Lean-ing on Quality: How High-Quality Data Beats Diverse Multilingual Data in AutoFormalization
Keywords: llm, large language models, autoformalization, lean
TL;DR: High-quality prompting beats diverse multilingual datasets in fine-tuning for autoformalization.
Abstract: Autoformalization, the process of transforming informal mathematical language into formal specifications and proofs remains a difficult task for state-of-the-art (large) language models. Existing works point to competing explanations for the performance gap. On one hand, large language models exhibit exceptional performance on translation tasks, suggesting their significant potential for autoformalization. On the other hand, the quantitative reasoning capabilities of standard language models remain limited, leading to suboptimal performance on autoformalization and the subsequent task of formal theorem proving. To this end, we introduce a novel methodology that leverages backtranslation with hand-curated prompts to enhance the mathematical capabilities of language models, particularly addressing the challenge posed by the scarcity of labeled data. Specifically, we evaluate three primary variations of this strategy: (1) on-the-fly (online) backtranslation, (2) distilled (offline) backtranslation with few-shot amplification, and (3) line-by-line proof analysis integrated with proof state information. Each variant is designed to optimize data quality over quantity, focusing on the high fidelity of generated proofs rather than sheer data scale. Our findings provide evidence that employing our proposed approaches to generate synthetic data, which prioritizes quality over volume, improves the autoformalization performance of LLMs as measured by standard benchmarks such as ProofNet. Crucially, our approach outperforms pretrained models using a minimal number of tokens. We also show, through strategic prompting and backtranslation, that our approaches surpass the performance of finetuning with extensive multilingual datasets such as MMA on ProofNet with only 1/150th of the tokens. Taken together, our methods show a promising new approach to significantly reduce the resources required to formalize proofs, thereby accelerating AI for math.
Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
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Submission Number: 8846
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