gravermistakes/NuminaMath-1.5-RL-Verifiable

---
license: apache-2.0
task_categories:
- text-generation
- question-answering
language:
- en
tags:
- math
- post-training
- RL
- verifiable
- reasoning
pretty_name: NuminaMath 1.5 RL Verifiable
dataset_info:
features:
- name: problem
dtype: string
- name: solution
dtype: string
- name: answer
dtype: string
- name: problem_type
dtype: string
- name: question_type
dtype: string
- name: problem_is_valid
dtype: string
- name: solution_is_valid
dtype: string
- name: source
dtype: string
- name: synthetic
dtype: bool
splits:
- name: train
num_bytes: 188626432
num_examples: 131063
download_size: 85718743
dataset_size: 188626432
configs:
- config_name: default
data_files:
- split: train
path: data/train-*
---

# Dataset Card for NuminaMath-1.5-RL-Verifiable

## Dataset Description

- **Homepage:** https://huggingface.co/datasets/nlile/NuminaMath-1.5-RL-Verifiable
- **Repository:** [NuminaMath-1.5-RL-Verifiable](https://huggingface.co/datasets/nlile/NuminaMath-1.5-RL-Verifiable)
- **Based on:** [NuminaMath-1.5](https://huggingface.co/datasets/AI-MO/NuminaMath-1.5)

### Dataset Summary

NuminaMath-1.5-RL-Verifiable is a curated subset of the NuminaMath-1.5 dataset, specifically filtered to support reinforcement learning applications requiring verifiable outcomes. This collection consists of 131,063 math word problems from the original dataset that meet strict filtering criteria: all problems have definitive numerical answers, validated problem statements and solutions, and come from high-quality, non-synthetic sources.

The filtering process removes multiple-choice questions, proofs, problems without clear numerical answers, and all synthetic content, while preserving the rich diversity of mathematical domains from the original collection.

### Filtering Methodology

The dataset was created by applying the following filters to the original NuminaMath-1.5 dataset:

- **Removed question types**: Multiple-choice questions and proofs
- **Answer validation**: Retained only problems with non-empty, numerical answers (excluded 'proof', 'notfound' answers)
- **Source selection**: Excluded potentially lower-quality sources (cn_k12, orca_math, synthetic_math, metamath)
- **Quality filters**: Retained only problems with validated problem statements and solutions
- **Authenticity**: Excluded all synthetic problems

These filtering steps reduced the original dataset from 896,215 problems to 131,063 problems (approximately 14.6% of the original dataset), all with verifiable outcomes.

## Dataset Structure

### Data Instances

Each instance in the dataset contains:
- A math word problem statement
- A Chain of Thought (CoT) solution
- A definitive numerical answer
- Problem metadata including math domain type

### Data Fields

- `problem`: Text description of the mathematical problem
- `ref_solution`: Step-by-step Chain of Thought (CoT) solution
- `answer`: Definitive numerical result
- `problem_type`: Mathematical domain (Algebra, Geometry, Number Theory, etc.)
- `question_type`: Always "math-word-problem" in this filtered dataset
- `source`: Origin of the problem (olympiads, cn_contest, aops_forum, etc.)
- `problem_is_valid`: Always "Yes" in this filtered dataset
- `solution_is_valid`: Always "Yes" in this filtered dataset
- `synthetic`: Always false in this filtered dataset

### Dataset Statistics

#### Distribution by Source

| Source | Problem Count |
|--------|---------------|
| olympiads | 92,487 |
| cn_contest | 15,828 |
| aops_forum | 15,092 |
| amc_aime | 4,893 |
| inequalities | 1,145 |
| olympiads_ref | 1,001 |
| number_theory | 617 |
| **Total** | **131,063** |

#### Distribution by Problem Type

| Problem Type | Problem Count | Percentage |
|--------------|---------------|------------|
| Algebra | 42,972 | 32.79% |
| Geometry | 31,405 | 23.96% |
| Number Theory | 22,071 | 16.84% |
| Combinatorics | 17,144 | 13.08% |
| Logic and Puzzles | 7,250 | 5.53% |
| Calculus | 4,954 | 3.78% |
| Inequalities | 4,000 | 3.05% |
| Other | 1,267 | 0.97% |

