Duplicate from openbmb/UltraData-Math

Co-authored-by: Yudong Wang <BigDong@users.noreply.huggingface.co>

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+*.pcm filter=lfs diff=lfs merge=lfs -text
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README.md

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+---
+language:
+- en
+- zh
+license: apache-2.0
+size_categories:
+- 100B<n<1T
+task_categories:
+- text-generation
+pretty_name: UltraData-Math
+arxiv: xxxx.xxxxx
+tags:
+- llm
+- pretraining
+- math
+- data-synthesis
+- data-filtering
+- high-quality
+- mathematical-reasoning
+configs:
+- config_name: UltraData-Math-L3-Conversation-Synthetic
+  data_files: "data/UltraData-Math-L3/Conversation-Synthetic/*.parquet"
+- config_name: UltraData-Math-L3-Multi-Style-Synthetic
+  data_files: "data/UltraData-Math-L3/Multi-Style-Synthetic/*.parquet"
+- config_name: UltraData-Math-L3-QA-Synthetic
+  data_files: "data/UltraData-Math-L3/QA-Synthetic/*.parquet"
+- config_name: UltraData-Math-L3-Textbook-Exercise-Synthetic
+  data_files: "data/UltraData-Math-L3/Textbook-Exercise-Synthetic/*.parquet"
+- config_name: UltraData-Math-L2-preview
+  data_files: "data/UltraData-Math-L2-preview/**/*.parquet"
+- config_name: UltraData-Math-L1
+  data_files: "data/UltraData-Math-L1/**/*.parquet"
+default_config_name: UltraData-Math-L3-Conversation-Synthetic
+---
+
+# UltraData-Math
+
+<div align="center">
+  <img src="assets/ultradata-math-logo.png" width="600"/>
+</div>
+
+<p align="center">
+<a href="https://huggingface.co/datasets/openbmb/UltraData-Math">🤗 Dataset</a> | <a href="https://github.com/UltraData-OpenBMB/UltraData-Math">💻 Source Code</a> | <a href="https://huggingface.co/datasets/openbmb/UltraData-Math/blob/main/README_ZH.md">🇨🇳 中文 README</a>
+</p>
+
+***UltraData-Math*** is a large-scale, high-quality mathematical pre-training dataset totaling **290B+ tokens** across three progressive tiers—**L1** (170.5B tokens web corpus), **L2** (33.7B tokens quality-selected), and **L3** (88B tokens multi-format refined)—designed to systematically enhance mathematical reasoning in LLMs. It has been applied to the mathematical pre-training of the [MiniCPM Series](https://huggingface.co/collections/openbmb/minicpm4) models.
+
+## 🆕 What's New
+
+- **[2026.02.09]**: **UltraData-Math**, a large-scale high-quality mathematical pre-training dataset with 290B+ tokens across three progressive tiers (L1/L2-preview/L3), is now available on Hugging Face. Released as part of the [UltraData](https://ultradata.openbmb.cn/) ecosystem. 🔥🔥🔥
+- **[2026.02.10]**: **UltraData-Math** tops the Hugging Face Datasets Trending list, reaching the #1 spot! ⭐️⭐️⭐️
+
+## 📚 Introduction
+
+High-quality pre-training data is crucial for enhancing the mathematical reasoning capabilities of large language models (LLMs). However, existing mathematical pre-training data construction schemes have the following shortcomings:
+
+- **HTML Parsing**: General parsers (such as trafilatura, readability) are mainly designed for news/article parsing, lacking specialized processing for mathematical formulas and other content, often leading to formula structure destruction or loss; meanwhile, mathematical discussions on forum-like pages are difficult to extract completely.
+- **Data Quality**: Existing datasets generally lack a systematic quality grading mechanism, with high-value mathematical content mixed with low-quality noise.
+- **Data Diversity**: Mainstream datasets mostly originate from textbooks or competition question banks, lacking mathematical discussions and application scenarios in real web pages; synthetic data formats are single, difficult to cover diverse needs such as multi-turn dialogues and multi-style expressions.
