13 citations · 36 across the 15 of their papers we have counts for
17 papers
Quantum mixing on large Schreier graphs
Charles Bordenave, Cyril Letrouit, Mostafa Sabri
We prove quantum ergodicity and quantum mixing for sequences of finite Schreier graphs converging to an infinite Cayley graph whose adjacency operator has absolutely continuous spe…
Token Sample Complexity of Attention
Léa Bohbot, Cyril Letrouit, Gabriel Peyré +1
As context windows in large language models continue to expand, it is essential to characterize how attention behaves at extreme sequence lengths. We introduce token sample complex…
Unstable optimal transport maps
Cyril Letrouit
The stability of optimal transport maps with respect to perturbations of the marginals is a question of interest for several reasons, ranging from the justification of the lineariz…
Stability of optimal transport maps on Riemannian manifolds
Jun Kitagawa, Cyril Letrouit, Quentin Mérigot
We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure under variations of the target measure , when…
Gluing methods for quantitative stability of optimal transport maps
Cyril Letrouit, Quentin Mérigot
We establish quantitative stability bounds for the quadratic optimal transport map between a fixed probability density and a probability measure on . Un…
Delocalized eigenvectors of transitive graphs and beyond
Nicolas Burq, Cyril Letrouit
We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly pro…
Generic controllability of equivariant systems and applications to particle systems and neural networks
Andrei Agrachev, Cyril Letrouit
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, fu…
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…
Propagation of singularities for subelliptic wave equations
Cyril Letrouit
H{ö}rmander's propagation of singularities theorem does not fully describe the propagation of singularities in subelliptic wave equations, due to the existence of doubly characteri…
Observability of Baouendi-Grushin-Type Equations Through Resolvent Estimates
Cyril Letrouit, Chenmin Sun
In this article, we study the observability (or, equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed o…
Observability and Controllability for the Schr{ö}dinger Equation on Quotients of Groups of Heisenberg Type
Clotilde Fermanian Kammerer, Cyril Letrouit
We give necessary and sufficient conditions for the controllability of a Schr\''odinger equation involving the sub-Laplacian of a nilmanifold obtained by taking the quotient of a g…
Quantum limits of sub-Laplacians via joint spectral calculus
Cyril Letrouit
We establish two results concerning the Quantum Limits (QLs) of some sub-Laplacians. First, under a commutativity assumption on the vector fields involved in the definition of the…
Subelliptic wave equations are never observable
Cyril Letrouit
It is well-known that observability (and, by duality, controllability) of the elliptic wave equation, i.e., with a Riemannian Laplacian, in time is almost equivalent to the G…
Catching all geodesics of a manifold with moving balls and application to controllability of the wave equation
Cyril Letrouit
We address the problem of catching all speed geodesics of a Riemannian manifold with a moving ball: given a compact Riemannian manifold and small parameters $\varepsilo…