13 citations · 36 across the 15 of their papers we have counts for
4 papers · 1 filter
A mathematical perspective on Transformers
Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy +1
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 int…
Maximal multiplicity of Laplacian eigenvalues in negatively curved surfaces
Cyril Letrouit, Simon Machado
In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus g. Our proof relies on a t…
The emergence of clusters in self-attention dynamics
Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy +1
Viewing Transformers as interacting particle systems, we describe the geometry of learned representations when the weights are not time dependent. We show that particles, represent…
Nodal sets of eigenfunctions of sub-Laplacians
Suresh Eswarathasan, Cyril Letrouit
Nodal sets of eigenfunctions of elliptic operators on compact manifolds have been studied extensively over the past decades. In this note, we initiate the study of nodal sets of ei…