Exploring Autoformalization in Small Language Models

Abstract

Autoformalization, the process of converting informal mathematical statements into formal representations, has emerged as a pivotal challenge in the realm of artificial intelligence and computational linguistics. This paper delves into the potential of small language models to execute autoformalization tasks, which have traditionally been reserved for more computationally intensive, large-scale models. The study systematically evaluates the proficiency of small language models in transforming natural language mathematical expressions into formal logical constructs, thereby assessing their capacity to contribute to automated theorem proving and mathematical knowledge management.

Through a series of controlled experiments, we explore the capabilities and limitations of small language models in understanding and formalizing mathematical discourse. The models are trained and tested on a curated dataset comprising a diverse array of mathematical problems, ranging from elementary arithmetic to more complex algebraic expressions. The evaluation criteria focus on the accuracy of the formal representations generated, the computational efficiency of the models, and their adaptability to varied mathematical contexts.

The findings reveal that, while small language models exhibit promising potential in handling basic mathematical formalization tasks, significant challenges persist in scaling these capabilities to more intricate mathematical domains. The models demonstrate moderate success in parsing and formalizing straightforward expressions but encounter difficulty when tasked with nuanced, context-dependent mathematical language. This highlights the need for enhanced training methodologies and potentially hybrid approaches that combine small models with specialized mathematical reasoning tools.

Ultimately, this research contributes to the broader understanding of autoformalization in computational linguistics, advocating for a nuanced approach that leverages the strengths of small language models while acknowledging their current limitations. The insights garnered from this study aim to inform future research directions, fostering advancements in the development of efficient, scalable autoformalization techniques.