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Characterizing Paraphrase-Induced Failures in Lean 4 Autoformalization

Lean 4 autoformalization has become increasingly popular in recent years, with frontier language models and open-weight autoformalizers now producing valid formalizations of mathematical theorems. However, these evaluations often rely on single canonical phrasings of theorems and rarely probe whether outputs are robust to natural variation in inputs, while prior work has shown that semantically equivalent paraphrases often induce divergent formal outputs. We study the structure of these divergences in Lean 4 by applying deterministic paraphrase rules to datasets of undergraduate and Olympiad-level math problems. Across four frontier models and three open-weight autoformalizers, we find that paraphrase sensitivity is dominated by failures at the code-generation layer, and that these failures are typed differently by dataset. Furthermore, these patterns generalize to open-weight models, showing that state-of-the-art autoformalizers still struggle to generate valid Lean code. Our results provide a failure-mode taxonomy for autoformalization and motivate training-time interventions targeted at specific compilation failures.

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