Proposed research subject :
Frontier models have demonstrated rapid progress in producing correct Lean code, saturating existing Lean benchmarks of advanced problems in both the IMO and Putnam competitions, and can produce Fields Medal-level formalizations of research math. However, while Lean code that type checks might be reasonably declared "correct", for formalizations to be useful to humans we need to extend our assessment beyond mere correctness to code quality, such as concision, transparency, maintainability, human readability, elegance (e.g. “correct” abstractions), and execution efficiency. In this postdoc project, we aim to develop novel and multidimensional metrics of Lean code quality and establish new benchmarks and datasets to assess model performance. We believe that these benchmarks will expose new dimensions for improvement in frontier models, especially in long-horizon autoformalizations of modern research mathematics. Potential metrics include code complexity, code volume, style adherence and idiomatic expression, passing linter checks, elaboration time. Evaluation methods can combine multiple techniques: including static analysis, resource profiling, LLM-as-a-judge techniques, and optimally using feedback from human expert user studies. This project proposal fills a gap in the field because as frontier models generate increasingly correct Lean code, improving generated code quality to Mathlib standards becomes crucial to accelerate adoption in the mathematical community.
By shifting the evaluation of autoformalization from a single-bit correctness check to a rich, multidimensional quality assessment, this project will:
- reveal underexplored weaknesses in current LLMs (e.g., long planning for abstraction),
- provide actionable training signals for future models by reinforcement learning,
- lower the barrier to adoption of AI-generated formalizations in mathematical research.
Responsibilities :
The person recruited is responsible for defining, implementing and validating a multidimensional suite of Lean‑code‑quality metrics and will take initiatives for creating benchmark datasets, integrating metric suites into continuous‑evaluation pipelines, and organising human studies to calibrate automated scores against expert judgement.
Steering/Management :
The person recruited will be in charge of leading the Lean Quality Benchmark work package, interacting with other project members and interested third-parties/partners labs, and possibly coordinating the contributions of interns.
