A mathematical perspective on Transformers

TL;DR

This paper introduces a mathematical framework viewing Transformers as interacting particle systems, revealing cluster formation over time, and offers new insights for both mathematicians and computer scientists.

Contribution

It presents a novel mathematical perspective on Transformers, modeling them as particle systems to analyze their long-term behavior and cluster emergence.

Findings

Clusters emerge in Transformers over long time scales.

Provides a new theoretical framework for understanding Transformers.

Bridges mathematical theory with practical insights for AI models.

Abstract

Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters emerge in long time. Our study explores the underlying theory and offers new perspectives for mathematicians as well as computer scientists.