FormalEvolve: Neuro-Symbolic Evolutionary Search for Diverse Autoformalization

Autoformalization aims to produce formal statements that compile and faithfully preserve the intended meaning of informal mathematics. Yet standard single-output evaluation collapses this many-to-many structure into a single prediction. For downstream proving, this granularity is too coarse: a formal statement is not merely a faithful translation endpoint, but also a prover-facing interface whose structure can alter proof search under a fixed budget. We therefore recast autoformalization as budgeted test-time search: FormalEvolve maintains a compilation-feasible archive for reuse and returns a deduplicated, semantically accepted repertoire for evaluation and downstream proving. It expands...

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