Xiao Li, Bolin Zhu, Kaiwen Shi et al.
The application of formulas (e.g., physics formulas) is a fundamental human ability in solving numerical reasoning problems. Existing numerical reasoning datasets rarely explicitly state the formulas employed, as their questions often rely on implicit commonsense mathematical knowledge. To address this gap, we introduce FormulaReasoning, a new dataset specifically designed for formula-based numerical reasoning. It consists of 5,324 questions that require numerical calculations grounded in external physics formulas. We provide normalized, fine-grained annotations in both English and Chinese, including formula structures, parameter names, symbols, numerical values, and units-curated through extensive manual effort with LLM-assisted validation to ensure high quality. Additionally, we offer a consolidated formula database to serve as an external knowledge source. We analyze various reasoning approaches on FormulaReasoning, with emphasis on comparative evaluation of different architectural and methodological frameworks. Our assessment includes retrieval-augmented methods, approaches that decompose reasoning into formula generation, parameter extraction, and numerical calculation, as well as optimization techniques using preference data. We identify key challenges in formula-based numerical reasoning that require further investigation across different reasoning paradigms, highlighting opportunities for methodological advancement.