+
+To address these issues, we propose ***UltraData-Math***—a large-scale high-quality pre-training dataset for mathematical reasoning tasks. This dataset is developed based on the [UltraData](https://ultradata.openbmb.cn/blog/position-paper) L0-L4 Tiered Data Management Framework, containing four progressive levels:
+
+- **L0 Raw Data**: Develops a mathematical parser based on *magic-html*, combined with *w3m* layout preservation rendering and multi-level fallback strategies, standardizing MathML, KaTeX, and AsciiMath into LaTeX format.
+- **L1 Filtered Data**: Cleans noise through heuristic rules and performs document-level deduplication.
+- **L2 Selected Data**: Uses proprietary large models to annotate seed data and distills it into a lightweight embedding classifier to achieve efficient quality grading of the full corpus.
+- **L3 Refined Data**: Produces structured content with clear reasoning through rewriting, synthetic generation, and refinement in various formats such as Q&A, multi-turn dialogues, multi-style rewriting, and knowledge-grounded textbooks.
+
+Experiments show that on the MiniCPM-1.2B architecture, ***UltraData-Math*** achieves a score of **37.02pp** on the MATH500 benchmark, an improvement of **+3.62pp** compared to Nemotron-CC 4plus; it achieves **61.79pp** on GSM8K, an improvement of **+3.34pp**, while maintaining code generation and general knowledge capabilities.
+
+***UltraData-Math*** has been applied to the mathematical pre-training of the [MiniCPM Series](https://huggingface.co/collections/openbmb/minicpm-4-6841ab29d180257e940baa9b) models.
+
+- **[UltraData-Math-L1](https://huggingface.co/datasets/openbmb/UltraData-Math)**: Large-scale high-quality mathematical pre-training dataset, containing 170.5B tokens of web mathematical corpus. 
+- **[UltraData-Math-L2](https://huggingface.co/datasets/openbmb/UltraData-Math-L2)**: High-quality mathematical pre-training dataset selected by the quality model, containing 33.7B tokens of high-quality web mathematical corpus.
+- **[UltraData-Math-L3](https://huggingface.co/datasets/openbmb/UltraData-Math-L3)**: High-quality refined mathematical dataset, containing 88B tokens of multi-format refined data (Q&A, multi-turn dialogues, knowledge textbooks, etc.).
+
+## 🏗️ Data Processing Pipeline
+
+To break through the limitations of existing mathematical datasets in quality and diversity, we established a refined grading standard centered on "mathematical content integrity" and "information density". ***UltraData-Math*** adopts the **L0-L4 Tiered Data Management Framework** proposed by the [UltraData](https://ultradata.openbmb.cn/blog/position-paper) paper. Through standardized level definitions, it achieves orderly management and efficient flow of mathematical data assets. Each level represents higher data purity and mathematical value, while also corresponding to a more refined degree of processing.
+
+<div align="center">
+  <img src="assets/ultradata-math-pipeline.png" width="900"/>
+</div>
+
+### L0: Raw Data Parsing and Standardization
+
+**Goal**: Address the poor support of general HTML parsers for mathematical formulas and maximize the preservation of mathematical semantics in web pages.
+
+The L0 phase mainly processes raw web data obtained from sources such as Common Crawl. Given the specificity of mathematical web pages, we develop specialized parsing strategies through the [UltraData-Math-Parser](https://huggingface.co/spaces/openbmb/UltraData-Math-L0-Parser) instead of directly using general parsers like trafilatura or readability.
+
+- **Unified Parsing Mode**: Automatically identifies page types to ensure complete content extraction as much as possible.
+- **Multi-level Fallback Strategy**: To prevent data loss due to parsing failures, we implement a multi-level fallback mechanism to ensure text content is captured even if structured parsing fails.
+- **Mathematical Formula Standardization**: We unify different mathematical expressions in web pages into standard LaTeX format, achieving data format normalization for unified model learning.
+
+### L1: Heuristic Cleaning and Filtering
+
+**Goal**: Remove format noise and improve data readability and standardization.
+
+After obtaining text containing complete mathematical formulas, we clean the L0 data through a series of heuristic rules:
+
+- **Format Repair**:
+  - Clean invisible characters, garbled text, and unnatural continuous line breaks.
+  - Remove irrelevant web noise such as navigation bars, footers, ad pop-ups, and "read more".
