What Formal Languages Can Transformers Express? A Survey

TL;DR

This survey reviews recent theoretical research on the expressive power of transformer models in formal language recognition, clarifying their capabilities, limitations, and the influence of architectural choices.

Contribution

It provides a comprehensive overview and unifies diverse findings on what formal languages transformers can recognize, highlighting assumptions and frameworks used.

Findings

Transformers can recognize certain classes of formal languages.

Architectural choices significantly influence the computational power of transformers.

The survey clarifies conflicting results in existing research.

Abstract

As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help clarify the power of transformers relative to other models of computation, their fundamental capabilities and limits, and the impact of architectural choices. Work in this subarea has made considerable progress in recent years. Here, we undertake a comprehensive survey of this work, documenting the diverse assumptions that underlie different results and providing a unified framework for harmonizing seemingly contradictory findings.