ProofCompass: Enhancing Specialized Provers with LLM Guidance
This addresses computational resource challenges in formal theorem proving for researchers and practitioners, though it is incremental as it builds on existing specialized provers.
The paper tackled the problem of computational inefficiency in formal mathematical reasoning by introducing ProofCompass, a hybrid method that guides specialized provers with an LLM, achieving a 25x reduction in attempts (from 3200 to 128) and improving accuracy from 54.9% to 55.3% on the miniF2F benchmark.
Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates substantial resource efficiency: it outperforms DSP-v1.5 ($54.9\% \rightarrow 55.3\%$) while using 25x fewer attempts ($3200 \rightarrow 128$). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.