DistilQwen2.5-R1发布：知识蒸馏助推小模型深度思考

阿里云大数据AI技术

已于 2025-03-26 14:18:50 修改

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文章标签： DistilQwen 人工智能阿里云 PAI 知识蒸馏

于 2025-03-26 14:05:28 首次发布

本文链接：https://blog.youkuaiyun.com/weixin_48534929/article/details/146527500

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作者：蔡文睿（清素）、汪诚愚（熊兮）、严俊冰（玖烛）、黄俊（临在）

引言

随着 DeepSeek-R1 和 QwQ-32B 等面向深度推理的大语言模型的开源，“大模型+慢思考”已成为拓展大语言模型智能边界的标准配置。然而，这些模型在资源受限的移动设备和边缘计算场景中的普及仍面临巨大挑战。因此，学术界和工业界迫切需要解决如何有效利用知识蒸馏技术，将这些超大规模深度推理模型的知识迁移到小模型中，从而提升计算效率并降低部署成本的问题。为此，我们在 DistilQwen2.5 系列蒸馏小模型（看这里）的基础上，推出了更为强大的 DistilQwen2.5-R1 系列深度推理模型。

DistilQwen2.5-R1 系列以少量来自 DeepSeek-R1 的思维链蒸馏数据为基础，通过一系列创新的蒸馏策略，有效强化了小模型的深度思考能力。实验评估结果显示，DistilQwen2.5-R1 系列中的多种小规模模型在各项基准测试中表现优异（见下图）。例如，DistilQwen2.5-R1-7B 性能显著超越了其他开源蒸馏模型，包括 OpenThinker-7B。

为方便开发者和企业在实际应用中使用 DistilQwen2.5-R1 系列模型，其所有的 Checkpoint 已在 Hugging Face 和 Model Scope 开源社区中公开。本文将深入阐述 DistilQwen2.5-R1 的蒸馏算法、性能评估，并且提供在阿里云人工智能平台 PAI 上的使用指南及相关下载教程。

DistilQwen2.5-R1中的知识蒸馏技术

本节中，我们主要描述 DistilQwen2.5-R1 模型训练中使用的数据增强与知识蒸馏技术。

由于自身参数量的显著差异，大模型与小模型的认知与推理轨迹有时并不完全一致。以数学问题为例：对于有的数学问题，小模型由于自身参数量的限制，会倾向于使用更基础的方法去解决问题。而大模型基于其强大的推理能力，会采用较为高阶的方法。比如经典的鸡兔同笼问题，小模型倾向于使用简单枚举法逐一试错，而大模型会直接通过列方程的较高级方法求解。

正是由于大小模型的认知轨迹偏差，小模型有时无法有效理解大模型的思维链，此时如果直接该思维链（Chain-of-Thought，CoT）蒸馏到小模型中，往往效果不佳。为此，我们设计了一种小型推理模型训练框架，以消除这种认知轨迹偏差带来的负面影响。在后续训练中，我们还利用这种偏差数据进一步提升小模型的推理能力，最终推出基于该训练框架的 DistilQwen2.5-R1 系列模型。我们提出的训练技术框架包含两个阶段：CoT 数据“评价-改进-验证”机制，以及基于不同认知轨迹数据的偏好优化算法。总体而言，DistilQwen2.5-R1 模型蒸馏的详细算法框架如下图所示：

给定原始的大模型思维链数据集，例如从 DeepSeek-R1 蒸馏的数据集，在一阶段，我们先对其进行数据难度评价，接着根据数据的难度等级对其进行相应的优化，优化之后还要对结果进行验证。我们使用改进且被验证的 CoT 数据集对模型进行 SFT 训练，获取模型的基础推理能力。在二阶段，我们利用一阶段已有的不同难度的 CoT 数据构造偏好数据集，在一阶段的基础上进一步提升小模型的推理能力。

CoT 数据“评价-改进-验证”机制

正如上文中提到的，大小模型间的认知推理轨迹有时存在显著偏差。因此，对于待蒸馏的大模型思维链数据集，小模型无法完全理解。阶段一正是基于这种认知偏差对数据集进行优化，采用了 LLM-as-a-Judge 的范式，对大模型的推理过程进行评价并改进。

给定问题、大模型的推理过程和问题的答案，我们使用模型判断这个推理过程是简单、中等还是困难。难度等级的核心标准是小模型是否能够遵循给定的推理过程得到问题的答案。以下是思维链的难度等级及定义：

中等：小模型可以遵循该推理过程得到问题的答案。
简单：给定的推理过程过于简单，缺少小模型所需的必要步骤，导致大模型依赖其强大的推理能力解决问题，而小模型无法遵循该过程得到答案。
困难：给定的推理过程过于复杂或过于困难，导致小模型无法遵循该过程得到答案。

基于一个大模型的问题与思维链集合，我们可以将其分为简单、中等和困难三类。对于评级为中等的部分，我们予以保留。对于被评为简单和困难的数据，我们使用模型对思维链进行改进。具体来说：对于简单部分，我们扩展其推理过程，直至小模型可以遵循扩展的过程得到答案。对于评级为困难的部分，我们精简其推理过程，直至小模型可以遵循精简的过程得到答案。

我们之后对改进结果进行进一步验证，包括：对改进后的思维链再次评价难度等级，检测其是否被归类为中等难度，以及验证小模型是否能够遵循改进的思维链解决问题。如果改进后的思维链通过验证，说明改进有效，该数据可以被小模型有效理解，我们将其保留。如果验证不通过，说明改进无效，我们将返回到改进步骤，重新进行改进，直至通过验证。最终，我们获取了优化后的思维链数据集，其组成部分如下：

初始难度评级为中等的数据。
初始难度评级为简单，经过改进扩展后评为中等并通过验证的数据。
初始难度评级为困难，经过改进精简后评为中等并通过验证的数据。

此时，数据集内所有思维链的最终难度评级均为中等，意味着小模型可以有效理解数据集内的所有思维链，并能遵循这些思维链解决相应推理问题。上文提到的大小模型认知轨迹偏差问题在改进后的数据集中得到妥善解决，其可能带来的负面影响也被消除。我们使用优化后的思维链数据集对 Qwen2.5 系列基座模型进行监督微调（SFT），得到 DistilQwen2.5-R1 系列模型的基础结果。

基于多种认知轨迹数据的偏好优化

在第二阶段，我们基于第一阶段得到的不同难度等级数据对模型进行进一步提升。

具体来说，在第一阶段中，评级难度为中等的思维链数据是正确且适合小模型的思维链，小模型能够有效理解该思维链并解决问题。而难度评级为简单或困难的思维链数据依然是正确的思维链，只是不适合小模型。在此基础上，我们使用模型将正确的推理过程改写为一个错误的推理过程。错误的推理过程没有逻辑性，且会误导小模型，使得小模型完全无法遵循该错误的推理过程解决问题。

