arXiv:2605.22257v1 Announce Type: new Abstract: Formal theorem provers based on large language models (LLMs) are highly sensitive to superficial variations in problem representation: semantically equivalent statements can exhibit drastically different proof success rates, revealing a failure to respect structural symmetries inherent in formal mathematics. This raises a central question: what are the right symmetries for formal theorem proving? We introduce rewriting categories, a category-theoretic framework capturing the compositional, generally non-invertible transformations induced by proof
The rapid advancement and increased application of large language models in formal reasoning highlight the current limitations in their ability to handle structural symmetries, prompting immediate research into fundamental improvements.
Improving formal theorem provers' ability to respect structural symmetries is crucial for their reliability, efficiency, and broader adoption in critical applications like software verification and mathematical discovery, enhancing the trustworthiness of AI in formal reasoning.
The understanding and implementation of how LLMs process mathematical structures will evolve, moving towards more robust and generalizable reasoning capabilities rather than relying on superficial pattern matching.
- · AI research institutions
- · Formal verification software developers
- · Mathematics community
- · LLM developers
- · Companies relying on brittle LLM-based provers
- · Traditional symbolic AI approaches (if outpaced by hybrid systems)
More robust and reliable AI-driven formal theorem proving becomes achievable.
This capability accelerates progress in software engineering, drug discovery, and hardware design by automating complex verification tasks.
It could lead to the discovery of new mathematical theorems and a paradigm shift in how mathematical research is conducted.
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Read at arXiv cs.LG