{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/naturalprover-grounded-mathematical-proof","title":"NaturalProver: Grounded Mathematical Proof Generation with Language Models","arxiv_id":"2205.12910","date":"2022-05-25","proceeding":null,"authors":["Sean Welleck","Jiacheng Liu","Ximing Lu","Hannaneh Hajishirzi","Yejin Choi"],"abstract":"Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study large-scale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NaturalProver, a language model that generates proofs by conditioning on background references (e.g. theorems and definitions that are either retrieved or human-provided), and optionally enforces their presence with constrained decoding. On theorems from the NaturalProofs benchmark, NaturalProver improves the quality of next-step suggestions and generated proofs over fine-tuned GPT-3, according to human evaluations from university-level mathematics students. NaturalProver is capable of proving some theorems that require short (2-6 step) proofs, and providing next-step suggestions that are rated as correct and useful over 40% of the time, which is to our knowledge the first demonstration of these capabilities using neural language models.","url_abs":"https://arxiv.org/abs/2205.12910v2","url_pdf":"https://arxiv.org/pdf/2205.12910v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"naturalprover-grounded-mathematical-proof","repo_url":"https://github.com/wellecks/naturalprover","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"},{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"}],"methods":[{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"attention-dropout","method_name":"Attention Dropout"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"cosine-annealing","method_name":"Cosine Annealing"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"gpt-3","method_name":"GPT-3"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"linear-warmup-with-cosine-annealing","method_name":"Linear Warmup With Cosine Annealing"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"weight-decay","method_name":"Weight Decay"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2205.12910","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2205.12910"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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