+- **Content Filtering**:
+  - *Length Filtering*: Remove overly short text fragments, which usually lack context and are difficult to support effective mathematical reasoning training.
+  - *Language Identification*: Ensure the dataset is composed mainly of high-quality English and Chinese mathematical content.
+  - *Document Deduplication*: Perform deduplication at the document level to prevent duplicate content from biasing model training.
+
+### L2: Selection Based on Quality Models
+
+**Goal**: Identify core corpora with high value from massive data.
+
+Although L1 data has a clean format, the content quality varies. The L2 phase introduces a model-based quality assessment system:
+
+- **Seed Data Annotation**: Use proprietary large models to score a portion of seed data across multiple dimensions.
+- **Classifier Training and Distillation**: Train lightweight embedding classifiers based on annotated data to equip them with the ability to identify high-value mathematical content.
+- **Full-scale Inference**: Use the trained classifier to score and screen L1 data in full.
+  - *Retention*: Content containing detailed problem-solving steps, mathematical concept explanations, and high-level academic discussions.
+  - *Exclusion*: Simple stacking of nouns, meaningless lists of numbers, juvenile content, or noise from non-mathematical fields.
+
+### L3: Refined Data
+
+**Goal**: Produce structured content with clear reasoning and explicit educational intent through rewriting, synthetic generation, and refinement, achieving textbook-quality standards and ensuring maximum learnability.
+
+Natural web data is mostly declarative text, lacking structured reasoning steps and diverse pedagogical formats. To enhance the model's chain-of-thought (CoT) capabilities and multi-turn interaction skills, we build the L3 refined data layer through the [UltraData-Math-Generator](https://huggingface.co/spaces/openbmb/UltraData-Math-L3-Generator):
+
+- **Q&A Pair Generation**: Use high-performance models to rewrite declarative documents into "Question-Answer" pairs, constructing QA-style data with explicit reasoning steps.
+- **Multi-turn Dialogue Synthesis**: Simulate "Teacher-Student" tutoring scenarios to generate multi-turn dialogue data containing follow-up questions, corrections, and guidance.
+- **Multi-style Rewriting**: Rewrite single-source data into multiple styles (such as rigorous textbook style, competition problem-solving style, intuitive popular science style) to improve model generalization.
+- **Knowledge Point Textbook Generation**: Generate systematic textbook-like content based on specific knowledge points to ensure the model masters core mathematical concepts.
+- **Format Repair and Enhancement**: Fix formatting issues in the source data (e.g., broken LaTeX formulas, inconsistent notation) and enhance content coherence to achieve textbook-quality standards.
+
+Based on the above methodology, we produce the following ***UltraData-Math*** datasets:
+
+| Dataset | # Tokens | # Documents |
+|:---|:---:|:---:|
+| UltraData-Math-L1 | 170.5B | 85.6M |
+| UltraData-Math-L2-preview | 33.7B | 14.98M |
+| UltraData-Math-L3 | 88B | 81.4M |
+
+## 🚀 Quick Start
+
+You can load the dataset directly from Hugging Face:
+
+```python
+from datasets import load_dataset
+
+# Load UltraData-Math-L1
+ds = load_dataset("openbmb/UltraData-Math", "UltraData-Math-L1")
+
+# Load UltraData-Math-L2-preview
+ds = load_dataset("openbmb/UltraData-Math", "UltraData-Math-L2-preview")
+
+# Load UltraData-Math-L3 (default: Conversation-Synthetic)
+ds = load_dataset("openbmb/UltraData-Math", "UltraData-Math-L3-Conversation-Synthetic")
+
+# Other L3 configs:
+# - UltraData-Math-L3-Multi-Style-Synthetic
+# - UltraData-Math-L3-QA-Synthetic
+# - UltraData-Math-L3-Textbook-Exercise-Synthetic
+```
+
+## 📈 Experimental Results
+
+We evaluated data quality using the **Decay Verification** method: continuing pre-training of a **MiniCPM-1.2B** base model (pre-trained on 1.3T tokens with **MiniCPM3-4B** tokenizer) with **~100B tokens** (30% target data + 70% general data). We used [OpenCompass](https://github.com/open-compass/opencompass) as our evaluation framework. Evaluation benchmarks include:
+
+- **General English:** MMLU, ARC-E, ARC-C, BigBench Hard (BBH), CommonSenseQA, HellaSwag, OpenbookQA, PIQA, SIQA, Winogrande
+- **General Chinese:** C-Eval, CMMLU
+- **Math Reasoning:** MATH500, GSM8K, Math-Bench, R-Bench-Math
+- **Code Reasoning:** MBPP, HumanEval
+
+### Effectiveness of L0 Parsing Strategy
+
+To fairly compare different parsing strategies, we conducted experiments on a data subset sampled from the **2023-2024** distribution. We re-parsed the raw HTML from this source using different parsers. This comparison demonstrates the **effectiveness of our L0 Parser** against other parsers.