基于改写得到的错误思维链，我们将其与简单、中等和困难的思维链进行两两组合，组成多种偏好数据对。这些偏好数据对中有的偏差大，有的偏差小。基于不同种类的偏好数据对及其特点，我们分别使用针对性的参数配置，在第一阶段模型的基础上，采用 DPO 算法进一步优化小模型的推理能力。

最终，我们利用第一阶段得到的不同难度等级的认知轨迹（思维链）数据以及基础模型结果，得到了 DistilQwen2.5-R1 系列模型。

DistilQwen2.5-R1 模型效果评测

在本节中，我们从多个角度评测 DistilQwen2.5-R1 系列蒸馏小模型的实际效果；同时，我们将 DistilQwen2.5-R1 系列模型和当前业界的前沿模型对比效果。

模型综合能力评测

我们在多个模型推理能力评测基准上测试了 DistilQwen2.5-R1 系列模型的能力，涵盖数学、代码和科学问题三个主流推理领域。

在数学领域，我们使用 AIME2024 和 MATH-500 这两个基准进行测试，AIME2024 是美国数学邀请赛的2024年测试集，包含30道高难度数学题，用于评估大语言模型在复杂数学推理和问题解决能力，尤其考察代数、几何等领域的综合应用。MATH-500 是一个数学推理能力的基准测试，包含500个测试样本，旨在全面考察模型在数学解题上的能力。它与 AIME2024 类似，但有其独特的测试目标和对比结果，用于衡量模型在不同数学题目上的准确性。

在代码领域，我们使用 LiveCodeBench 基准，LiveCodeBench 是一个动态更新的基准测试平台，用于全面评估大型语言模型在复杂编码场景中的能力。它通过从顶级竞赛平台收集高难度编程任务来测试模型的代码生成、自我修复代码执行和测试等能力，是一个综合性、无污染的评价基准。在本次评测中，我们使用 LiveCodeBench 基准的V2版本，其包含2023年5月-2024年5月的511个代码问题。

在科学问题领域，我们使用 GPQA-Diamond（Grade-Level Problems in Question Answering Diamond）基准，其由纽约大学、CohereAI 及 Anthropic 的研究人员联合发布，包含198条结果，是 GPQA 系列中最高质量的评测数据，用于评估模型解决专家级科学问题的能力。

如下图所示，DistilQwen2.5-R1 系列模型在3B、7B、14B和32B四个参数量级的模型中，与原始 Qwen2.5 模型的效果进行了对比。可以看出，本文描述的小型推理模型训练框架显著提升了现有语言模型的推理能力，并在多个评测基准上取得了一致而明显的效果提升。

AIME2024实验结果对比：

MATH-500实验结果对比：

GPQA Diamond实验结果对比：

LiveCodeBench V2实验结果对比：

与其他模型能力对比

为了横向比较同期发布的不同参数规模的推理模型效果，下表分别是 DistilQwen2.5-R1 系列模型在各个参数量级上与其他前沿推理模型在上文提到的4个基准的评测结果。我们重点对比了 DistilQwen2.5-R1 系列与 OpenThinker、DeepSeek-R1-Distill-Qwen等系列模型。

以下是7B量级的对比结果，可以看出，DistilQwen2.5-R1-7B 模型超越了 Bespoke-Stratos-7B 和 OpenThinker-7B。值得注意的是，相较于 OpenThinker-7B，DistilQwen2.5-R1-7B 在使用更少训练数据的情况下在所有基准上达到了更高的结果。DeepSeek-R1-Distill-Qwen-7B 使用了800k闭源训练数据，而 DistilQwen2.5-R1-7B 使用了开源数据进行训练（OpenThoughts数据集过滤和改写得到的子集），在基于开源数据模型领域内处于领先地位。

模型	训练数据量	AIME2024	MATH-500	GPQA Diamond	LiveCodeBench V2
DeepSeek-R1-Distill-Qwen-7B (reported)	800k	55.5	92.8	49.1	-
Bespoke-Stratos-7B (reported)	17k	20.0	82.0	37.8	36.1
OpenThinker-7B (reported)	114k	31.3	83.0	42.4	39.9
DistilQwen2.5-R1-7B	105k	43.33	88.4	42.93	46.38

以下是32B量级的对比结果。同样地，DistilQwen2.5-R1-32B 在所有已知基准上超越了 Sky-T1-32B-Preview，以及在绝大多数基准上超越了 OpenThinker-32B。

模型	训练数据量	AIME2024	MATH-500	GPQA Diamond	LiveCodeBench V2
DeepSeek-R1-Distill-Qwen-32B (reported)	800k	72.6	94.3	62.1	-
Sky-T1-32B-Preview (reported)	17k	43.3	86.4	56.8	-
OpenThinker-32B (reported)	114k	66.0	90.6	61.6	68.9
DistilQwen2.5-R1-32B	105k	70.0	93.8	62.12	65.95

模型多次推理评测

我们还测试了 DistilQwen2.5-R1 系列模型在上文提到的四个基准上多次推理的结果，模型会对同一个问题生成k个回答进行评测，即 Pass@k 指标。以下是 DistilQwen2.5-R1-7B 和 DistilQwen2.5-R1-32B 在四个基准上Pass@k结果（k=2、4、8、16、32、64）。

可以看出，随着模型推理次数k的逐步增加，两个模型在所有基准上的评测准确率大幅提高。值得注意的是，随着k的增加，DistilQwen2.5-R1-7B 在 MATH-500和GPQA-Diamond 上涨幅巨大，并且不断逼近 DistilQwen2.5-R1-32B 水准。这表明我们的推理模型训练框架在小模型领域内拥有巨大潜力。我们可以通过多次推理的方式使7B模型拥有媲美32B模型的能力，极大减少了推理所需的计算资源。

模型输出案例

对同一数学问题，我们对比了 DistilQwen2.5-R1 系列模型在7B、32B量级和同等量级模型的推理结果。从输出结果可以看出，DistilQwen2.5-R1 系列模型在同量级推理模型中处于领先地位。

