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地址

论文地址：https://www.arxiv.org/abs/2511.21734

时间

2025年11月21日

作者

清华大学

To enhance the reasoning capabilities of Large Language Models (LLMs) without high costs of training, nor extensive test-time sampling, we introduce Verification-First (VF), a strategy that prompts models to verify a provided candidate answer, even a trivial or random one, before generating a solution. This approach triggers a "reverse reasoning" process that is cognitively easier and complementary to standard forward Chain-of-Thought (CoT), effectively invoking the model's critical thinking to reduce logical errors. We further generalize the VF strategy to Iter-VF, a sequential test-time scaling (TTS) method that iteratively cycles the verification-generation process using the model's previous answer. Extensive experiments across various benchmarks (from mathematical reasoning to coding and agentic tasks) and various LLMs (from open-source 1B to cutting-edge commercial ones) confirm that VF with random answer consistently outperforms standard CoT with minimal computational overhead, and Iter-VF outperforms existing TTS strategies.

为了在无需高昂训练成本和大量测试时采样的情况下提升大型语言模型（LLM）的推理能力，我们引入了“验证优先”（VF）策略，该策略促使模型在生成解决方案之前先验证所提供的候选答案，哪怕是一个微不足道或随机的答案。这种方法触发了一种“逆向推理”过程，这种过程在认知上更简单，且与标准的正向“思维链”（CoT）相辅相成，能有效激发模型的批判性思维，从而减少逻辑错误。我们进一步将 VF 策略推广为迭代验证优先（Iter-VF），这是一种测试时的序列扩展（TTS）方法，通过使用模型的先前答案来反复循环验证-生成过程。在涵盖从数学推理到编程和代理任务的各类基准测试以及从开源 10 亿参数模型到前沿商业模型的各种 LLM 上进行的大量实验表明，使用随机答案的 VF 以极小的计算开销始终优于标准 CoT，而 Iter-VF 则优于现有的 TTS 策略。

To make LLMs adept at complex reasoning tasks, it is common to convert a complex problem into multi-step, modular and primary reasoning steps within their capacity. A fundamental technique is to ask the LLM to "think step by step", forming chain-of-thought (CoT) (Wei et al., 2022). Though generating such a reasoning path leading to the final solution would be much more simpler than directly output the final solution, their reliability is still of-ten undermined by their tendency to generate plau-sible but incorrect solutions. This fallibility stems from their autoregressive, maximum-likelihood na-ture to generate coherent natural language, which can prioritize fluency over factual or logical rigor.

To enhance LLM reasoning, existing methods incur significant costs across three dimensions: prior knowledge, test-time computation, and train-ing. Strategies typically involve crafting problem-specific prompts (Wei et al., 2022; Chia et al., 2023; Alazraki et al., 2025), increasing inference budgets through expensive parallel sampling (Wang et al., 2022) or sequential reflection (Madaan et al., 2023; Shinn et al., 2023), fine-tuning models (Cobbe et al., 2021; Kumar et al., 2025), or involving multi-ple above perspectives (Yao et al., 2023; Lightman et al., 2023; Besta et al., 2024; Snell et al., 2024; Muennighoff et al., 2025; Setlur et al., 2025). This suggests a prevailing understanding: better reason-ing can only be attained at a significant cost.

为了让大型语言模型（LLM）擅长复杂的推理任务，通常会将复杂问题分解为多个步骤，使其能够进行模块化和初级推理。一种基本的技术是让 LLM“逐步思考”，形成链式思维（CoT）（Wei 等人，2022 年）。尽管生成这样一条通向最终解决方案的推理路径要比直接输出最终答案简单得多，但它们的可靠性仍常常因倾向于生成看似合理但错误的答案而受到损害。这种错误源于其自回归、最大似然的特性，即生成连贯的自然语言时，可能会优先考虑流畅性而非事实或逻辑的严谨性。

为了提升 LLM 的推理能力，现有的方法在三个维度上都带来了显著的成本：先验知识、测试时的计算以及训练。策略通常包括针对特定问题设计提示（Wei 等人，2022 年；Chia 等人，2023 年；Alazraki 等人，2025 年），通过昂贵的并行采样（Wang 等人，2022 年）或顺序反思（Madaan 等人，2023 年；Shinn 等人，2023 年）增加推理预算，对模型进行微调（Cobbe 等人，2021 年；Kumar 等人，2025 年），或者综合运用上述多种视角（Yao 等人，2023 年；Lightman 等人，2023 年；Besta 等人，2024 年；Snell 等人，2024 年；Muennighoff 等人，2025 年；Setlur 等人，2025 年）。这表明了一种普遍的认识：更好的推理只能以高昂的代价来实现。

In this paper, we propose a method that is ex-treme cheap to improve LLM reasoning. The core is Verification-First strategy, providing an answer (regard its correctness or not) along with the prob-lem and ask LLM to first verify/evaluate the pro-vided answer then give correct answer, in contrast to ordinary reasoning that reaches the final answer starting from the problem only. The key insights are (i) logically, verifying an answer is easier than generating a correct answer (Baker et al., 1975), while implies a informative reverse reasoning path that is complementary to standard CoT to be help-ful (Polya, 1957); (ii) psychologically, asking one to critic an answer from others could naturally in-voke one’s critical thinking by overcoming egocen-trism (Piaget, 1976; Brookfield, 1987).