#### Detailed Breakdown by Problem Type and Source

<details>
<summary>Click to expand detailed breakdown</summary>

**Algebra**
- olympiads: 31,752
- cn_contest: 6,776
- amc_aime: 1,886
- aops_forum: 1,684
- inequalities: 531
- olympiads_ref: 265
- number_theory: 78

**Geometry**
- olympiads: 22,091
- cn_contest: 4,377
- aops_forum: 3,316
- amc_aime: 1,454
- olympiads_ref: 99
- inequalities: 60
- number_theory: 8

**Number Theory**
- olympiads: 14,848
- aops_forum: 3,614
- cn_contest: 1,916
- amc_aime: 744
- number_theory: 489
- olympiads_ref: 329
- inequalities: 131

**Combinatorics**
- olympiads: 11,219
- aops_forum: 3,176
- cn_contest: 1,724
- amc_aime: 612
- olympiads_ref: 266
- inequalities: 125
- number_theory: 22

**Logic and Puzzles**
- olympiads: 5,677
- aops_forum: 1,197
- cn_contest: 212
- amc_aime: 136
- inequalities: 16
- number_theory: 7
- olympiads_ref: 5

**Calculus**
- olympiads: 3,894
- aops_forum: 907
- cn_contest: 139
- inequalities: 8
- amc_aime: 4
- olympiads_ref: 1
- number_theory: 1

**Inequalities**
- olympiads: 2,292
- aops_forum: 717
- cn_contest: 657
- inequalities: 273
- olympiads_ref: 34
- amc_aime: 25
- number_theory: 2

**Other**
- olympiads: 714
- aops_forum: 481
- amc_aime: 32
- cn_contest: 27
- number_theory: 10
- olympiads_ref: 2
- inequalities: 1

</details>

#### Original NuminaMath-1.5 Source Breakdown

| source | problems | question_type:proof | question_type:mcq | question_type:word |
|:---------------|-----------:|----------------------:|--------------------:|---------------------:|
| olympiads | 197084 | 62970 | 13529 | 117845 |
| olympiads_ref | 3638 | 2246 | nan | 1392 |
| amc_aime | 5872 | 208 | 4374 | 963 |
| aops_forum | 67841 | 24532 | 5924 | 33486 |
| cn_contest | 29944 | 8663 | 5602 | 15649 |
| inequalities | 7314 | 5780 | 49 | 1478 |
| number_theory | 4043 | 2591 | 15 | 1239 |
| cn_k12 | 268819 | 3966 | 115800 | 149010 |
| orca_math | 151934 | 1 | 17 | 151916 |
| synthetic_math | 148712 | 41 | 1057 | 147612 |
| metamath | 11014 | nan | 82 | 10932 |
| Total | 896215 | 110998 | 146449 | 631522 |

## Additional Information

### Licensing Information

The dataset follows the licensing of the original NuminaMath-1.5 dataset and is available under the [Apache License, Version 2.0](https://www.apache.org/licenses/LICENSE-2.0).

### Citation Information

```
@misc{nlile2025numinamath15rlverifiable,
author = {nlile},
title = {NuminaMath-1.5-RL-Verifiable},
year = {2025},
publisher = {Hugging Face},
journal = {Hugging Face Dataset Repository},
howpublished = {\url{https://huggingface.co/datasets/nlile/NuminaMath-1.5-RL-Verifiable}}
}

@misc{numina_math_datasets,
author = {Jia LI and Edward Beeching and Lewis Tunstall and Ben Lipkin and Roman Soletskyi and Shengyi Costa Huang and Kashif Rasul and Longhui Yu and Albert Jiang and Ziju Shen and Zihan Qin and Bin Dong and Li Zhou and Yann Fleureau and Guillaume Lample and Stanislas Polu},
title = {NuminaMath},
year = {2024},
publisher = {Numina},
journal = {Hugging Face repository},
howpublished = {\url{https://github.com/project-numina/aimo-progress-prize/blob/main/report/numina_dataset.pdf}}
}
```

