on average than uniform scaling benchmarks, proving that attentive resource allocation outperforms brute-force compute scaling.

3. 通过离散度指标利用分歧

LLM 生成过程中的分歧经常被当作噪声忽略。作者引入了一种无需训练的离散度指标，映射出一种结构化关系：探索输出之间越高的分歧直接对应着收敛阶段更大的准确率提升，这揭示了智能体 LLM 系统中涌现的扩展定律（scaling law）。

3. Exploiting Disagreement via Dispersion Metrics

Disagreement in LLM generation is frequently dismissed as noise. The authors introduce a training-free dispersion metric that maps a structured relationship: higher disagreement among exploration outputs directly correlates with larger accuracy improvements during the convergent phase, revealing an emerging scaling law for agentic LLM systems.