Update README: Align terminology with paper (MATH500, OpenCompass, Refined Data, etc.)

README.md

@@ -52,14 +52,14 @@ High-quality pre-training data is crucial for enhancing the mathematical reasoni
 - **Data Quality Level**: Existing datasets generally lack a systematic quality grading mechanism, with high-value mathematical content mixed with low-quality noise.
 - **Data Diversity Level**: 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 [Ultra-Data](xxx) L0-L4 hierarchical data processing framework, containing four progressive levels:
+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](xxx) L0-L4 Tiered Data Management Framework, containing four progressive levels:
 
 - **L0 Raw Data Layer**: Developed 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 Layer**: Cleans noise through heuristic rules and performs document-level deduplication.
 - **L2 Selected Data Layer**: Uses closed-source large models to annotate seed data and distills it into a lightweight Embedding classifier to achieve efficient quality grading of the full corpus.
-- **L3 Synthetic Data Layer**: Generates synthetic data in various formats such as Q&A, multi-turn dialogues, multi-style rewriting, and knowledge-grounded textbooks based on multi-model ensemble.
+- **L3 Refined Data Layer**: 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-1B architecture, ***UltraData-Math*** achieves a score of **37.02** on the MATH benchmark, an improvement of **+3.62** compared to Nemotron-CC 4plus; it achieves **61.79** on GSM8K, an improvement of **+3.34**, while maintaining code generation and general knowledge capabilities.
+Experiments show that on the MiniCPM-1.2B architecture, ***UltraData-Math*** achieves a score of **37.02** on the MATH500 benchmark, an improvement of **+3.62** compared to Nemotron-CC 4plus; it achieves **61.79** on GSM8K, an improvement of **+3.34**, 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.
 
@@ -69,7 +69,7 @@ Experiments show that on the MiniCPM-1B architecture, ***UltraData-Math*** achie
 
 ## 🏗️ 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 Data Grading System** proposed by the UltraData position 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.
+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](xxx) 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"/>
@@ -111,9 +111,9 @@ Although L1 data has a clean format, the content quality varies. The L2 phase in
   - *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: Synthetic and Augmented Data
+### L3: Refined Data
 
-**Goal**: Compensate for the singularity of natural corpora in format and scenarios through synthetic data, enhancing the model's Chain of Thought (CoT) capabilities.
+**Goal**: Compensate for the singularity of natural corpora in format and scenarios through rewriting, synthetic generation, and refinement, enhancing the model's Chain of Thought (CoT) capabilities.
 
 Natural web data is mostly declarative text. To enhance the model's instruction following and multi-turn interaction capabilities, we built the L3 synthetic data layer:
 
@@ -130,9 +130,9 @@ Natural web data is mostly declarative text. To enhance the model's instruction
 
 ## 📈 Experimental Results
 
-We used the **MiniCPM-1.2B** model architecture and **MiniCPM3-4B** tokenizer for experimental verification. Each experiment was conducted with a training volume of **100 billion Tokens**, using the **Decay Verification** method (annealing from a 1.3T base model). We used the Lighteval library for model evaluation. Evaluation benchmarks include:
+We used the **MiniCPM-1.2B** model architecture and **MiniCPM3-4B** tokenizer for experimental verification. Each experiment was conducted with a training volume of **100 billion Tokens**, using the **Decay Verification** method (annealing from a 1.3T base model). We used [OpenCompass](https://github.com/open-compass/opencompass) as our evaluation framework. Evaluation benchmarks include:
 
-- **Mathematical Reasoning:** GSM8K, MATH, Math-Bench, R-Bench-Math
+- **Mathematical Reasoning:** GSM8K, MATH500, Math-Bench, R-Bench-Math
 - **Code Generation:** HumanEval, MBPP
 - **Comprehensive Knowledge:** MMLU, MMLU-STEM
 
@@ -144,9 +144,9 @@ We evaluated data quality using the **Decay Verification** method: continuing pr
 
 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 and **applied the same L1 cleaning operators to all baselines**. This comparison demonstrates the **overall benefit of our L0 Parser + L1 Filtering pipeline** against other parsers under identical cleaning conditions.
 
-| Parser | Average | MMLU | MMLU-STEM | Math | GSM8K | MBPP | HumanEval |
+| Parser | Average | MMLU | MMLU-STEM | MATH500 | GSM8K | MBPP | HumanEval |
 |:---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
-| **UltraData-Math-L0-Parser (Ours)** | **43.44** | 51.41 | 46.76 | **28.72** | 54.97 | 47.10 | **31.71** |
+| **UltraData-Math-Parser (Ours)** | **43.44** | 51.41 | 46.76 | **28.72** | 54.97 | 47.10 | **31.71** |
 | trafilatura + w3m | 42.33 | 50.95 | 45.52 | 27.64 | 54.51 | **47.93** | 27.44 |
 | trafilatura | 42.44 | 51.42 | 46.62 | 28.08 | **56.03** | 45.64 | 26.83 |
 | Megamath | 42.32 | **51.46** | **46.81** | 26.04 | 54.06 | 45.64 | 29.88 |
@@ -157,19 +157,19 @@ To fairly compare different parsing strategies, we conducted experiments on a da
 
 To validate the effectiveness of our L0-L3 hierarchical 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**.
 
-| Dataset | Average | MMLU | MMLU-STEM | Math | GSM8K | MBPP | HumanEval |
+| Dataset | Average | MMLU | MMLU-STEM | MATH500 | GSM8K | MBPP | HumanEval |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
 | **UltraData-Math-L1** | 42.31 | 51.41 | 45.44 | 27.78 | 54.66 | 44.71 | 29.88 |
 | **UltraData-Math-L2** | 42.57 | 50.93 | 45.52 | 29.20 | 52.92 | 44.50 | 32.32 |
 | **UltraData-Math-L3** | **46.44** | **51.67** | **45.93** | **37.02** | **61.79** | **49.27** | **32.93** |
 
-*Note: Results demonstrate that higher-tier data (L3) significantly boosts mathematical reasoning (MATH, GSM8K) and general capabilities.*
+*Note: Results demonstrate that higher-tier data (L3) significantly boosts mathematical reasoning (MATH500, GSM8K) and general capabilities.*
 
 ### 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:
 
-| Model | Average | MMLU | MMLU-STEM | Math | GSM8K | MBPP | HumanEval | R-Bench-Math | Math-Bench |
+| Model | Average | MMLU | MMLU-STEM | MATH500 | GSM8K | MBPP | HumanEval | R-Bench-Math | Math-Bench |
 |:---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
 | **UltraData-Math (Ours)** | **43.79** | 51.67 | 45.93 | **37.02** | **61.79** | **49.27** | 32.93 | 23.38 | **48.33** |
 | Nemotron-cc 4plus mind | 43.45 | 52.09 | 45.99 | 35.96 | 59.97 | 48.03 | 34.76 | **23.51** | 47.25 |