Duplicate from HuggingFaceTB/finemath

Co-authored-by: Anton Lozhkov <anton-l@users.noreply.huggingface.co>

.gitattributes

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+*tfevents* filter=lfs diff=lfs merge=lfs -text
+# Audio files - uncompressed
+*.pcm filter=lfs diff=lfs merge=lfs -text
+*.sam filter=lfs diff=lfs merge=lfs -text
+*.raw filter=lfs diff=lfs merge=lfs -text
+# Audio files - compressed
+*.aac filter=lfs diff=lfs merge=lfs -text
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+*.mp3 filter=lfs diff=lfs merge=lfs -text
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+*.wav filter=lfs diff=lfs merge=lfs -text
+# Image files - uncompressed
+*.bmp filter=lfs diff=lfs merge=lfs -text
+*.gif filter=lfs diff=lfs merge=lfs -text
+*.png filter=lfs diff=lfs merge=lfs -text
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+*.jpg filter=lfs diff=lfs merge=lfs -text
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+*.webp filter=lfs diff=lfs merge=lfs -text
+# Video files - compressed
+*.mp4 filter=lfs diff=lfs merge=lfs -text
+*.webm filter=lfs diff=lfs merge=lfs -text

README.md

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+---
+license: odc-by
+dataset_info:
+- config_name: finemath-3plus
+  features:
+  - name: url
+    dtype: string
+  - name: fetch_time
+    dtype: int64
+  - name: content_mime_type
+    dtype: string
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+    dtype: string
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+    dtype: int32
+  - name: warc_record_length
+    dtype: int32
+  - name: text
+    dtype: string
+  - name: token_count
+    dtype: int32
+  - name: char_count
+    dtype: int32
+  - name: metadata
+    dtype: string
+  - name: score
+    dtype: float64
+  - name: int_score
+    dtype: int64
+  - name: crawl
+    dtype: string
+  - name: snapshot_type
+    dtype: string
+  - name: language
+    dtype: string
+  - name: language_score
+    dtype: float64
+  splits:
+  - name: train
+    num_bytes: 137764105388.93857
+    num_examples: 21405610
+  download_size: 65039196945
+  dataset_size: 137764105388.93857
+- config_name: finemath-4plus
+  features:
+  - name: url
+    dtype: string
+  - name: fetch_time
+    dtype: int64
+  - name: content_mime_type
+    dtype: string
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+    dtype: float64
+  - name: int_score
+    dtype: int64
+  - name: crawl
+    dtype: string
+  - name: snapshot_type
+    dtype: string
+  - name: language
+    dtype: string
+  - name: language_score
+    dtype: float64
+  splits:
+  - name: train
+    num_bytes: 39101488149.09091
+    num_examples: 6699493
+  download_size: 18365184633
+  dataset_size: 39101488149.09091
+- config_name: infiwebmath-3plus
+  features:
+  - name: url
+    dtype: string
+  - name: metadata
+    dtype: string
+  - name: score
+    dtype: float64
+  - name: int_score
+    dtype: int64
+  - name: token_count
+    dtype: int64
+  - name: char_count
+    dtype: int64
+  - name: text
+    dtype: string
+  splits:
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+    num_bytes: 96485696853.10182
+    num_examples: 13882669
+  download_size: 46808660851
+  dataset_size: 96485696853.10182
+- config_name: infiwebmath-4plus
+  features:
+  - name: url
+    dtype: string
+  - name: metadata
+    dtype: string
+  - name: score
+    dtype: float64
+  - name: int_score
+    dtype: int64
+  - name: token_count
+    dtype: int64
+  - name: char_count
+    dtype: int64
+  - name: text
+    dtype: string
+  splits:
+  - name: train
+    num_bytes: 40002719500.1551
+    num_examples: 6296212
+  download_size: 19234328998
+  dataset_size: 40002719500.1551
+configs:
+- config_name: finemath-3plus
+  data_files:
+  - split: train
+    path: finemath-3plus/train-*
+- config_name: finemath-4plus
+  data_files:
+  - split: train
+    path: finemath-4plus/train-*
+- config_name: infiwebmath-3plus
+  data_files:
+  - split: train
+    path: infiwebmath-3plus/train-*
+- config_name: infiwebmath-4plus
+  data_files:
+  - split: train
+    path: infiwebmath-4plus/train-*
+---
+
+# 📐 FineMath
+
+
+![image/png](https://cdn-uploads.huggingface.co/production/uploads/61c141342aac764ce1654e43/0GAdY8wZx6bGtUzqX4Lvi.png)
+
+## What is it?
+
+📐 FineMath consists of **34B tokens** (FineMath-3+) and **54B tokens** (FineMath-3+ with InfiMM-WebMath-3+) of mathematical educational content filtered from CommonCrawl. To curate this dataset, we trained a mathematical content [classifier](https://huggingface.co/HuggingFaceTB/finemath-classifier) using annotations generated by LLama-3.1-70B-Instruct. We used the classifier to retain only the most educational mathematics content, focusing on clear explanations and step-by-step problem solving rather than advanced academic papers.
+
+The [Dataset Curation](#dataset-curation) section details the process for creating the dataset.  More details in our paper: https://arxiv.org/abs/2502.02737v1.
+
+<img src="assets/train_curves.png" width="800"/>
+
+## What is being released?
+
+The dataset is released in two versions:
+- **FineMath-3+**: 34B tokens, 21.4M documents containing mathematical reasoning and problem solving, formatted with Markdown and LaTeX.  
+- **FineMath-4+** (a subset of FineMath-3+): 9.6B tokens, 6.7M documents of higher quality with detailed explanations. Models trained on this dataset perform better on GSM8k and MATH.
+
+<!-- (the image looks kinda meh) <img src="assets/stats.png" width="512"/> -->
+
+We also release a filtered English text-only portion of the **[InfiMM-WebMath-40B](https://huggingface.co/datasets/Infi-MM/InfiMM-WebMath-40B)** dataset, classified using the same approach as FineMath:
+- **InfiMM-WebMath-3+**: 20.5B tokens, 13.9M documents.
+- **InfiMM-WebMath-4+** (a subset of InfiMM-WebMath-3+): 8.5B tokens, 6.3M documents.
+
+## How to load the dataset
+
+Use one of the available configs: `finemath-3plus`, `finemath-4plus`, `infiwebmath-3plus`, or `infiwebmath-4plus`.
+
+```python
+from datasets import load_dataset
+
+# Load the high-quality subset
+data = load_dataset("HuggingFaceTB/finemath", "finemath-4plus", split="train", num_proc=8)
+
+# Or load the larger subset
+data = load_dataset("HuggingFaceTB/finemath", "finemath-3plus", split="train", num_proc=8)
+```
+
+## Dataset curation
+
+Recent language models like DeepSeekMath and MathStral have demonstrated strong mathematical capabilities, trained on specialized datasets that aren't publicly available. We developed a pipeline to identify and extract high-quality mathematical content from CommonCrawl, with several iterations of refinement to improve quality.
+
+### Phase 1: Initial content extraction and classification
+We began by re-extracting pages from CommonCrawl WARCs using URLs from the FineWeb dataset, collecting both the latest and largest versions of each page to capture the evolution of pages across the years. 
