arXiv:2410.04753v2 Announce Type: replace-cross Abstract: Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its downstream use. For example, we may want a proof to adhere to a certain style, or to be readable, concise, or modularly structured. Having suitably optimized proofs is also important for learning tasks, especially since human-written proofs may not optimal for that purpose. To this end, we study a new problem
The increasing sophistication of large language models and the formal verification community's efforts are converging, making automated proof optimization a key area of development for practical AI applications.
Optimized formal proofs are critical for reliability, efficiency, and human interpretability in AI-generated reasoning, impacting fields from software engineering to scientific discovery.
The ability to automatically refine and optimize AI-generated formal proofs introduces an important feedback loop, potentially making AI-assisted reasoning more robust and widely adopted.
- · AI agents developers
- · Formal verification platforms
- · Mathematics and logic researchers
- · Software and hardware engineering
- · Manual proof optimizers (long-term)
- · Systems relying on unoptimized AI outputs
More efficient and reliable AI-generated formal proofs become available for industrial and scientific applications.
The development of more sophisticated AI agents capable of self-improvement and optimization in complex logical tasks accelerates.
The definition of 'proof' itself might evolve, incorporating metrics like conciseness or modularity as primary considerations, potentially leading to new paradigms in formal verification.
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Read at arXiv cs.LG