Mathematical Language Models: A Survey

TL;DR

This survey reviews recent advances in mathematical language models, categorizing key research, datasets, and methodologies, and discusses challenges and future directions to guide ongoing innovation in the field.

Contribution

It provides a comprehensive categorization of mathematical LMs, compares their characteristics and performance, and compiles extensive datasets to support future research.

Findings

Numerous mathematical LLMs have been proposed with diverse methodologies.

A large collection of over 60 datasets supports benchmarking and training.

The survey identifies key challenges and future research directions.

Abstract

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, advanced CoT methodologies and multi-modal methods. To comprehend the benefits of mathematical LMs more thoroughly, we carry out an in-depth contrast of their characteristics and performance. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is poised to facilitate and inspire future innovation among researchers invested in advancing this domain.