+Unlike FineWeb which uses Trafilatura, we employed Resiliparse for text extraction as it better preserves forum discussions and QA answers that often contain crucial reasoning steps and solutions.
+
+For initial quality assessment, we used [Llama-3.1-70B-Instruct](https://huggingface.co/meta-llama/Llama-3.1-70B-Instruct) to generate annotations on a 3-point scale:
+1. Contains general mathematical content
+2. Shows logical reasoning in mathematical context
+3. Contains clear step-by-step solutions at appropriate level
+
+A `multilingual-e5-small`-based classifier finetuned on these annotations was used to score the initial corpus. 
+However, this first version performed below the OpenWebMath baseline, leading to several important refinements.
+
+### Phase 2: Recalling more candidate pages
+Analysis revealed that FineWeb's C4 filter removes pages containing '{' characters, inadvertently filtering out content with LaTeX notation. To address this and expand coverage, we:
+
+1. Identified promising website domains by selecting those where at least 10% of pages received a classifier score ≥ 2
+2. Added URLs from OpenWebMath and InfiMM-WebMath datasets
+3. Recovered URLs of pages filtered by FineWeb's '{' rule from its rejection logs
+4. Re-extracted all content from scratch using the [OpenWebMath pipeline](https://github.com/keirp/OpenWebMath), which properly handles mathematical notation across various HTML markup formats and standardizes them to LaTeX
+
+### Phase 3: Refined quality assessment
+The expanded corpus underwent a more fine-grained quality evaluation:
+
+Once again, we used LLama-3.1-70B-Instruct to score a sample of newly extracted pages on a 5-point scale (full prompt available in [here](assets/prompt.txt)):
+We finetuned a new [classifier](https://huggingface.co/HuggingFaceTB/finemath-classifier) on these annotations and scored the entire corpus.
+After leaving only pages with a score of 3 or higher, and deduplicating the samples using simple single-band MinHash-LSH, we obtained FineMath-3+ with 34B tokens.
+
+The same classifier was applied to InfiMM-WebMath's text content, focusing more on reasoning rather than advanced mathematics.
+
+Both datasets were additionally filtered using FineWeb's language classification pipeline to remove non-English content.
+
+### Decontamination
+Following Qwen2.5-Math's approach, we removed samples with 13-gram overlaps against test sets from GSM8k, MATH, MMLU and ARC. Decontamination logs are available at [HuggingFaceTB/finemath_contamination_report](https://huggingface.co/datasets/HuggingFaceTB/finemath_contamination_report).
+
+## Results and Performance
+
+<img src="assets/eval_bar.png" width="600"/>
+
+Our evaluations show several key findings:
+
+1. FineMath-3+ outperforms the base InfiWebMath on GSM8k and MATH benchmarks
+2. FineMath-4+ demonstrates superior performance compared to both FineMath-3+ and InfiWebMath-4+ on GSM8k and MATH
+3. Combining the datasets (50% FineMath-3+ with 50% InfiWebMath-3+) yields approximately 50B tokens while matching the performance of FineMath-3+
+4. Deduplicating the pages repeated between FineMath and InfiWebMath reduces performance compared to a non-deduplicated combination
+
+## Dataset Schema
+
+```python
+{
+    'url': string,               # Source page URL
+    'fetch_time': int64,         # Crawler timestamp
+    'content_mime_type': string, # MIME type
+    'warc_filename': string,     # Common Crawl WARC source file
+    'warc_record_offset': int32, # WARC record offset, in bytes
+    'warc_record_length': int32, # WARC record size, in bytes
+    'text': string,             # Page content
+    'token_count': int32,       # Number of Llama tokens
+    'char_count': int32,        # Character count
+    'metadata': string,         # Additional OpenWebMath metadata
+    'score': float64,           # Raw quality score
+    'int_score': int64,         # Integer quality score
+    'crawl': string,            # Common Crawl crawl identifier
+    'snapshot_type': string,    # Whether the page is the latest or the largest for this URL
+    'language': string,         # Document language
+    'language_score': float64   # LangID probability
+}
+```
+
+## Considerations for Using the Data
+
+### Social Impact of Dataset
+With the release of this dataset, we aim to make high-quality mathematical educational content more accessible to the machine learning community. While multiple language models have demonstrated strong mathematical capabilities, the datasets used to train these capabilities are often not publicly available. By releasing FineMath, we hope to:
+- Make the dataset creation process more transparent
+- Reduce the barrier to entry for training models with strong mathematical capabilities
+- Provide a benchmark for mathematical content quality filtering
+
+### Discussion of Biases
+The dataset may have certain inherent biases:
+- Focus on English language content
+- Emphasis on popular educational approaches to mathematics
+- Bias towards certain types of mathematical notation and formatting
+
+### Other Known Limitations
+- The dataset is limited to English language content
+- The filtering criteria may not capture advanced mathematical content (e.g. advanced research subjects)
+- Some mathematical notation (e.g. image-based) may not be preserved
+- Long-form content may have varying quality even within high-scoring documents
+
+## Licensing Information
+The dataset is released under the **Open Data Commons Attribution License (ODC-By) v1.0** [license](https://opendatacommons.org/licenses/by/1-0/). The use of this dataset is also subject to [CommonCrawl's Terms of Use](https://commoncrawl.org/terms-of-use).
+
+## Future work
+There are several avenues for future work:
+- Expand language coverage beyond English
+- Improve mathematical notation extraction and preservation
+- Develop more sophisticated quality metrics
+- Create specialized subsets for different educational levels
+
+### Citation Information
+
+```
+@misc{allal2025smollm2smolgoesbig,
+      title={SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model}, 
+      author={Loubna Ben Allal and Anton Lozhkov and Elie Bakouch and Gabriel Martín Blázquez and Guilherme Penedo and Lewis Tunstall and Andrés Marafioti and Hynek Kydlíček and Agustín Piqueres Lajarín and Vaibhav Srivastav and Joshua Lochner and Caleb Fahlgren and Xuan-Son Nguyen and Clémentine Fourrier and Ben Burtenshaw and Hugo Larcher and Haojun Zhao and Cyril Zakka and Mathieu Morlon and Colin Raffel and Leandro von Werra and Thomas Wolf},
+      year={2025},
+      eprint={2502.02737},
+      archivePrefix={arXiv},
+      primaryClass={cs.CL},
+      url={https://arxiv.org/abs/2502.02737}, 
+}
+```