+
+<div align="center">
+  <img src="assets/ultradata-math-l0-parser-comparison.png" width="700"/>
+</div>
+
+
+### Pipeline Effectiveness (L1 vs L2 vs L3)
+
+To validate the effectiveness of our L0-L3 tiered framework, we conducted ablation studies comparing models trained on different tiers of UltraData-Math. Unlike the L0 parser comparison above (which used a 2023-2024 subset), these results are based on the **full dataset**. Results demonstrate that higher-tier data (L3) significantly boosts mathematical reasoning (MATH500, GSM8K) and general capabilities.
+
+<div align="center">
+  <img src="assets/ultradata-math-l1l2l3-comparison.png" width="700"/>
+</div>
+
+### Full Evaluation Results
+
+To compare against existing public mathematical pre-training datasets, we trained models independently on each dataset using the same model architecture and training budget (~100B tokens). The baselines include [Nemotron-CC-Math](https://huggingface.co/datasets/nvidia/Nemotron-CC-Math-v1), [MegaMath-Web-Pro](https://huggingface.co/datasets/LLM360/MegaMath), and [FineMath](https://huggingface.co/datasets/HuggingFaceTB/finemath). All models are evaluated under identical conditions for a fair comparison:
+
+<div align="center">
+  <img src="assets/ultradata-math-full-comparison.png" width="700"/>
+</div>
+
+## ❤️ Acknowledgements
+
+- **L0 Parsing Layer**: [magic-html](https://github.com/opendatalab/magic-html), [w3m](http://w3m.sourceforge.net/), [trafilatura](https://github.com/adbar/trafilatura)
+- **L3 Synthesis Layer**: [Qwen2.5-72B-Instruct](https://huggingface.co/Qwen/Qwen2.5-72B-Instruct), [Qwen3-32B](https://huggingface.co/Qwen/Qwen3-32B), [GLM-4.5](https://huggingface.co/zai-org/GLM-4.5)
+- **Seed Data**: [Nemotron-CC-Math](https://huggingface.co/datasets/nvidia/Nemotron-CC-Math-v1), [MegaMath](https://huggingface.co/datasets/LLM360/MegaMath), [FineMath](https://huggingface.co/datasets/HuggingFaceTB/finemath)
+
+## 📖 Citation
+
+If you find **UltraData-Math** useful in your research, please consider citing:
+
+```bibtex
+@misc{ultradata-math,
+  title={UltraData-Math},
+  author={UltraData Team},
+  year={2026},
+  url={https://huggingface.co/datasets/openbmb/UltraData-Math},
+  publisher={Hugging Face}
+}
+```
+
+## 📜 License
+
+This project is licensed under the [Apache 2.0](./LICENSE) license.

