What are the Right Symmetries for Formal Theorem Proving?
Researchers have introduced a new category-theoretic framework called rewriting categories to address the sensitivity of large language model (LLM) based formal theorem provers to problem representation. These provers often fail to respect structural symmetries in formal mathematics, leading to drastically different proof success rates for semantically equivalent statements. The new framework formalizes two key symmetry notions: proof equivariance and success invariance. The study found that current LLM provers satisfy neither, and proposes test-time methods to aggregate over equivalent rewritings, improving robustness and performance. AI
IMPACT Introduces a theoretical framework and practical methods to improve the robustness and performance of LLM-based theorem provers by addressing symmetry issues.