Improving Lean4 Autoformalization via Cycle Consistency Fine-tuning
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910072456609792 |
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| author | Shebzukhov, Arsen |
| author_facet | Shebzukhov, Arsen |
| contents | Autoformalization - automatically translating natural language mathematical texts into formal proof language such as Lean4 - can help accelerate AI-assisted mathematical research, be it via proof verification or proof search. I fine-tune Qwen3.5-2B with LoRA for natural language to Lean4 formalization on FineLeanCorpus and consider three training regimes: supervised fine-tuning (SFT) with curriculum learning (difficulty 1 to 10), SFT without curriculum ordering, and reinforcement learning using group relative policy optimization (GRPO) with a cycle consistency reward. Cycle consistency measures how well the meaning of a statement is preserved through a NL to Lean4 to NL' loop, computed as cosine similarity of off-the-shelf sentence embeddings. On an unseen subset of FineLeanCorpus (FLC) and on PutnamBench, RL substantially outperforms both SFT variants (mean cycle consistency 0.669 vs. 0.513 on FLC; 0.561 vs. 0.422 on PutnamBench), while increasing cross-entropy loss by only 0.011 nats, with minimal impact on formalization quality. Curriculum ordering provides no measurable benefit over shuffled training. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24372 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improving Lean4 Autoformalization via Cycle Consistency Fine-tuning Shebzukhov, Arsen Computation and Language Autoformalization - automatically translating natural language mathematical texts into formal proof language such as Lean4 - can help accelerate AI-assisted mathematical research, be it via proof verification or proof search. I fine-tune Qwen3.5-2B with LoRA for natural language to Lean4 formalization on FineLeanCorpus and consider three training regimes: supervised fine-tuning (SFT) with curriculum learning (difficulty 1 to 10), SFT without curriculum ordering, and reinforcement learning using group relative policy optimization (GRPO) with a cycle consistency reward. Cycle consistency measures how well the meaning of a statement is preserved through a NL to Lean4 to NL' loop, computed as cosine similarity of off-the-shelf sentence embeddings. On an unseen subset of FineLeanCorpus (FLC) and on PutnamBench, RL substantially outperforms both SFT variants (mean cycle consistency 0.669 vs. 0.513 on FLC; 0.561 vs. 0.422 on PutnamBench), while increasing cross-entropy loss by only 0.011 nats, with minimal impact on formalization quality. Curriculum ordering provides no measurable benefit over shuffled training. |
| title | Improving Lean4 Autoformalization via Cycle Consistency Fine-tuning |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2603.24372 |