README_ZH.md

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+# UltraData-Math
+
+<div align="center">
+  <img src="assets/ultradata-math-logo.png" width="600"/>
+</div>
+
+<p align="center">
+<a href="https://huggingface.co/datasets/openbmb/UltraData-Math">🤗 数据集</a> | <a href="https://github.com/UltraData-OpenBMB/UltraData-Math">💻 源代码</a> | <a href="README.md">🇺🇸 English README</a>
+</p>
+
+***UltraData-Math*** 是一个面向数学推理的大规模高质量预训练数据集，总计 **290B+ tokens**，涵盖三个递进层级——**L1**（170.5B tokens 网页语料）、**L2**（33.7B tokens 质量精选）、**L3**（88B tokens 多格式精炼），旨在系统性提升大语言模型的数学推理能力。已应用于 [MiniCPM 系列](https://huggingface.co/collections/openbmb/minicpm-4-6841ab29d180257e940baa9b) 模型的数学预训练。
+
+## 📚 简介
+
+高质量预训练数据对提升大语言模型的数学推理能力至关重要。然而，现有数学预训练数据构建方案存在以下不足：
+
+- **HTML 解析层面**：通用提取器（如 trafilatura、readability）主要面向新闻/文章场景设计，对数学公式等内容缺乏专门处理，常导致公式结构破坏或丢失；同时论坛类页面的数学讨论部分，难以完整提取。
+- **数据质量层面**：现有数据集普遍缺乏系统的质量分级机制，高价值数学内容与低质噪声混杂。
+- **数据多样性层面**：主流数据集多源自教科书或竞赛题库，缺少真实网页中的数学讨论与应用场景；合成数据格式单一，难以覆盖多轮对话、多风格表达等多样化需求。
+
+针对上述问题，我们提出 ***UltraData-Math***——一个面向数学推理任务的大规模高质量预训练数据集。本数据集基于 [UltraData](https://ultradata.openbmb.cn/blog/position-paper) 的 L0-L4 分级数据管理框架开发，包含四个递进层级：
+
+- **L0 原始数据层**：基于 *magic-html* 开发数学解析器，结合 *w3m* 布局保持渲染与多级回退策略，将 MathML、KaTeX、AsciiMath 标准化为 LaTeX 格式。
+- **L1 过滤数据层**：通过启发式规则清洗噪声并进行文档级去重。
+- **L2 精选数据层**：使用闭源大模型标注种子数据并蒸馏至轻量 embedding 分类器，实现全量语料的高效质量分级。
+- **L3 精炼数据层**：通过改写、合成生成与精炼，生成具有清晰推理链条的结构化内容，涵盖 Q&A、多轮对话、多风格改写、知识教材等多种格式。
+
+实验表明，在 MiniCPM-1.2B 架构上，***UltraData-Math*** 在 MATH500 基准上达到 **37.02pp**，相较 Nemotron-CC 4plus 提升 **+3.62pp**；在 GSM8K 上达到 **61.79pp**，提升 **+3.34pp**，同时保持代码生成与通用知识能力。
+
+***UltraData-Math*** 已应用于 [MiniCPM 系列](https://huggingface.co/collections/openbmb/minicpm-4-6841ab29d180257e940baa9b) 模型的数学预训练。
+
+- **[UltraData-Math-L1](https://huggingface.co/datasets/openbmb/UltraData-Math)**: 大规模高质量数学预训练数据集，包含 170.5B tokens 的网页数学语料。
+- **[UltraData-Math-L2](https://huggingface.co/datasets/openbmb/UltraData-Math-L2)**: 经质量模型精选的高质量数学预训练数据集，包含 33.7B tokens 的高质量网页数学语料。
+- **[UltraData-Math-L3](https://huggingface.co/datasets/openbmb/UltraData-Math-L3)**: 高质量精炼数学数据集，包含 88B tokens 的多格式精炼数据（Q&A、多轮对话、知识教材等）。
+
+## 🏗️ 数据处理流水线
+
+为突破现有数学数据集在质量与多样性上的局限，我们建立了一套以"数学内容完整性"和"信息密度"为核心的精细化分级标准。***UltraData-Math*** 采用了 [UltraData](https://ultradata.openbmb.cn/blog/position-paper) 论文提出的 **L0-L4 分级数据管理框架**，通过标准化的层级定义，实现数学数据资产的有序管理与高效流转。每一级都代表了更高的数据纯度与数学价值，同时也对应着更精细的加工程度。
+
+<div align="center">
