Verbalized-Sampling-Synthetic-Data-Generation

This dataset showcases how Verbalized Sampling (VS) can be used to generate high-quality, diverse synthetic training data for mathematical reasoning tasks. From the paper Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversity.

Dataset Description

The Synthetic Data Generation dataset contains mathematical problem-solution pairs generated by different methods using state-of-the-art LLMs. This dataset demonstrates:

• Quality of synthetic data: How well different methods generate valid solutions
• Solution diversity: Variety in solution approaches and explanations
• Scaling synthetic data: Using VS to generate diverse training examples
• Method comparison: Direct vs. Verbalized Sampling approaches for data synthesis

Key Findings

Verbalized Sampling methods produce more diverse solution strategies while maintaining solution correctness, enabling creation of richer synthetic training datasets. Models like GPT-4.1 and Gemini-2.5-Flash generate complementary types of solutions when prompted with different methods.

Dataset Structure

Configs/Subsets

Each config represents a different model used for generation:

• gpt_4_1: Data generated using GPT-4.1
• gemini_2_5_flash: Data generated using Gemini-2.5-Flash

Splits

Each split represents a different generation method:

• Direct: Standard prompting for solution generation
• CoT: Chain-of-thought reasoning
• VS-Standard: Verbalized Sampling with probabilities
• VS-CoT: Verbalized Sampling with chain-of-thought
• VS-Multi: Combined verbalized sampling approach
• Sequence: Sequential verbalized generation
• Multi-turn: Multi-turn verbalized sampling

Data Fields

Fields vary by source dataset but typically include:

• Mathematical problem statement
• Generated solution(s)
• Solution steps or reasoning
• Metadata: model, method, source_dataset

fields:

• messages: [{'role': 'user', 'content': The generated problem by GPT-4.1 or Gemini-2.5-Flash}, {'role': 'assistant', 'content': The generated solution by Qwen3-32B}]
• model: GPT-4.1 or Gemini-2.5-Flash
• method: Direct, CoT, VS_Standard, VS_CoT, VS_Multi, Sequence, Multi_turn

Resources

• 📄 Paper: https://arxiv.org/abs/2510.01171
• 🏠 Homepage: https://www.verbalized-sampling.com/
• 💻 GitHub: https://github.com/CHATS-lab/verbalize-sampling
• 📦 PyPI Package: https://pypi.org/project/verbalized-sampling/
• 📝 Blog: https://simonucl.notion.site/verbalized-sampling
• 🎨 Examples: https://tinyurl.com/vs-gallery
• 💡 Practical Tips: https://x.com/dch/status/1978471395173740900
• 🎙️ Podcast: https://www.youtube.com/watch?v=VoBdywmdim0

Usage

Loading the Dataset

from datasets import load_dataset

# Load GPT-4.1 generated data with VS-Multi method
dataset = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gpt_4_1"
)
vs_multi_data = dataset["VS-Multi"]

print(f"Number of examples: {len(vs_multi_data)}")
print(f"Fields: {list(vs_multi_data.features.keys())}")

Comparing Methods

from datasets import load_dataset

# Load all methods for GPT-4.1
gpt_data = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gpt_4_1"
)

# Compare dataset sizes across methods
for method in ["Direct", "CoT", "VS-Standard", "VS-CoT", "VS-Multi", "Sequence", "Multi-turn"]:
    if method in gpt_data:
        print(f"{method}: {len(gpt_data[method])} examples")

Combining Models and Methods

from datasets import load_dataset, concatenate_datasets

# Load same method from different models
gpt_data = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gpt_4_1"
)["VS-CoT"]

gemini_data = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gemini_2_5_flash"
)["VS-CoT"]

# Combine for more diverse training data
combined = concatenate_datasets([gpt_data, gemini_data])
print(f"Combined VS-CoT data: {len(combined)} examples")

Analyzing Solution Diversity

from datasets import load_dataset
from collections import Counter

def analyze_solution_diversity(dataset):
    """Analyze diversity of solutions"""
    # This is a simple example - adapt based on your data fields
    solution_lengths = []
    unique_starts = set()

    for example in dataset:
        # Adapt field names based on your dataset
        solution = example.get("solution", "") or example.get("answer", "")
        solution_lengths.append(len(solution.split()))