assets/prompt.txt

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+Evaluate the following text extract for its potential usefulness for studying mathematics up to high school and early undergraduate levels. Use the following 5-point scoring system described below. Points are accumulated based on the satisfaction of each criterion:
+
+- Add 1 point if the extract contains some mathematical content, even if it's not very useful for studying, or if it contains non-academic content such as advertisements and generated pages for converting weight and currencies.
+- Add another point if the extract touches on mathematical topics, even if it's poorly written if it's too complex such as an academic paper that is too advanced. 
+- Award a third point if the extract demonstrates problem solving or logical reasoning in a mathematical context, even if it lacks step-by-step explanations.
+- Grant a fourth point if the extract is at an appropriate level (up to high school and early undergraduate levels) and contains clear mathematical deductions and step-by-step solutions to mathematical problems. It should be similar to a chapter from a textbook or a tutorial.
+- Give a fifth point if the extract is outstanding in its educational value for teaching and studying mathematics in middle school and high school. It should include very detailed and easy to follow explanations.
+
+Question-answer formats (e.g., from educational websites or forums) are acceptable if they meet the criteria.
+
+The text extract:
+```
+{}
+```
+
+After examining the extract:
+- Briefly justify your total score, up to 100 words.
+- Conclude with the score using the format: Final score: <total points>.

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