@inproceedings{lu-etal-2026-formalevolve,
title = "{F}ormal{E}volve: Neuro-Symbolic Evolutionary Search for Diverse Autoformalization",
author = "Lu, Haijian and
Wang, Wei and
Liu, Jing",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.317/",
pages = "6694--6722",
ISBN = "979-8-89176-462-0",
abstract = "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 the archive with LLM-driven mutation, crossover, bounded patch repair, and symbolic abstract syntax tree (AST) rewrites for structural diversity. Under a generator-call budget of T=100 with a fixed LLM semantic judge, FormalEvolve reaches SH@100 of 58.0{\%} on CombiBench and 84.9{\%} on ProofNet, improving over all no-archive controls while reducing the cross-problem concentration of semantic successes. Under a fixed B=64 prover budget, these repertoires improve theorem-complete proving over the matched no-archive control. Additional stronger-base statement-generation experiments show that archive-search gains persist with stronger seed and repair models."
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<abstract>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 the archive with LLM-driven mutation, crossover, bounded patch repair, and symbolic abstract syntax tree (AST) rewrites for structural diversity. Under a generator-call budget of T=100 with a fixed LLM semantic judge, FormalEvolve reaches SH@100 of 58.0% on CombiBench and 84.9% on ProofNet, improving over all no-archive controls while reducing the cross-problem concentration of semantic successes. Under a fixed B=64 prover budget, these repertoires improve theorem-complete proving over the matched no-archive control. Additional stronger-base statement-generation experiments show that archive-search gains persist with stronger seed and repair models.</abstract>
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%0 Conference Proceedings
%T FormalEvolve: Neuro-Symbolic Evolutionary Search for Diverse Autoformalization
%A Lu, Haijian
%A Wang, Wei
%A Liu, Jing
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F lu-etal-2026-formalevolve
%X 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 the archive with LLM-driven mutation, crossover, bounded patch repair, and symbolic abstract syntax tree (AST) rewrites for structural diversity. Under a generator-call budget of T=100 with a fixed LLM semantic judge, FormalEvolve reaches SH@100 of 58.0% on CombiBench and 84.9% on ProofNet, improving over all no-archive controls while reducing the cross-problem concentration of semantic successes. Under a fixed B=64 prover budget, these repertoires improve theorem-complete proving over the matched no-archive control. Additional stronger-base statement-generation experiments show that archive-search gains persist with stronger seed and repair models.
%U https://aclanthology.org/2026.findings-emnlp.317/
%P 6694-6722
Markdown (Informal)
[FormalEvolve: Neuro-Symbolic Evolutionary Search for Diverse Autoformalization](https://aclanthology.org/2026.findings-emnlp.317/) (Lu et al., Findings 2026)
ACL