NaturalProver: Grounded Mathematical Proof Generation with Language Models

• URL: http://arxiv.org/abs/2205.12910v1
• Date: Wed, 25 May 2022 17:01:18 GMT
• Title: NaturalProver: Grounded Mathematical Proof Generation with Language Models
• Authors: Sean Welleck, Jiacheng Liu, Ximing Lu, Hannaneh Hajishirzi, Yejin Choi
• Abstract summary: Theorem proving in natural mathematical language plays a central role in mathematical advances and education. We develop NaturalProver, a language model that generates proofs by conditioning on background references. 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.
• Score: 84.2064569475095
• License: http://creativecommons.org/licenses/by/4.0/
• 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. Naively applying language models to these problems yields proofs riddled with hallucinations and logical incoherence. 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.

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