示例一：7B量级模型对比

问题	Peter has $70 and wishes to spend an equal amount each day for one week. From Sunday through Wednesday, he spent his money on wooden action figures which cost $5 each. For the rest of the week, he will buy plastic action figures which cost $2 each. How many total action figures will he have by the end of the week?
答案	There are 7 days in a week so if he wishes to spend an equal amount of $70 each day that would be $70/7 = $<<70/7=10>>10\nFor four days (Sunday through Wednesday) he will spend 4$10 = $<<410=40>>40\nHe will spend $40 on wooden action figures of $5 each which gives $40/$5 = <<40/5=8>>8 wooden action figures\nFor the remaining 3 days he will spend 3$10 = $<<310=30>>30\nHe will spend $30 on plastic action figures of $2 each which gives $30/$2 = <<30/2=15>>15 plastic action figures\nAltogether, he will have 8+15 = <<8+15=23>>23 action figures.\n#### 23
DistilQwen2.5-R1-7B	<\|begin_of_thought\|> Okay, let's try to figure out how many action figures Peter can buy. First, I need to understand the problem step by step. So, Peter has $70 and wants to spend an equal amount each day for one week. That means seven days total. From Sunday through Wednesday, he spends money on wooden action figures that cost $5 each. Then, for the rest of the week (which would be Thursday and Friday, I guess, since the week ends on Saturday or Sunday?), he buys plastic ones that cost $2 each. The question is asking how many total action figures he'll have by the end of the week. Wait, the problem says "from Sunday through Wednesday," so that's four days. Then "for the rest of the week," which would be Thursday and Friday, making two days. So total days: 4 + 2 = 6 days? Wait, a week is seven days. If he's spending from Sunday through Wednesday (4 days), then the rest would be Thursday and Friday (2 days), but that's only 6 days. Wait, maybe the "rest of the week" includes Saturday as well? Because Sunday to Wednesday is four days, then Thursday to Saturday would be three days left. Hmm, maybe I need to clarify that. Wait, the problem says "for the rest of the week," which could be interpreted differently. Let me check again. The problem states: "From Sunday through Wednesday, he spent his money on wooden action figures..." So that's four days. Then "For the rest of the week, he will buy plastic action figures which cost $2 each." So "rest of the week" would be the remaining days of the week after Sunday through Wednesday. Since Sunday is the first day, the week would be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday. So from Sunday to Wednesday is four days. The rest would be Thursday, Friday, Saturday. That's three days. So total days: 4 + 3 = 7 days, which is a week. Okay, so that makes sense. So he spends four days on wooden figures ($5 each) and three days on plastic ones ($2 each). The total amount he spends is $70, and he wants to spend an equal amount each day. So first, we need to figure out how much he spends each day, then calculate how many action figures he can buy each day, and sum them up. Wait, but the problem says he has $70 and wishes to spend an equal amount each day for one week. So the total amount he spends is $70, divided equally over seven days. So each day he spends $70 / 7 = $10 per day. So $10 per day total for the week. But then, from Sunday through Wednesday (four days), he spends on wooden figures ($5 each), and the remaining three days (Thursday, Friday, Saturday) he spends on plastic figures ($2 each). So the total amount he spends on wooden figures is 4 days * $10/day = $40. Then the remaining amount is $70 - $40 = $30, which he spends over three days at $2 each. So $30 / 3 days = $10 per day, which matches the total daily spending of $10. So that checks out. Now, how many wooden action figures does he buy? Each costs $5, and he spends $10 on them each day for four days. Wait, but if each day he spends $10 on wooden figures, then each day he can buy $10 / $5 = 2 action figures per day. So over four days, that's 2 * 4 = 8 wooden action figures. Then, for the plastic figures, he spends $10 per day for three days. Each plastic figure is $2, so per day he can buy $10 / $2 = 5 action figures per day. Over three days, that's 5 * 3 = 15 plastic action figures. Total action figures: 8 + 15 = 23. Wait, but let me verify this again. Let's check the total money spent. Wooden: 8 figures * $5 = $40. Plastic: 15 figures * $2 = $30. Total: $40 + $30 = $70. Which matches the total he has. So that's correct. Alternatively, another way to look at it: since he spends $10 each day, total $70 over 7 days. So each day he spends $10. For the first four days, he uses $10 each day on $5 action figures. So each day, $10 / $5 = 2 per day. 4 days: 8. Then the remaining three days, $10 each day on $2 action figures: $10 / $2 = 5 per day. 3 days: 15. Total 23. Yes, that seems to be the answer. <\|end_of_thought\|> <\|begin_of_solution\|> Peter has $70 to spend over 7 days. He spends $10 each day ($70 ÷ 7 = $10/day). Wooden action figures (Sunday–Wednesday, 4 days): Each costs $5. Daily purchase: $10 ÷ $5 = 2 figures/day. Total: 2 × 4 = 8 figures. Plastic action figures (Thursday–Saturday, 3 days): Each costs $2. Daily purchase: $10 ÷ $2 = 5 figures/day. Total: 5 × 3 = 15 figures. Total action figures: 8 (wooden) + 15 (plastic) = 23. \boxed{23} <\|end_of_solution\|>
DeepSeek-R1-Distill-Qwen-7B	<think> Okay, let's see. Peter has $70 and wants to spend an equal amount each day for one week. So first, I need to figure out how much he spends each day. A week has seven days, right? From Sunday through Wednesday, he buys wooden action figures that cost $5 each. Then, for the rest of the week, which would be Thursday and Friday, he buys plastic ones that cost $2 each. The question is asking how many total action figures he'll have by the end of the week. Wait, hold on. Wait, a week is seven days. Sunday through Wednesday is four days, and then the rest is Thursday and Friday, that's two days. So total of six days? Wait, Sunday, Monday, Tuesday, Wednesday is four days. Then Thursday and Friday, that's two days. So total of six days he's spending money, leaving Saturday out? The problem says "for one week," so maybe he starts on Sunday and goes through Saturday? But the problem mentions spending from Sunday through Wednesday, and then the rest of the week. Hmm. Wait, the problem says: "From Sunday through Wednesday, he spent his money on wooden action figures which cost $5 each. For the rest of the week, he will buy plastic action figures which cost $2 each." So Sunday to Wednesday is four days, then the rest of the week would be Thursday to Saturday, which is three days. Wait, that's three days. So total of seven days? Wait, no. Sunday to Saturday is a week. If Sunday through Wednesday is four days, then the remaining days are Thursday, Friday, Saturday, which is three days. So total of seven days. So he spends money on four days buying wooden figures and three days buying plastic ones. But the problem says he spends an equal amount each day for one week. So total spending per day is consistent. So first, I need to find out how much he spends each day. Let me denote the daily amount as x dollars. So total spending for the week would be 7x because it's one week. But he has $70. So 7x = $70. Therefore, x = 10. So he spends $10 each day. Wait, but that seems high. Let me check. If he spends $10 each day for seven days, that's $70 total. That makes sense. So each day he spends $10. Then, from Sunday through Wednesday, which is four days, he spends 4 days * $10/day = $40 on wooden action figures. Then, for the rest of the week, which is three days (Thursday, Friday, Saturday), he spends 3 days * $10/day = $30 on plastic action figures. So total $40 + $30 = $70, which matches his total money. That checks out. Now, the problem is asking for the total number of action figures he will have by the end of the week. So we need to calculate how many wooden figures he bought during the four days and how many plastic figures he bought during the three days, then sum them up. First, wooden action figures cost $5 each. He spent $40 on them. So the number of wooden figures is $40 divided by $5 per figure. That's 40 / 5 = 8 figures. Then, plastic action figures cost $2 each. He spent $30 on them. So the number of plastic figures is $30 divided by $2 per figure. That's 30 / 2 = 15 figures. Adding them together: 8 wooden + 15 plastic = 23 total action figures. Wait a second, but let me verify again to make sure I didn't make a mistake. So total days are seven. He spends $10 each day. Total $70. From Sunday to Wednesday: four days. 4 days * $10 = $40. Then Thursday, Friday, Saturday: three days * $10 = $30. Correct. Then wooden figures: $40 / $5 = 8. Plastic: $30 / $2 = 15. Total 23. That seems right. But wait, the problem says "for the rest of the week, he will buy plastic action figures which cost $2 each." So does "rest of the week" mean the remaining days after Sunday through Wednesday? Sunday through Wednesday is four days, so the remaining three days would be Thursday, Friday, Saturday. So three days. So three days of $10 each day, totaling $30. Correct. Therefore, the total number of action figures is 8 + 15 = 23. So the answer is 23. </think> Peter spends $10 each day for 7 days, totaling $70. From Sunday to Wednesday (4 days), he buys wooden action figures at $5 each: \[ \frac{4 \text{ days} \times \$10}{\$5/\text{figure}} = \frac{\$40}{\$5} = 8 \text{ figures}. \] For the remaining 3 days (Thursday to Saturday), he buys plastic action figures at $2 each: \[ \frac{3 \text{ days} \times \$10}{\$2/\text{figure}} = \frac{\$30}{\$2} = 15 \text{ figures}. \] Total action figures: \[ 8 + 15 = \boxed{23}. \]
Bespoke-Stratos-7B	<\|begin_of_thought\|> First, I need to determine how many days Peter spends buying wooden action figures. From Sunday to Wednesday is 4 days. Each wooden action figure costs $5, and Peter spends a total of $70 for the week. Next, I'll calculate how much money Peter spends on wooden action figures each day by dividing the total amount for these days by the number of days: $70 ÷ 4 = $17.50 per day. Then, I'll find out how many wooden action figures he buys each day by dividing the daily spending by the cost per figure: $17.50 ÷ $5 = 3.5 figures per day. Since he can't buy half a figure, I'll assume he buys 3 figures each day for 4 days, totaling 12 wooden figures, spending $60. The remaining $10 will be spent on plastic action figures, which cost $2 each. Dividing $10 by $2 gives 5 plastic figures. Finally, adding both types of figures together, Peter will have 12 + 5 = 17 action figures by the end of the week. <\|end_of_thought\|> <\|begin_of_solution\|> To determine how many total action figures Peter will have by the end of the week, let's break down his spending step by step. 1. Total Money and Days: - Total Money: \$70 - Number of Days in a Week: 7 days 2. Spending Pattern: - From Sunday to Wednesday: 4 days spending on wooden action figures. - From Thursday to Sunday: 3 days spending on plastic action figures. 3. Calculations: - Wooden Action Figures: - Cost per Wooden Action Figure: \$5 - Total Spent on Wooden Figures: \[ 4 \text{ days} \times \$5/\text{figure} = \$20 \] - Number of Wooden Action Figures Purchased: \[ \frac{\$20}{\$5/\text{figure}} = 4 \text{ figures} \] - Plastic Action Figures: - Remaining Money: \[ \$70 - \$20 = \$50 \] - Cost per Plastic Action Figure: \$2 - Number of Plastic Action Figures Purchased: \[ \frac{\$50}{\$2/\text{figure}} = 25 \text{ figures} \] - Total Action Figures: \[ 4 \text{ (wooden)} + 25 \text{ (plastic)} = 29 \text{ figures} \] Final Answer: \[ \boxed{29} \] <\|end_of_solution\|>
OpenThinker-7B	<\|begin_of_thought\|> Okay, let's see. So Peter has $70 and wants to spend an equal amount each day for one week. The week is from Sunday to Saturday, right? So that's seven days. He spent money on wooden action figures from Sunday through Wednesday, and then from Thursday to Saturday, he'll buy plastic ones. Each wooden figure costs $5, and each plastic one is $2. The question is, how many total action figures does he have by the end of the week? First, I need to figure out how much money Peter spends each day. Since he has $70 over 7 days, he spends 70 divided by 7, which is 10 dollars per day. That makes sense. So each day he spends $10. Now, from Sunday to Wednesday, that's 5 days. He spends $10 each day on wooden figures. Each figure is $5. So how many can he buy each day? If he spends $10 a day and each figure is $5, then he can buy 10 divided by 5, which is 2 action figures per day. So over 5 days, that's 2 times 5, which is 10 wooden action figures. Then, from Thursday to Saturday, that's 3 days left. He'll spend $10 each day on plastic figures, which cost $2 each. So how many can he buy each day? 10 divided by 2 is 5. So each day he buys 5 plastic figures. Over 3 days, that's 5 times 3, which is 15 plastic action figures. Adding those together: 10 wooden plus 15 plastic equals 25 total action figures. Wait, but let me double-check the calculations to make sure I didn't make a mistake. Wait, spending $10 each day. From Sunday to Wednesday is 5 days. Each wooden figure is $5. So per day, he can buy 10/5 = 2. So 5 days * 2 = 10. Correct. Then Thursday to Saturday is 3 days. Each plastic figure is $2, so 10/2 = 5 per day. 3 days 5 =15. Total 25. That seems right. But wait, another way to check: total money spent on wooden figures is 10 days 5 figures 5 dollars? Wait, no. Wait, each day he spends $10 on wooden figures. So each day, 2 figures. So total wooden figures: 5 days 2 =10. Total spent on wooden: 10 days 10 dollars = $100? Wait, that can't be. Wait, no. Wait, he has $70. Wait, this is a problem. Wait, hold on. If he spends $10 each day for 7 days, that's 70 dollars. But if he spends 5 days on wooden figures at $10 per day, that's 510=50 dollars. Then the remaining 2 days (Thursday and Friday? Wait, no, from Thursday to Saturday is 3 days. Wait, Sunday to Wednesday is 5 days. Then Thursday to Saturday is 3 days. So total days: 5+3=8 days. Wait, but the week is only 7 days. Wait, maybe there's a mistake here. Wait, the problem says "from Sunday through Wednesday" which is 5 days, and "for the rest of the week" which would be Thursday through Saturday, another 3 days. So total 8 days? But the problem says he spends an equal amount each day for one week. A week is 7 days. So there's a contradiction here. Wait, the problem says "from Sunday through Wednesday, he spent his money on wooden action figures... For the rest of the week, he will buy plastic action figures..." But Sunday through Wednesday is 5 days, and the rest of the week would be Thursday through Saturday, which is 3 days. That totals 8 days. But the problem states he spends for one week, which is 7 days. So perhaps there's an error in the problem statement? Or maybe "rest of the week" refers to after Wednesday, which would be Thursday, Friday, Saturday, Sunday? Wait, that doesn't make sense. Alternatively, maybe "rest of the week" is interpreted differently. Wait, perhaps the problem is structured as follows: he spends from Sunday to Wednesday (5 days) on wooden figures, and then from Thursday to Saturday (3 days) on plastic ones. But that totals 8 days. But the problem says "for one week", which is 7 days. Therefore, there's a mistake here. Wait, maybe the problem meant that he spends from Sunday to Wednesday (5 days) and then the remaining 2 days (Thursday and Friday) on plastic figures? But the problem says "for the rest of the week", which would imply the remaining days after Wednesday. Hmm. Alternatively, maybe the problem has a typo, and "rest of the week" is supposed to be 2 days. But as per the problem statement, it's 3 days. So perhaps the problem is correct, and there's a miscalculation. Wait, let me check again. The problem says: Peter has $70 and wishes to spend an equal amount each day for one week (7 days). From Sunday through Wednesday (5 days), he spends on wooden figures. For the rest of the week (3 days), he spends on plastic ones. So total days: 5+3=8. But that's more than a week. Therefore, there must be a mistake here. Wait, perhaps "rest of the week" refers to the remaining days after Wednesday, which would be Thursday, Friday, Saturday, Sunday? No, that's 4 days. Alternatively, maybe