To implement with minimal additional prior knowledge, VF only needs to provide a ran-dom/trivial answer in the prompt. The verification process turns out to have much fewer output to-kens than an ordinary CoT path, some times even no explicit verification-only process, thus require very small additional test-time computation. To generalize across tasks and control test-time cost, we propose Iter-VF as a TTS strategy, and human providing initial answer is no longer necessary. Iter-VF iterates the VF process with model-generated answer in previous output. Such Iter-VF method turns out to be more effective and efficient than other TTS methods applicable with minimal prior knowledge and no training.

在本文中，我们提出了一种极其廉价的改进大语言模型推理的方法。其核心是“验证优先”策略，即在给出问题的同时提供一个答案（不论其正确与否），要求大语言模型首先验证/评估所提供的答案，然后再给出正确答案，这与通常从问题出发直接得出最终答案的推理方式形成了鲜明对比。关键见解在于：（一）从逻辑上讲，验证一个答案比生成正确答案更容易（贝克等人，1975 年），这暗示了一条信息丰富的反向推理路径，与标准的“解释性推理”相辅相成，有助于解决问题（波利亚，1957 年）；（二）从心理学角度而言，要求一个人批评他人的答案能够自然地激发其批判性思维，克服自我中心主义（皮亚杰，1976 年；布鲁克菲尔德，1987 年）。

为了在几乎不增加额外先验知识的情况下实现这一目标，验证框架（VF）只需在提示中提供一个随机/平凡的答案。验证过程所需的输出标记明显少于普通“解释性推理”路径，有时甚至无需明确的验证过程，因此所需的额外测试时间计算量非常小。为了在不同任务间进行泛化并控制测试时间成本，我们提出迭代验证框架（Iter-VF）作为测试时策略，且不再需要人类提供初始答案。迭代验证框架通过在前一次输出中使用模型生成的答案来迭代验证框架过程。事实证明，这种迭代验证框架方法比其他仅需极少先验知识且无需训练的测试时策略更有效、更高效。

Our contribution can be summarized as follows:

>> We propose VF strategy, an extreme cheap way to improve LLM reasoning by providing an answer along with the problem to ask LLM to first verify then generate.

>> We implement VF strategy with simple algo-rithms for scenarios from one-step prompting to TTS.

>> Extensive experiments show that the proposed al-gorithms outperforms standard CoT and existing TTS methods across various tasks and models, including agentic tasks and thought-hidden com-mercial LLMs.

我们的贡献可以总结如下：

>> 我们提出了 VF 策略，这是一种极其廉价的方法，通过在问题后附上答案，让大语言模型先验证再生成，从而提升其推理能力。

>> 我们针对从单步提示到文本转语音的多种场景，用简单的算法实现了 VF 策略。

>> 大量实验表明，所提出的算法在各种任务和模型中均优于标准的链式思维和现有的文本转语音方法，包括代理任务和隐藏思维的商业大语言模型。

In this paper, we introduced Verification-First (VF), a cost-effective prompting strategy that sig-nificantly enhances the reasoning capabilities of LLMs by instructing them to verify a candidate answer—even a random or trivial one—before gen-erating a solution. By triggering a "reverse rea-soning" process that is cognitively less demanding than generation and complementary to standard for-ward CoT, VF effectively reduces logical errors and mitigates egocentric biases without the need for ad-ditional training or expensive sampling. We further generalized this approach into Iter-VF, a sequen-tial test-time scaling method that iteratively refines answers in a Markovian manner, avoiding the con-text overflow and error accumulation common in existing self-correction strategies. Extensive exper-iments confirm that VF consistently outperforms standard baselines and offers a robust, versatile solution for improving performance with minimal computational overhead.

在本文中，我们介绍了“验证优先”（VF）这一成本效益高的提示策略，它通过指示大型语言模型（LLM）在生成解决方案之前先验证候选答案（即使是随机或微不足道的答案），显著增强了其推理能力。VF 触发了一种认知负担低于生成且与标准正向 CoT 相辅相成的“逆向推理”过程，从而有效减少了逻辑错误并减轻了自我中心偏差，且无需额外训练或昂贵的采样。我们进一步将此方法推广为迭代 VF（Iter-VF），这是一种序列测试时间缩放方法，以马尔可夫方式迭代优化答案，避免了现有自我修正策略中常见的上下文溢出和错误累积问题。大量实验表明，VF 一直优于标准基线，并提供了一种计算开销极小的稳健、通用的性能提升方案。