HenryShan/MathLlama3.2

MathLlama 3.2 - Enhanced Mathematical Reasoning Model

Model Overview

MathLlama 3.2 is a fine-tuned version of Meta's Llama-3.2-3B-Instruct model, specifically enhanced for advanced mathematical reasoning tasks. This model demonstrates significant improvements in mathematical problem-solving capabilities through targeted fine-tuning with synthetic Chain-of-Thought (CoT) data.

Key Improvements

Mathematical Reasoning Enhancement

• 12% improvement on abstract_algebra in MMLU compared to the base Llama-3.2-3B-Instruct model
• Enhanced capability in complex mathematical reasoning tasks
• Improved performance across various mathematical domains including algebra, calculus, and abstract mathematical concepts

Training Methodology

• Synthetic Dataset: Utilized the Gemini-MMLU-CoT dataset consisting of 7,000 advanced math problems
• Chain-of-Thought Training: Each training example includes detailed step-by-step reasoning processes

Model Architecture

• Base Model: Meta Llama-3.2-3B-Instruct
• Parameters: 3 billion parameters
• Context Length: 128k tokens
• Architecture: Transformer-based with optimized attention mechanisms

Usage

Basic Usage

# Load model directly
from transformers import AutoTokenizer, AutoModelForCausalLM

tokenizer = AutoTokenizer.from_pretrained("HenryShan/MathLlama3.2")
model = AutoModelForCausalLM.from_pretrained("HenryShan/MathLlama3.2")
messages = [
    {"role": "user", "content": "Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q. Answer Choices: A: "0", B: "4", C: "2", D: "6"},
]
inputs = tokenizer.apply_chat_template(
    messages,
    add_generation_prompt=True,
    tokenize=True,
    return_dict=True,
    return_tensors="pt",
).to(model.device)

outputs = model.generate(**inputs, max_new_tokens=40)
print(tokenizer.decode(outputs[0][inputs["input_ids"].shape[-1]:]))

Training Details

Dataset Creation

• Synthetic Dataset: 7,000 carefully designed advanced mathematical problems
• Chain-of-Thought Format: Each row includes:
  1. Clear problem statement
  2. Step-by-step reasoning process
  3. Final answer with justification

Fine-tuning Process

• Learning Rate: Optimized for mathematical reasoning tasks
• Batch Size: Configured for stable training with mathematical data
• Training Steps: Sufficient iterations to achieve mathematical reasoning improvements
• Hardware: Trained on an Apple M4 Max Computer using MLX

Training Performance

The model was trained for 50 epochs, and its performance was tracked using Weights & Biases (wandb). The graph below shows the training loss and validation loss (val_loss) throughout the fine-tuning process.

Applications

This model is particularly well-suited for:

• Mathematical tutoring systems
• Automated theorem proving assistance
• Advanced mathematical problem solving
• STEM education applications
• Research assistance in mathematical domains

Limitations

While MathLlama 3.2 shows significant improvements in mathematical reasoning, it:

• Should not be used for safety-critical mathematical applications without verification
• May occasionally make reasoning errors on extremely complex problems
• Performance may vary across different mathematical domains

Ethical Considerations

This model is designed to enhance mathematical education and research. Users should:

• Verify critical mathematical results independently
• Use the model as a tool to augment, not replace, human mathematical reasoning
• Be aware of potential biases in synthetic training data

Citation

@misc{mathllama2025,
      title={MathLlama 3.2: Enhanced Mathematical Reasoning with Synthetic CoT Data}, 
      author={Haotian Shan},
      year={2025},
      note={Fine-tuned Llama-3.2 model for advanced mathematical reasoning}
}

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