the problem meant that after Wednesday, he spends the remaining days of the week. But a week is 7 days, so if he spends Sunday to Wednesday (5 days), then the remaining days are Thursday, Friday, Saturday, Sunday. That's 4 days. But the problem says "rest of the week", which is ambiguous. Alternatively, maybe the problem is correct, and the answer is 25, but we need to check if the total days add up to 7. Wait, 5 days (Sunday to Wednesday) plus 3 days (Thursday to Saturday) is 8 days, which is more than a week. Therefore, there's a contradiction here. This suggests that there's an error in the problem statement. Alternatively, maybe the problem is correct, and the answer is 25, but the total days are 8. However, the problem states "for one week", which is 7 days. Therefore, this is a contradiction. So perhaps the problem is intended to have 5 days for wooden and 2 days for plastic, but the problem states 3 days. Alternatively, maybe "rest of the week" is 2 days. But according to the problem, it's 3 days. Hmm. Alternatively, maybe the problem is correct, and we should proceed with 5 days (Sunday to Wednesday) and 3 days (Thursday to Saturday) as the days he spends money. But then the total is 8 days, which is a week and a day. That's impossible. Therefore, perhaps the problem has a typo, and "rest of the week" should be 2 days. Alternatively, maybe the problem is correct, and we need to proceed with 5 days and 3 days, totaling 8 days, but the problem says "for one week". Therefore, this is a contradiction. Therefore, perhaps the problem is intended to have 5 days (Sunday to Thursday) and 2 days (Friday and Saturday) as the rest. But the problem says "rest of the week" from Wednesday. Alternatively, maybe the problem is correct, and the answer is 25, but the total days are 8. However, the problem says "for one week", which is 7 days. Therefore, this is a problem. Therefore, perhaps the problem is correct, and we need to proceed with 5 days and 3 days, but the total is 8 days, which is more than a week. Therefore, the problem might have a mistake. However, assuming that the problem is correct, and the answer is 25, but the total days are 8, which is a week and a day. But since the problem states "for one week", perhaps the problem is intended to have 7 days, but the "rest of the week" is 2 days. Alternatively, maybe the problem is correct, and we proceed with 5 days and 3 days, but the answer is 25. However, given that the problem states "for one week", which is 7 days, but the days spent are 8, this is a contradiction. Therefore, perhaps the problem is correct, and the answer is 25, but the total days are 8. However, since the problem says "for one week", which is 7 days, this is confusing. Therefore, perhaps the problem is intended to have 5 days (Sunday to Wednesday) and 2 days (Thursday and Friday) as the rest, but the problem says "rest of the week" from Wednesday. Alternatively, maybe the problem is correct, and the answer is 25. But let's proceed with the given information, assuming that the problem is correct, and the total days are 7. Therefore, perhaps the problem intended that from Sunday to Wednesday (5 days) and the remaining 2 days (Thursday and Friday) are the rest. But the problem says "rest of the week" from Wednesday. Alternatively, maybe "rest of the week" is interpreted as the remaining days after Wednesday, which would be Thursday, Friday, Saturday, Sunday. But that's 4 days. Alternatively, maybe the problem has a typo, and "rest of the week" is 2 days. But according to the problem, it's 3 days. Therefore, perhaps the problem is correct, and we proceed with 5 days and 3 days, totaling 8 days. But the problem says "for one week". Therefore, this is a contradiction. Therefore, perhaps the problem is correct, and the answer is 25, but the total days are 8. However, given that the problem states "for one week", which is 7 days, this is confusing. Therefore, perhaps the problem is correct, and we need to proceed with 5 days and 3 days, but the answer is 25. However, given that the problem says "for one week", which is 7 days, the answer might be different. Wait, perhaps the problem is that he spends $10 each day for 7 days, so total $70. From Sunday to Wednesday (5 days), he spends $10 each day on wooden figures. Each wooden figure is $5. Therefore, per day, he can buy 2 figures. So 5 days * 2 = 10 wooden figures. Then, the remaining 2 days (Thursday and Friday) he spends $10 each day on plastic figures at $2 each. So 10/2 =5 per day. 2 days 5 =10 plastic figures. Total 10+10=20. But the problem says "for the rest of the week", which would be Thursday to Saturday, 3 days. But if we assume that the problem intended that after Wednesday, there are 2 days left (Thursday and Friday), then the answer is 20. But according to the problem statement, it's 3 days. Therefore, this is a problem. Therefore, perhaps the problem is intended to have 5 days and 2 days, but the problem says 3 days. Therefore, perhaps there's a mistake in the problem statement. Alternatively, maybe the problem is correct, and the answer is 25, but the total days are 8, which is a week and a day. However, since the problem says "for one week", which is 7 days, this is conflicting. Therefore, perhaps the problem is correct, and the answer is 25. Therefore, we proceed with 5 days and 3 days. So total action figures: 10 wooden +15 plastic=25. Therefore, the answer is 25. But I need to check again. Wait, let's recalculate. If he spends $10 each day for 7 days, total $70. From Sunday to Wednesday: 5 days. Each day, he spends $10 on wooden figures at $5 each. So per day, 2 figures. 5 days 2=10 wooden. Then, the remaining days: Thursday to Saturday is 3 days. Each day, he spends $10 on plastic figures at $2 each. So per day, 5 plastic figures. 3 days 5=15 plastic. Total 25. So even though the total days are 8, the problem says "for one week", which is 7 days. Therefore, there's a discrepancy. Therefore, perhaps the problem is correct, and the answer is 25. But given that the problem says "for one week", which is 7 days, but the days spent are 8, this is confusing. However, since the problem states that he spends from Sunday to Wednesday (5 days) and the rest of the week (3 days), totaling 8 days, but the problem says "for one week", which is 7 days, this is a contradiction. Therefore, perhaps the problem has a typo, and "rest of the week" should be 2 days. Alternatively, maybe the problem is correct, and we should proceed. Therefore, the answer is 25. Therefore, the final answer is 25. But I need to confirm again. Alternatively, maybe the problem is correct, and the answer is 25. Therefore, the answer is 25. Therefore, the final answer is 25. But I need to check again. Let me verify the calculations. Total money: $70. Spent each day: $10. From Sunday to Wednesday: 5 days. Cost per wooden figure: $5. So per day, he can buy 10/5=2. So 5 days 2=10 wooden. Then, remaining days: Thursday to Saturday is 3 days. Cost per plastic figure: $2. So per day, 10/2=5. 3 days 5=15 plastic. Total 10+15=25. Yes, that's correct. Even though the total days are 8, the problem says "for one week", which is 7 days. Therefore, there's a discrepancy, but given the problem statement, the answer is 25. Therefore, the final answer is 25. <\|end_of_thought\|> <\|begin_of_solution\|> Peter has $70 to spend equally over 7 days. Each day, he spends $10. 1. Wooden Action Figures (Sunday to Wednesday):* - 5 days × $10/day = $50 spent. - Each wooden figure costs $5, so he buys $10/$5 = 2 per day. - Total wooden figures: 5 days × 2 = 10. 2. Plastic Action Figures (Thursday to Saturday): - Remaining days: 3 days × $10/day = $30 spent. - Each plastic figure costs $2, so he buys $10/$2 = 5 per day. - Total plastic figures: 3 days × 5 = 15. Total Action Figures: 10 (wooden) + 15 (plastic) = 25. The final answer is \boxed{25}. Note: The problem states "one week" (7 days), but the calculation involves 8 days. This discrepancy arises from the problem's wording ("rest of the week" after Wednesday), which likely intended 3 days but may have a typo. Despite this, the solution adheres to the given information. <\|end_of_solution\|>

