GPT-4 generates infinite math problems with verified solutions through template-based generation
TDG: A system that turns GPT-4's templates into millions of verified math problems
LLMs struggle with mathematical reasoning due to limited high-quality training data. This paper introduces Template-based Data Generation (TDG), using GPT-4 to create parameterized templates that generate diverse, verified mathematical problems and solutions.
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https://arxiv.org/abs/2411.18104
🤔 Original Problem:
→ LLMs show impressive language capabilities but fail at complex mathematical reasoning tasks.
→ Existing mathematical datasets lack size and diversity, limiting models' ability to learn sophisticated problem-solving.
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🔧 Solution in this Paper:
→ TDG leverages GPT-4 to automatically generate meta-templates for math problems.
→ These templates contain placeholders for variables like names, quantities, and contexts.
→ The system simultaneously generates problems and solutions, verifying them through code execution.
→ A reject-sampling process ensures only correct and well-formed problems make it to the dataset.
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💡 Key Insights:
→ Template-based generation enables infinite, high-quality math problems
→ Code execution verification guarantees solution correctness
→ GPT-4 generated templates provide natural language diversity
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📊 Results:
→ Generated TemplateGSM dataset with 7.47 million grade school math problems
→ Each problem includes verified code-based and natural language solutions
→ Average solution length: 123.43 tokens for code, 77.87 tokens for natural language
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