IsarStep: a Benchmark for High-level Mathematical Reasoning
Wenda Li, Lei Yu, Yuhuai Wu, Lawrence C. Paulson
Abstract
A well-defined benchmark is essential for measuring and accelerating research progress of machine learning models. In this paper, we present a benchmark for high-level mathematical reasoning and study the reasoning capabilities of neural sequence-to-sequence models. We build a non-synthetic dataset from the largest repository of proofs written by human experts in a theorem prover. The dataset has a broad coverage of undergraduate and research-level mathematical and computer science theorems. In our defined task, a model is required to fill in a missing intermediate proposition given surrounding proofs. This task provides a starting point for the long-term goal of having machines generate human-readable proofs automatically. Our experiments and analysis reveal that while the task is challenging, neural models can capture non-trivial mathematical reasoning. We further design a hierarchical transformer that outperforms the transformer baseline.
BibTeX
@inproceedings{
li2021isarstep,
title={IsarStep: a Benchmark for High-level Mathematical Reasoning},
author={Wenda Li and Lei Yu and Yuhuai Wu and Lawrence C. Paulson},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=Pzj6fzU6wkj}
}