FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline
This work addresses the problem of optimizing synthetic data pipelines for LLM math reasoning, providing actionable insights for researchers and practitioners, though it is incremental in building on existing data synthesis methods.
The paper tackles the lack of systematic comparison in synthetic data strategies for improving LLM math reasoning by introducing FLAMES, a framework that analyzes 10 existing strategies and identifies optimal difficulty-diversity balances, leading to a new dataset that outperforms public datasets on multiple benchmarks and achieves 81.4% on MATH with a 7B model.
Recent works improving LLM math reasoning with synthetic data have used unique setups, making comparison of data synthesis strategies impractical. This leaves many unanswered questions about the roles of different factors in the synthetic data pipeline, such as the impact of filtering low-quality problems. To address this gap, we introduce FLAMES, a Framework for LLM Assessment of Math rEasoning Data Synthesis, and perform a systematic study of 10 existing data synthesis strategies and multiple other factors impacting the performance of synthetic math reasoning data. Our FLAMES experiments provide several valuable insights about the optimal balance of difficulty and diversity of synthetic data. First, data agents designed to increase problem complexity lead to best improvements on most math metrics. Second, with a fixed data generation budget, keeping higher problem coverage is more important than keeping only problems with reliable solutions. Third, GSM8K- and MATH-based synthetic data can lead to improvements on competition-level benchmarks, showcasing easy-to-hard generalization. Leveraging insights from our FLAMES experiments, we design two novel data synthesis strategies for improving out-of-domain generalization and robustness. Further, we develop the FLAMES dataset, an effective blend of our novel and existing data synthesis strategies, outperforming public datasets on OlympiadBench (+15.7), CollegeMath (+4.5), GSMPlus (+6.5), and MATH (+3.1). Fine-tuning Qwen2.5-Math-7B on the FLAMES dataset achieves 81.4% on MATH, surpassing larger Llama3 405B, GPT-4o and Claude 3.5 Sonnet.