Formula-One Prompting: Adaptive Reasoning Through Equations For Applied Mathematics
This addresses the challenge of recalling or deriving governing equations in applied mathematics problems for domains like finance and physics, representing an incremental improvement over existing prompting techniques.
The paper tackled the problem of improving LLM mathematical reasoning in applied domains by proposing Formula-One Prompting (F-1), which uses equations as an intermediate step and adaptively selects solving strategies, resulting in average performance gains of +5.76% over Chain-of-Thought and +8.42% over Program-of-Thought across benchmarks.
Prompting techniques such as Chain-of-Thought (CoT) and Program-of-Thought (PoT) improve LLM mathematical reasoning by structuring intermediate steps in natural language or code. However, applied mathematics problems in domains like finance, physics, and cryptography often require recalling or deriving governing equations, a step that current approaches do not explicitly leverage. We propose Formula-One Prompting (F-1), a two-phase approach that uses mathematical equations as an intermediate representation before adaptive solving. F-1 first formulates governing equations from problem descriptions, then selects a solving strategy among CoT, PoT, or direct computation based on the generated equations, all within a single LLM call. Results across five models and four benchmarks show F-1 outperforms CoT by +5.76% and PoT by +8.42% on average. Crucially, gains are largest in applied domains: +13.30% on FinanceMath over CoT, and within OlympiadBench, larger gains on physics (+2.55%) than pure math (+0.44%). This demonstrates that F-1 is more effective than CoT in applied mathematics problems.