示例二：32B量级模型对比

问题	A shoe store was having a weekend sale on a brand of popular tennis shoes. On Friday the store sold 14 pairs of tennis shoes. The next day they sold double that number of shoes. On the last day of the sale they sold one-half the amount that they did the day before, but six people returned their pairs because they didn't fit. How many pairs of tennis shoes were sold by the end of the sale?
答案	On Saturday 142=<<142=28>>28 shoes were sold\nOn Sunday 28/2=<<28/2=14>>14 shoes were sold\nBefore the returns were made 14+28+14=<<14+28+14=56>>56 pairs of shoes were sold\nAfter the returns were made 56-6=<<56-6=50>>50 pairs of shoe were sold\n#### 50
DistilQwen2.5-R1-32B 回复	<\|begin_of_thought\|> Okay, let me try to figure out this problem step by step. So, the shoe store had a sale on tennis shoes over the weekend. Let's break down the information given. First, on Friday, they sold 14 pairs of tennis shoes. That's straightforward. Then, the next day, which would be Saturday, they sold double that number. Double of 14 is 28, right? So, 28 pairs on Saturday. Then, on the last day of the sale, which is Sunday, they sold half the amount they did the day before. The day before Sunday is Saturday, so half of 28 is 14. So, 14 pairs on Sunday. But wait, there's a catch here. Six people returned their pairs because the shoes didn't fit. So, we need to subtract those 6 returned pairs from the Sunday sales. That means instead of 14, they effectively sold 14 minus 6, which is 8 pairs on Sunday. Now, to find the total number of tennis shoes sold by the end of the sale, we need to add up the sales from Friday, Saturday, and Sunday, taking into account the returns on Sunday. So, Friday: 14 pairs. Saturday: 28 pairs. Sunday: 14 - 6 = 8 pairs. Adding those together: 14 + 28 + 8. Let me calculate that. 14 plus 28 is 42, and then 42 plus 8 is 50. So, total pairs sold would be 50. Wait, but let me double-check to make sure I didn't make a mistake. Let's verify each step again. Friday: 14 pairs. Correct. Saturday is double, so 14*2=28. Correct. Sunday is half of Saturday's sales, which is 28/2=14. But then subtract the 6 returned pairs. So 14-6=8. Then total is 14+28+8=50. Yeah, that seems right. Hmm, another way to look at it: Total sold without returns would be 14 + 28 +14 = 56. Then subtract the 6 returned pairs, which would be 56 -6=50. Same result. So, that confirms it. I think that's all. So the final answer should be 50 pairs of tennis shoes sold. <\|end_of_thought\|> <\|begin_of_solution\|> The shoe store sold 14 pairs on Friday. On Saturday, they sold double that number, which is $14 \times 2 = 28$ pairs. On Sunday, they sold half of Saturday's sales, which is $28 \div 2 = 14$ pairs, but then subtract the 6 pairs returned. Therefore, the effective sales on Sunday are $14 - 6 = 8$ pairs. Adding up the sales from all three days: $14$ (Friday) + $28$ (Saturday) + $8$ (Sunday) = $14 + 28 + 8 = 50$. The final answer is $\boxed{50}$. <\|end_of_solution\|>
DeepSeek-R1-Distill-Qwen-32B 回复	<think> Okay, let's try to figure out how many tennis shoes were sold by the end of the sale. So, the problem is about a shoe store that had a weekend sale. I'll need to break it down day by day to make sure I understand each part correctly. First, on Friday, the store sold 14 pairs of tennis shoes. That seems straightforward. So, Friday sales are 14 pairs. Next, the problem says that on the next day, which would be Saturday, they sold double that number. Hmm, double of Friday's sales. So, double of 14 is 14 times 2. Let me calculate that: 14 * 2 = 28. So, they sold 28 pairs on Saturday. Now, moving on to the last day of the sale, which is Sunday. The problem states that on Sunday, they sold half the amount they did the day before. The day before Sunday is Saturday, so half of Saturday's sales. Saturday was 28 pairs, so half of that would be 28 / 2. Let me do that math: 28 divided by 2 is 14. So, they sold 14 pairs on Sunday before any returns. But wait, the problem mentions that six people returned their pairs because they didn't fit. So, we need to subtract those returns from Sunday's sales. So, Sunday's total after returns would be 14 minus 6. Let me calculate that: 14 - 6 = 8. So, they effectively sold 8 pairs on Sunday after the returns. Now, to find the total number of pairs sold by the end of the sale, I need to add up the sales from each day. That would be Friday's 14, plus Saturday's 28, plus Sunday's 8. Let me add them up step by step. First, 14 (Friday) + 28 (Saturday) = 42. Then, adding Sunday's 8 to that: 42 + 8 = 50. Wait, does that make sense? Let me double-check each step to make sure I didn't make a mistake. Friday was 14, Saturday was 28, Sunday was 14 before returns, which became 8 after subtracting 6. So, 14 + 28 is indeed 42, and 42 + 8 is 50. Yeah, that seems correct. But just to be thorough, maybe I should think about whether the returns affect the total sold or just the net sales. The problem says "they sold one-half the amount that they did the day before, but six people returned their pairs." So, I think the six returns are subtracted from Sunday's sales, so the total sold would be the initial sales minus the returns. Therefore, the calculation I did is correct. So, adding all three days together: 14 + 28 + (14 - 6) = 14 + 28 + 8 = 50. Yep, that looks right. </think> The total number of pairs sold by the end of the sale is 50. The final answer is 50.
Sky-T1-32B-Preview 回复	<\|begin_of_thought\|> Okay, let's try to figure out how many tennis shoes were sold by the end of the sale. Hmm, the problem mentions three days: Friday, Saturday, and Sunday. Let me break it down step by step. First, on Friday, they sold 14 pairs. That's straightforward. Each pair is two shoes, right? Wait, but the question asks for the number of tennis shoes sold, not pairs. So I need to remember to convert pairs to individual shoes. But maybe I should check if the problem wants the answer in pairs or individual shoes. The problem says "how many pairs of tennis shoes were sold," so individual shoes. So each pair is two shoes. So 14 pairs would be 142 = 28 shoes on Friday. Wait, but maybe I should handle the pairs first and then convert at the end. Let me see. Next, Saturday they sold double that number of shoes. So double of Friday's sales. Friday was 14 pairs, so Saturday is 142 = 28 pairs. Then Sunday, they sold half the amount they did the day before. The day before Sunday is Saturday, which was 28 pairs. Half of that is 14 pairs. But then six people returned their pairs. So we need to subtract those returns. But wait, the returns are pairs as well. So 14 pairs sold on Sunday, minus 6 returns. So 14 - 6 = 8 pairs sold on Sunday after returns. Now, let's total up the pairs sold each day: Friday 14, Saturday 28, Sunday 8. Total pairs would be 14 + 28 + 8 = 50 pairs. Then convert that to individual shoes: 50 pairs * 2 shoes per pair = 100 shoes. So the answer would be 100. But wait, let me double-check each step to make sure I didn't make a mistake. Starting again: Friday: 14 pairs. That's 142 = 28 shoes. Saturday: double Friday's pairs, so 142 = 28 pairs. 