---
许可证：Apache-2.0
任务类别：
- 文本生成
- 问答
语言：
- 英语
标签：
- 数学
- 后训练
- 强化学习（Reinforcement Learning，RL）
- 可验证
- 推理
美观名称：NuminaMath 1.5 RL 可验证版
数据集信息：
特征：
- 名称：problem
数据类型：字符串
- 名称：solution
数据类型：字符串
- 名称：answer
数据类型：字符串
- 名称：problem_type
数据类型：字符串
- 名称：question_type
数据类型：字符串
- 名称：problem_is_valid
数据类型：字符串
- 名称：solution_is_valid
数据类型：字符串
- 名称：source
数据类型：字符串
- 名称：synthetic
数据类型：布尔值
拆分：
- 名称：train
占用字节数：188626432
样本数：131063
下载大小：85718743
数据集总大小：188626432
配置：
- 配置名称：default
数据文件：
- 拆分：train
路径：data/train-*
---

# NuminaMath-1.5-RL-Verifiable 数据集卡片

## 数据集描述

- **"主页"**：https://huggingface.co/datasets/nlile/NuminaMath-1.5-RL-Verifiable
- **"代码仓库"**：[NuminaMath-1.5-RL-Verifiable](https://huggingface.co/datasets/nlile/NuminaMath-1.5-RL-Verifiable)
- **"基于数据集"**：[NuminaMath-1.5](https://huggingface.co/datasets/AI-MO/NuminaMath-1.5)

### 数据集概览
NuminaMath-1.5-RL-Verifiable 是 NuminaMath-1.5 数据集的精选子集，经筛选后专门支持需要可验证结果的强化学习应用。该集合包含原数据集中的131,063道数学应用题，均满足严格的筛选标准：所有题目均拥有明确的数值答案、经过验证的题干与解答，且均来自高质量的非合成数据源。

筛选过程移除了选择题、证明题、无明确数值答案的题目以及所有合成内容，同时保留了原数据集丰富的数学领域多样性。

### 筛选方法
本数据集通过对原始 NuminaMath-1.5 数据集应用以下筛选规则构建：
- **"移除的问题类型"**：选择题与证明题
- **"答案验证"**：仅保留拥有非空数值答案的题目（排除"proof""notfound"类答案）
- **"来源筛选"**：排除质量较低的数据源（cn_k12、orca_math、synthetic_math、metamath）
- **"质量过滤"**：仅保留经过验证的题干与解答
- **"真实性校验"**：排除所有合成生成的题目

经过上述筛选步骤，原始数据集的896,215道题目被缩减至131,063道（约占原数据集的14.6%），所有题目均拥有可验证的结果。

## 数据集结构
### 数据实例
数据集中的每个实例包含：
- 一道数学应用题题干
- 分步思维链（Chain of Thought，CoT）式解答
- 明确的数值答案
- 包含数学领域分类的元数据

### 数据字段
- `problem`：数学题目的文本描述
- `ref_solution`：分步思维链（Chain of Thought，CoT）式参考解答
- `answer`：明确的数值结果
- `problem_type`：数学领域分类（如代数、几何、数论等）
- `question_type`：在该筛选子集中固定为"math-word-problem"（数学应用题）
- `source`：题目的来源（如奥数竞赛、中国国内竞赛、AoPS论坛等）
- `problem_is_valid`：在该筛选子集中固定为"Yes"（有效）
- `solution_is_valid`：在该筛选子集中固定为"Yes"（有效）
- `synthetic`：在该筛选子集中固定为`false`（非合成）

### 数据集统计
#### 按来源分布
| 数据源 | 题目数量 |
|--------|---------------|
| 奥数竞赛（olympiads） | 92,487 |
| 中国国内竞赛（cn_contest） | 15,828 |
| AoPS论坛（aops_forum） | 15,092 |
| AMC/AIME竞赛 | 4,893 |
| 不等式题 | 1,145 |
| 官方奥数参考（olympiads_ref） | 1,001 |
| 数论题 | 617 |
| **总计** | **131,063** |

#### 按题型分布
| 题型 | 题目数量 | 占比 |
|--------------|---------------|------------|
| 代数 | 42,972 | 32.79% |
| 几何 | 31,405 | 23.96% |
| 数论 | 22,071 | 16.84% |
| 组合数学 | 17,144 | 13.08% |
| 逻辑与谜题 | 7,250 | 5.53% |
| 微积分 | 4,954 | 3.78% |
| 不等式 | 4,000 | 3.05% |
| 其他 | 1,267 | 0.97% |

