OpenThoughts-114k-math-open-r1

This is a filtered and metadata enriched version of [`open-thoughts/OpenThoughts-114k`](https://huggingface.co/datasets/open-thoughts/OpenThoughts-114k).

While the original dataset is a valuable resource containing [DeepSeek-R1](https://huggingface.co/deepseek-ai/DeepSeek-R1) outputs, it has very little metadata (only 2 fields: `system` and `conversations`). It does not contain, for instance, the original solution label, which means that we can not verify the model answers.

## What we did
- filtered the dataset for math content (math questions were prefixed by "Return your final response within \\boxed{}." -- see [here](https://github.com/open-thoughts/open-thoughts/blob/main/open_thoughts/math/reason.py#L16C43-L16C90))
- found the original questions in the [`AI-MO/NuminaMath-CoT`](https://huggingface.co/datasets/AI-MO/NuminaMath-CoT) and mapped them back to each generation
- verified model generations using our [Math-Verify library](https://github.com/huggingface/Math-Verify)
- added a metadata field with the token count of each DeepSeek-R1 completion

## Data structure
- `source`: original `source` from Numina-Math
- `problem`: problem statement, from Numina-Math
- `solution`: original solution/gold label, from Numina-Math
- `messages`: message turns for finetuning on the correct solutions, from Numina-Math
- `system`: system prompt sent to DeepSeek-R1, from OpenThoughts
- `conversations`: message turns from the DeepSeek-R1 generation. The last turn is the model output, from OpenThoughts
- `generated_token_count`: number of tokens (counted using the DeepSeek-R1 tokenizer) of the model output.
- `correct`: label indicating if the DeepSeek-R1 generated solution matches the ground truth `solution`. Checked with [Math-Verify library](https://github.com/huggingface/Math-Verify)

## Some statistics
- The original OpenThoughts-114k dataset has **89120/113957 (78%)** math rows
- Of those, **56730/89120 (63%)** have correct answers, as checked by Math-Verify
- There is a single generation per question
- Token count distribution: mean=6366.67, std_dev=4662.88 tokens


本数据集是对 [`open-thoughts/OpenThoughts-114k`](https://huggingface.co/datasets/open-thoughts/OpenThoughts-114k) 进行过滤与元数据增强后的版本。

原始数据集作为包含[DeepSeek-R1](https://huggingface.co/deepseek-ai/DeepSeek-R1)输出的优质资源，仅自带极少量元数据（仅含`system`与`conversations`两个字段），例如缺少原始解答标签，导致无法验证模型生成答案的正确性。

### 我们所开展的工作
- 针对数学类内容完成数据集过滤：数学题目均以“Return your final response within oxed{}.”作为前缀（详见[此处](https://github.com/open-thoughts/open-thoughts/blob/main/open_thoughts/math/reason.py#L16C43-L16C90)）
- 从 [`AI-MO/NuminaMath-CoT`](https://huggingface.co/datasets/AI-MO/NuminaMath-CoT) 数据集内获取原始问题，并将其与每条模型生成结果进行映射关联
- 借助我们开发的[Math-Verify工具库](https://github.com/huggingface/Math-Verify)对模型生成内容进行正确性校验
- 新增元数据字段，用于统计并记录每条DeepSeek-R1生成结果的Token数量

### 数据结构
- `source`：源自Numina-Math的原始来源字段
- `problem`：源自Numina-Math的问题题干
- `solution`：源自Numina-Math的原始标准解答（金标签）
- `messages`：用于针对正确解答进行微调的对话轮次数据，源自Numina-Math
- `system`：发送给DeepSeek-R1的系统提示词，源自OpenThoughts数据集
- `conversations`：DeepSeek-R1生成的对话轮次数据，最后一轮为模型输出结果，源自OpenThoughts数据集
- `generated_token_count`：模型输出结果的Token数量（采用DeepSeek-R1对应的Tokenizer进行统计）
- `correct`：用于标识DeepSeek-R1生成的解答是否与基准`solution`一致的标签，通过[Math-Verify工具库](https://github.com/huggingface/Math-Verify)完成校验

### 统计信息
- 原始OpenThoughts-114k数据集中共有**89120/113957（78%）**条数学相关条目
- 其中**56730/89120（63%）**的条目经Math-Verify校验后拥有正确答案
- 每个问题仅对应一条模型生成结果
- Token数量分布：均值为6366.67，标准差为4662.88个Token