282 = 56 shoes. Sunday: half of Saturday's sales, which is 28/2 = 14 pairs. Then 6 returns. So 14 - 6 = 8 pairs. 82 = 16 shoes. Total shoes: Friday (28) + Saturday (56) + Sunday (16) = 28+56=84, 84+16=100. Yes, same result. Wait, but another way: total pairs first. 14 + 28 + (14 -6) = 14 +28 +8 =50 pairs. 502=100. Either way, same answer. Is there any detail I missed? The problem says "sold by the end of the sale." Returns are subtracted from Sunday's sales. So yes, that's accounted for. So the total is 100 shoes. That seems right. Let me check again. Friday: 28 pairs. Saturday: 56 pairs. Sunday:16 pairs. Total: 28+56+16=100. Yep. I think that's correct. So I think the answer is 100. <\|end_of_thought\|> <\|begin_of_solution\|> The final answer is 100. Step-by-Step Explanation:* 1. Friday Sales: - Sold 14 pairs of shoes. - Convert to individual shoes: $14 \text{ pairs} \times 2 = 28 \text{ shoes}$. 2. Saturday Sales: - Sold double Friday's pairs: $14 \times 2 = 28 \text{ pairs}$. - Convert to individual shoes: $28 \times 2 = 56 \text{ shoes}$. 3. Sunday Sales: - Sold half of Saturday's pairs: $28 \div 2 = 14 \text{ pairs}$. - Subtract returns (6 pairs): $14 - 6 = 8 \text{ pairs}$. - Convert to individual shoes: $8 \times 2 = 16 \text{ shoes}$. 4. Total Sales: - Sum all pairs sold: $28 + 56 + 16 = 100 \text{ shoes}$. Answer: 100 pairs of tennis shoes were sold by the end of the sale. <\|end_of_solution\|>
OpenThinker-32B	<\|begin_of_thought\|> Okay, let's try to figure out how many pairs of tennis shoes were sold by the end of the sale. The problem says a shoe store sold some pairs over three days: Friday, Saturday, and Sunday. Let's break down each day's sales step by step. Starting with Friday. The store sold 14 pairs that day. So Friday's sales are straightforward: 14 pairs. But wait, the question mentions tennis shoes sold by the end of the sale. Since each pair is two shoes, do we need to convert pairs to individual shoes? The problem says "how many tennis shoes," not pairs. Hmm, so maybe we need to consider each pair as two shoes. Let me note that down as a possible point of confusion. Next, Saturday. The problem states they sold double the number from Friday. So if Friday was 14 pairs, Saturday would be 14 * 2 = 28 pairs. Again, same as Friday, so 28 pairs. But again, converting to individual shoes would mean 28 * 2 = 56 shoes. But let's hold off on converting until we know if the final answer requires pairs or shoes. The question specifically says "tennis shoes," which are individual, so we need to calculate the total number of shoes, not pairs. That's important. So each pair is two shoes, so each day's sales in pairs should be multiplied by 2 to get shoes. Then, on Sunday, they sold half of Saturday's amount but then had six returns. Wait, let's parse that carefully. On the last day, Sunday, they sold one-half the amount they did the day before (which is Saturday). So Sunday's sales before returns would be 28 pairs / 2 = 14 pairs. But then six people returned their pairs. Each return is a pair, right? Because you can't return half a pair. So six pairs returned. So Sunday's net sales would be 14 pairs - 6 pairs = 8 pairs. But wait, is the return happening after the sale on Sunday? The problem says "six people returned their pairs because they didn't fit." So the returns would reduce the total sold. So Sunday's total sold is 14 pairs minus 6 pairs, which is 8 pairs. Therefore, converting that to shoes, it's 8 pairs * 2 = 16 shoes. Now, let's sum up all three days. Friday: 28 pairs. Saturday: 56 pairs. Sunday: 16 pairs. Total shoes sold: 28 (Friday) + 56 (Saturday) + 16 (Sunday) = 100 pairs. Wait, but let me double-check. Alternatively, maybe the returns are considered per pairs, so subtracting 6 pairs from Sunday's sales. Let's re-express: Friday: 14 pairs. Saturday: 28 pairs. Sunday: 14 pairs sold, then 6 pairs returned. So net Sunday sales: 14 - 6 = 8 pairs. Total pairs sold: 14 + 28 + 8 = 50 pairs. Then convert to shoes: 50 * 2 = 100 shoes. Alternatively, maybe the problem expects pairs as the answer unit? Let me check the original question again: "how many pairs of tennis shoes were sold by the end of the sale?" The term "tennis shoes" refers to individual shoes, not pairs. So the answer should be in shoes, not pairs. Therefore, 100 shoes. But let me make sure I didn't make a mistake in the calculations. Let's go through each day step by step again. Friday: 14 pairs. Each pair is 2 shoes. So 14 * 2 = 28 shoes. Saturday: double Friday's pairs. 14 * 2 = 28 pairs. 28 * 2 = 56 shoes. Sunday: half of Saturday's pairs. 28 / 2 = 14 pairs. 14 * 2 = 28 shoes. Then 6 pairs returned. Each returned pair is 2 shoes, so 6 * 2 = 12 shoes returned. So net for Sunday: 28 - 12 = 16 shoes. Total: 28 + 56 + 16 = 100 shoes. That seems right. Wait, another way: total pairs sold before returns: 14 + 28 +14 = 56 pairs. Then returns: 6 pairs, so total pairs sold: 56 -6 = 50 pairs. Multiply by 2: 100 shoes. Same answer. Yes, so the final answer is 100. Let me check if there's any alternative interpretation. Is there a possibility that "six people returned their pairs" refers to six people returning one pair each, so 6 pairs total? Yes, that's what it says. So each return is a pair, so 6 pairs. So that part is correct. Another check: maybe the problem expects the answer in pairs, but the question specifically asks for shoes. So 100 is correct. Let me make sure the arithmetic is right. 14 + 28 + 14 = 56 pairs. Minus 6 pairs returned: 50 pairs. 50 2 = 100. Correct. Alternatively, adding up the shoes each day: 28 (Fri) + 56 (Sat) +16 (Sun) = 100. Correct. Yes, seems solid. So the answer is 100. <\|end_of_thought\|> <\|begin_of_solution\|> The final answer is 100. Step-by-Step Explanation:* 1. Friday's Sales: - Sold 14 pairs. - Convert to shoes: $14 \times 2 = 28$ shoes. 2. Saturday's Sales: - Doubled Friday's sales: $14 \times 2 = 28$ pairs. - Convert to shoes: $28 \times 2 = 56$ shoes. 3. Sunday's Sales Before Returns: - Half of Saturday's pairs: $28 \div 2 = 14$ pairs. - Convert to shoes: $14 \times 2 = 28$ shoes. 4. Returns on Sunday: - 6 pairs returned, equivalent to $6 \times 2 = 12$ shoes. 5. Net Sunday Sales: - $28 - 12 = 16$ shoes. 6. Total Shoes Sold: - Friday: 28, Saturday: 56, Sunday: 16. - Sum: $28 + 56 + 16 = 100$ pairs. <\|end_of_solution\|>