+  <img src="assets/ultradata-math-pipeline.png" width="900"/>
+</div>
+
+### L0：原始数据解析与标准化
+
+**目标**：解决通用 HTML 解析器对数学公式支持不佳的问题，最大限度保留网页中的数学语义。
+
+L0 阶段主要处理从 Common Crawl 等来源获取的原始网页数据。针对数学网页的特殊性，我们通过 [UltraData-Math-Parser](https://huggingface.co/spaces/openbmb/UltraData-Math-L0-Parser) 开发了专用的解析策略，而非直接使用通用的 trafilatura 或 readability。
+
+- **统一解析模式**：自动识别页面类型，尽可能保证完整内容提取。
+- **多级回退策略**：为了防止解析失败导致数据丢失，我们实施了多级回退机制，确保在结构化解析失败时仍能捕获文本内容。
+- **数学公式标准化**：我们将网页中不同的数学表达统一转换为标准的 LaTeX 格式，实现了数据格式的归一化，便于模型统一学习。
+
+### L1：启发式清洗与过滤
+
+**目标**：去除格式噪声，提升数据的可读性和规范性。
+
+在获取了包含完整数学公式的文本后，我们通过一系列启发式规则对 L0 数据进行清洗：
+
+- **格式修复**：
+  - 清理不可见字符、乱码及非自然的连续换行。
+  - 移除导航栏、页脚、广告弹窗及"阅读更多"等无关网页噪音。
+- **内容过滤**：
+  - *长度过滤*：移除过短的文本片段，这些片段通常缺乏上下文，难以支持有效的数学推理训练。
+  - *语言识别*：确保数据集主要由高质量的英文及中文数学内容组成。
+  - *文档去重*：在文档级别进行去重，防止重复内容对模型训练造成偏差。
+
+### L2：基于质量模型的精选
+
+**目标**：从海量数据中识别出具有高价值的核心语料。
+
+L1 数据虽然格式整洁，但内容质量参差不齐。L2 阶段引入了基于模型的质量评估体系：
+
+- **种子数据标注**：使用闭源大模型对一部分种子数据进行多维度打分。
+- **分类器训练与蒸馏**：基于标注数据训练轻量级的 embedding 分类器，使其具备识别高价值数学内容的能力。
+- **全量推理**：使用训练好的分类器对 L1 数据进行全量打分与筛选。
+  - *保留*：包含详细解题步骤、数学概念解释、高水平学术讨论的内容。
+  - *剔除*：简单的名词堆砌、无意义的数字列表、低幼或非数学领域的噪声。
+
+### L3：精炼数据
+
+**目标**：通过改写、合成生成与精炼，生成具有清晰推理链条和显式教学意图的结构化内容，达到教科书级质量标准，确保最大化可学习性。
+
+自然网页数据多为陈述性文本，缺乏结构化的推理步骤和多样化的教学格式。为了增强模型的推理链条（CoT）能力和多轮交互能力，我们通过 [UltraData-Math-Generator](https://huggingface.co/spaces/openbmb/UltraData-Math-L3-Generator) 构建了 L3 精炼数据层：
+
+- **Q&A 对生成**：利用高性能模型将陈述性文档改写为"问题-回答"对，构建包含显式推理步骤的 QA 风格数据。
+- **多轮对话合成**：模拟"老师-学生"的辅导场景，生成包含追问、纠错、引导的多轮对话数据。
+- **多风格改写**：将单一来源的数据改写为多种风格（如教科书严谨风格、竞赛解题风格、科普直观风格），提升模型的泛化能力。
+- **知识点教材生成**：基于特定知识点生成系统化的教材类内容，确保模型掌握核心数学概念。
+- **格式修复与增强**：修复源数据中的格式问题（如损坏的 LaTeX 公式、不一致的符号标记），并增强内容连贯性，以达到教科书级质量标准。
+
+基于上述方法，我们最终产出了以下 ***UltraData-Math*** 数据集：
+
+| 数据集 | # Tokens | # Documents |
+|:---|:---:|:---:|
+| UltraData-Math-L1 | 170.5B | 85.6M |
+| UltraData-Math-L2-preview | 33.7B | 14.98M |
+| UltraData-Math-L3 | 88B | 81.4M |
+
+## 🚀 快速开始
+
+你可以直接从 Hugging Face 加载数据集：
+
+```python
+from datasets import load_dataset
+
+# 加载 UltraData-Math-L1
+ds = load_dataset("openbmb/UltraData-Math", "UltraData-Math-L1")
+
+# 加载 UltraData-Math-L2-preview
+ds = load_dataset("openbmb/UltraData-Math", "UltraData-Math-L2-preview")
+
+# 加载 UltraData-Math-L3（默认：Conversation-Synthetic）
+ds = load_dataset("openbmb/UltraData-Math", "UltraData-Math-L3-Conversation-Synthetic")
+
+# 其他 L3 配置：
+# - UltraData-Math-L3-Multi-Style-Synthetic
