In plain words: Treating each token's representation as a particle that pushes and pulls on the others, this framework gives a mathematical way to study how Transformers process information. It shows that over time the particles naturally gather into distinct clusters.
Abstract · A mathematical perspective on Transformers
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.
Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy, Philippe Rigollet
arXiv:2312.10794 · cs.LG, math.AP, math.DS · submitted Dec 17, 2023 · updated Aug 21, 2025
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