#### 题型与来源的详细分布
<details>
<summary>点击展开详细分布</summary>

**代数**
- 奥数竞赛：31,752
- 中国国内竞赛：6,776
- AMC/AIME竞赛：1,886
- AoPS论坛：1,684
- 不等式题：531
- 官方奥数参考：265
- 数论题：78

**几何**
- 奥数竞赛：22,091
- 中国国内竞赛：4,377
- AoPS论坛：3,316
- AMC/AIME竞赛：1,454
- 官方奥数参考：99
- 不等式题：60
- 数论题：8

**数论**
- 奥数竞赛：14,848
- AoPS论坛：3,614
- 中国国内竞赛：1,916
- AMC/AIME竞赛：744
- 数论题：489
- 官方奥数参考：329
- 不等式题：131

**组合数学**
- 奥数竞赛：11,219
- AoPS论坛：3,176
- 中国国内竞赛：1,724
- AMC/AIME竞赛：612
- 官方奥数参考：266
- 不等式题：125
- 数论题：22

**逻辑与谜题**
- 奥数竞赛：5,677
- AoPS论坛：1,197
- 中国国内竞赛：212
- AMC/AIME竞赛：136
- 不等式题：16
- 数论题：7
- 官方奥数参考：5

**微积分**
- 奥数竞赛：3,894
- AoPS论坛：907
- 中国国内竞赛：139
- 不等式题：8
- AMC/AIME竞赛：4
- 官方奥数参考：1
- 数论题：1

**不等式**
- 奥数竞赛：2,292
- AoPS论坛：717
- 中国国内竞赛：657
- 不等式题：273
- 官方奥数参考：34
- AMC/AIME竞赛：25
- 数论题：2

**其他**
- 奥数竞赛：714
- AoPS论坛：481
- AMC/AIME竞赛：32
- 中国国内竞赛：27
- 数论题：10
- 官方奥数参考：2
- 不等式题：1

</details>

#### 原始NuminaMath-1.5数据集来源分布
| 数据源 | 题目总数 | 证明题数量 | 选择题数量 | 应用题数量 |
|:---------------|-----------:|----------------------:|--------------------:|---------------------:|
| 奥数竞赛 | 197084 | 62970 | 13529 | 117845 |
| 官方奥数参考 | 3638 | 2246 | 0 | 1392 |
| AMC/AIME竞赛 | 5872 | 208 | 4374 | 963 |
| AoPS论坛 | 67841 | 24532 | 5924 | 33486 |
| 中国国内竞赛 | 29944 | 8663 | 5602 | 15649 |
| 不等式题 | 7314 | 5780 | 49 | 1478 |
| 数论题 | 4043 | 2591 | 15 | 1239 |
| 中国K12教育材料 | 268819 | 3966 | 115800 | 149010 |
| Orca数学 | 151934 | 1 | 17 | 151916 |
| 合成数学题 | 148712 | 41 | 1057 | 147612 |
| Metamath | 11014 | 0 | 82 | 10932 |
| 总计 | 896215 | 110998 | 146449 | 631522 |

## 附加信息
### 许可信息
本数据集遵循原始 NuminaMath-1.5 数据集的许可协议，采用 Apache许可证2.0版（Apache-2.0）发布。

### 引用信息

@misc{nlile2025numinamath15rlverifiable,
author = {nlile},
title = {NuminaMath-1.5-RL-Verifiable},
year = {2025},
publisher = {Hugging Face},
journal = {Hugging Face 数据集仓库},
howpublished = {url{https://huggingface.co/datasets/nlile/NuminaMath-1.5-RL-Verifiable}}
}

@misc{numina_math_datasets,
author = {Jia LI and Edward Beeching and Lewis Tunstall and Ben Lipkin and Roman Soletskyi and Shengyi Costa Huang and Kashif Rasul and Longhui Yu and Albert Jiang and Ziju Shen and Zihan Qin and Bin Dong and Li Zhou and Yann Fleureau and Guillaume Lample and Stanislas Polu},
title = {NuminaMath},
year = {2024},
publisher = {Numina},
journal = {Hugging Face 仓库},
howpublished = {url{https://github.com/project-numina/aimo-progress-prize/blob/main/report/numina_dataset.pdf}}
}