        # Track unique solution starts (first 5 words)
        words = solution.split()[:5]
        unique_starts.add(tuple(words))

    return {
        "total_examples": len(dataset),
        "avg_solution_length": sum(solution_lengths) / len(solution_lengths) if solution_lengths else 0,
        "unique_solution_starts": len(unique_starts),
        "diversity_ratio": len(unique_starts) / len(dataset) if len(dataset) > 0 else 0
    }

# Compare diversity across methods
gpt_data = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gpt_4_1"
)

for method in ["Direct", "VS-Multi"]:
    if method in gpt_data:
        stats = analyze_solution_diversity(gpt_data[method])
        print(f"\n{method}:")
        print(f"  Examples: {stats['total_examples']}")
        print(f"  Avg solution length: {stats['avg_solution_length']:.1f} words")
        print(f"  Unique solution starts: {stats['unique_solution_starts']}")
        print(f"  Diversity ratio: {stats['diversity_ratio']:.2%}")

Creating Training Data

from datasets import load_dataset, concatenate_datasets

# Strategy 1: Use diverse methods from one model
gpt_data = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gpt_4_1"
)

# Combine multiple VS methods for maximum diversity
train_data = concatenate_datasets([
    gpt_data["VS-CoT"],
    gpt_data["VS-Multi"],
    gpt_data["Sequence"]
])

# Strategy 2: Use same method from multiple models
gpt_vs_cot = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gpt_4_1"
)["VS-CoT"]

gemini_vs_cot = load_dataset(
    "CHATS-Lab/Verbalized-Sampling-Synthetic-Data-Generation",
    "gemini_2_5_flash"
)["VS-CoT"]

train_data = concatenate_datasets([gpt_vs_cot, gemini_vs_cot])

print(f"Training dataset size: {len(train_data)}")

Dataset Creation

Generation Models

• GPT-4.1: OpenAI's GPT-4.1 model
• Gemini-2.5-Flash: Google's Gemini-2.5-Flash model

Both models show strong mathematical reasoning capabilities with different solution styles.

Use Cases

This dataset is valuable for:

1. Training Mathematical Reasoning Models: Use diverse solutions as training data
2. Evaluating Generation Methods: Compare quality and diversity across methods
3. Data Augmentation: Supplement existing training datasets with diverse solutions
4. Method Selection: Understand which generation method works best for synthetic data
5. Multi-Model Ensembles: Combine solutions from different models for robustness
6. Solution Diversity Analysis: Study variety in problem-solving approaches

Considerations for Using the Data

Recommended Use

Best Practices:

• ✅ Use for training/fine-tuning mathematical reasoning models
• ✅ Combine multiple methods for maximum diversity
• ✅ Validate solutions before treating as ground truth
• ✅ Mix with human-generated data when possible

Avoid:

• ❌ Using as sole source of truth without validation
• ❌ Claiming data is human-generated
• ❌ Applying to domains outside mathematical reasoning without adaptation

Dataset License Agreement

This Agreement contains the terms and conditions that govern your access and use of the Verbalized-Sampling-Synthetic-Data-Generation Dataset.

Key Terms:

• ✅ Permitted: Research use, commercial use, model training, fine-tuning, data augmentation
• ✅ Attribution Required: Must cite the original paper
• ⚠️ Restrictions: Must comply with original model terms of use (OpenAI, Google)
• ❌ Prohibited: Claiming solutions are human-generated, using without validation in critical applications

Subject to your compliance with these terms, we grant you a limited, non-exclusive, non-transferable, non-sublicensable license to use the dataset for research, development, and improvement of software, algorithms, machine learning models, techniques, and technologies for both research and commercial purposes.

Limitation of Liability: IN NO EVENT WILL WE BE LIABLE FOR ANY CONSEQUENTIAL, INCIDENTAL, EXEMPLARY, PUNITIVE, SPECIAL, OR INDIRECT DAMAGES ARISING OUT OF OR RELATING TO THIS AGREEMENT.

Citation

If you use this dataset in your research, please cite:

@misc{zhang2025verbalizedsamplingmitigatemode,
  title={Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversity},
  author={Jiayi Zhang and Simon Yu and Derek Chong and Anthony Sicilia and Michael R. Tomz and Christopher D. Manning and Weiyan Shi},
  year={2025},
  eprint={2510.01171},
  archivePrefix={arXiv},
  primaryClass={cs.CL},
  url={https://arxiv.org/abs/2510.01171}
}

Contact

For questions or issues, please open an issue on our GitHub repository.