IsarStep: a Benchmark for High-level Mathematical Reasoning

TL;DR

This paper introduces IsarStep, a benchmark dataset for high-level mathematical reasoning, and evaluates neural models' capabilities in generating human-readable proofs, highlighting the potential and challenges of current approaches.

Contribution

The paper presents a new non-synthetic, comprehensive dataset for mathematical reasoning and proposes a hierarchical transformer model that outperforms standard baselines.

Findings

Neural models can learn non-trivial mathematical reasoning.

Hierarchical transformer outperforms baseline models.

The task is challenging but feasible for advanced neural architectures.

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.