Math Natural Language Inference: this should be easy!

TL;DR

This paper evaluates whether large language models can perform natural language inference on mathematical texts, revealing both their potential and current limitations in understanding complex mathematical language.

Contribution

It introduces a new Math NLI corpus with human-labeled and LLM-generated hypotheses, and assesses LLM performance and consistency in mathematical inference tasks.

Findings

LLMs can match human performance with majority voting in some cases

Models still struggle with basic mathematical inferences

Current models are less prone to hypothesis-only inference

Abstract

We ask whether contemporary LLMs are able to perform natural language inference (NLI) tasks on mathematical texts. We call this the Math NLI problem. We construct a corpus of Math NLI pairs whose premises are from extant mathematical text and whose hypotheses and gold labels were provided by people with experience in both research-level mathematics and also in the NLI field. We also investigate the quality of corpora using the same premises but whose hypotheses are provided by LLMs themselves. We not only investigate the performance but also the inter-group consistency of the diverse group of LLMs. We have both positive and negative findings. Among our positive findings: in some settings, using a majority vote of LLMs is approximately equivalent to using human-labeled data in the Math NLI area. On the negative side: LLMs still struggle with mathematical language. They occasionally fail at even basic inferences. Current models are not as prone to hypothesis-only "inference" in our data the way the previous generation had been. In addition to our findings, we also provide our corpora as data to support future work on Math NLI.