+# - UltraData-Math-L3-QA-Synthetic
+# - UltraData-Math-L3-Textbook-Exercise-Synthetic
+```
+
+## 📈 实验结果
+
+我们使用 **衰减验证（Decay Verification）** 方法评估数据质量：在 **MiniCPM-1.2B** 基座模型（使用 **MiniCPM3-4B** 分词器，预训练 1.3T tokens）上继续训练 **~100B tokens**（30% 目标数据 + 70% 通用数据）。我们使用 [OpenCompass](https://github.com/open-compass/opencompass) 作为评估框架。评估基准包括：
+
+- **通用英文：** MMLU、ARC-E、ARC-C、BigBench Hard (BBH)、CommonSenseQA、HellaSwag、OpenbookQA、PIQA、SIQA、Winogrande
+- **通用中文：** C-Eval、CMMLU
+- **数学推理：** MATH500、GSM8K、Math-Bench、R-Bench-Math
+- **代码推理：** MBPP、HumanEval
+
+### L0 解析策略有效性
+
+为公平对比不同解析策略，我们在 **2023-2024** 年分布的数据子集上进行实验。我们使用不同解析器重新解析原始 HTML。该对比展示了我们 **L0 解析器的有效性**。
+
+<div align="center">
+  <img src="assets/ultradata-math-l0-parser-comparison.png" width="700"/>
+</div>
+
+
+### 流水线有效性（L1 vs L2 vs L3）
+
+为验证 L0-L3 分级框架的有效性，我们对使用不同层级 UltraData-Math 训练的模型进行了消融实验。与上文 L0 解析器对比（使用 2023-2024 子集）不同，以下结果基于**全量数据集**。结果表明，更高层级的数据（L3）显著提升了数学推理能力（MATH500、GSM8K）及通用能力。
+
+<div align="center">
+  <img src="assets/ultradata-math-l1l2l3-comparison.png" width="700"/>
+</div>
+
+### 完整评测结果
+
+为与现有公开数学预训练数据集进行对比，我们使用相同的模型架构和训练预算（~100B tokens）在每个数据集上独立训练模型。基线包括 [Nemotron-CC-Math](https://huggingface.co/datasets/nvidia/Nemotron-CC-Math-v1)、[MegaMath-Web-Pro](https://huggingface.co/datasets/LLM360/MegaMath) 和 [FineMath](https://huggingface.co/datasets/HuggingFaceTB/finemath)。所有模型在相同条件下评估以确保公平对比：
+
+<div align="center">
+  <img src="assets/ultradata-math-full-comparison.png" width="700"/>
+</div>
+
+## ❤️ 致谢
+
+- **L0 解析层**：[magic-html](https://github.com/opendatalab/magic-html)、[w3m](http://w3m.sourceforge.net/)、[trafilatura](https://github.com/adbar/trafilatura)
+- **L3 精炼层**：[Qwen2.5-72B-Instruct](https://huggingface.co/Qwen/Qwen2.5-72B-Instruct)、[Qwen3-32B](https://huggingface.co/Qwen/Qwen3-32B)、[GLM-4.5](https://huggingface.co/zai-org/GLM-4.5)
+- **种子数据**：[Nemotron-CC-Math](https://huggingface.co/datasets/nvidia/Nemotron-CC-Math-v1)、[MegaMath](https://huggingface.co/datasets/LLM360/MegaMath)、[FineMath](https://huggingface.co/datasets/HuggingFaceTB/finemath)
+
+## 📖 引用
+
+如果您觉得 **UltraData-Math** 对您的研究有帮助，请考虑引用：
+
+```bibtex
+@misc{ultradata-math,
+  title={UltraData-Math},
+  author={UltraData Team},
+  year={2026},
+  url={https://huggingface.co/datasets/openbmb/UltraData-Math},
+  publisher={Hugging Face}
+}
+```
+
+## 📜 许可证
+
+本项目基于 [Apache 2.0](./LICENSE) 许可证发布。

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