模型下载和使用

DistilQwen2.5-R1 在阿里云人工智能平台 PAI 上的实践

以下 HuggingFace transformers 库为例，简要介绍如何在 PAI-DSW 上使用 DistilQwen2.5-R1 模型。首先需要保证 PAI-DSW 镜像内 transformers 版本大于等于4.37.0，否则会在加载模型时报错：

KeyError: 'qwen2'

以 DistilQwen2.5-R1-7B 为例，我们可以使用如下代码调用模型：

from transformers import AutoModelForCausalLM, AutoTokenizer

model_name = "alibaba-pai/DistilQwen2.5-R1-7B"

model = AutoModelForCausalLM.from_pretrained(model_name)
tokenizer = AutoTokenizer.from_pretrained(model_name)

prompt = "xxxxx"
messages=[
    {"role": "system", "content": "Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop well-considered thinking process. Please structure your response into two main sections: Thought and Solution. In the Thought section, detail your reasoning process using the specified format: <|begin_of_thought|> {thought with steps separated with '\n\n'} <|end_of_thought|> Each step should include detailed considerations such as analisying questions, summarizing relevant findings, brainstorming new ideas, verifying the accuracy of the current steps, refining any errors, and revisiting previous steps. In the Solution section, based on various attempts, explorations, and reflections from the Thought section, systematically present the final solution that you deem correct. The solution should remain a logical, accurate, concise expression style and detail necessary step needed to reach the conclusion, formatted as follows: <|begin_of_solution|> {final formatted, precise, and clear solution} <|end_of_solution|> Now, try to solve the following question through the above guidelines:"},
    {"role": "user", "content": prompt},
]
text = tokenizer.apply_chat_template(
    messages,
    tokenize=False,
    add_generation_prompt=True
)
model_inputs = tokenizer([text], return_tensors="pt").to(model.device)

generated_ids = model.generate(
    **model_inputs,
    max_new_tokens=512
)
generated_ids = [
    output_ids[len(input_ids):] for input_ids, output_ids in zip(model_inputs.input_ids, generated_ids)
]

response = tokenizer.batch_decode(generated_ids, skip_special_tokens=True)[0]
print(response)

DistilQwen2.5-R1在开源社区的下载

我们在 Hugging Face 和 Model Scope 上开源了我们蒸馏后的模型，分别为DistilQwen2.5-R1-3B、DistilQwen2.5-R1-7B、DistilQwen2.5-R1-14B、DistilQwen2.5-R1-32B。以Hugging Face为例，用户可以使用如下代码下载这两个模型：

from huggingface_hub import snapshot_download

model_name = "alibaba-pai/DistilQwen2.5-R1-3B"
snapshot_download(repo_id=model_name, cache_dir="./DistilQwen2.5-R1-3B/")

model_name = "alibaba-pai/DistilQwen2.5-R1-7B"
snapshot_download(repo_id=model_name, cache_dir="./DistilQwen2.5-R1-7B/")

model_name = "alibaba-pai/DistilQwen2.5-R1-14B"
snapshot_download(repo_id=model_name, cache_dir="./DistilQwen2.5-R1-14B/")

model_name = "alibaba-pai/DistilQwen2.5-R1-32B"
snapshot_download(repo_id=model_name, cache_dir="./DistilQwen2.5-R1-32B/")

小结与未来工作

本文介绍了 DistilQwen2.5-R1 系列深度推理模型，它在少量来自 DeepSeek-R1 的思维链数据基础上，通过创新蒸馏策略增强了小模型的深度思考能力。实验结果表明，该系列模型在多个基准测试中表现出色，尤其是 DistilQwen2.5-R1-7B 的性能全面超越了其他开源蒸馏模型。为了方便实际应用，这些模型的 Checkpoint 已在 Hugging Face 和 Model Scope 社区中公开，并提供了在阿里云人工智能平台 PAI 上的操作指南。在未来，随着大语言模型和知识蒸馏技术更进一步的发展，我们将推出各种领域、各种规格的 DistilQwen 系列模型，充分促进大语言模型在实际应用中的降本增效。