Paper
Improving Lean4 Autoformalization via Cycle Consistency Fine-tuning
Authors
Arsen Shebzukhov
Abstract
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.24372v1</id>\n <title>Improving Lean4 Autoformalization via Cycle Consistency Fine-tuning</title>\n <updated>2026-03-25T14:53:48Z</updated>\n <link href='https://arxiv.org/abs/2603.24372v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.24372v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CL'/>\n <published>2026-03-25T14:53:48Z</published>\n <arxiv:comment>10 pages, 10 figures, pages 10-27 appendix</arxiv:comment>\n <arxiv:primary_category term='cs.CL'/>\n <author>\n <name>Arsen Shebzukhov</name>\n </author>\n </entry>"
}