48 citations · 137 across the 28 of their papers we have counts for
38 papers
On the Banach--Mazur radius of
Omer Friedland, Assaf Naor, Pierre Youssef
We prove that any -dimensional normed space is at Banach--Mazur distance from .
Log-Sobolev under random monotone censoring
Patrick Oliveira Santos, Raghavendra Tripathi, Pierre Youssef
We show that the logarithmic Sobolev inequality of the Boolean cube is stable under random monotone censoring. More precisely, if is chosen uniformly among…
Khintchine inequalities, trace monoids and Turán-type problems
Patrick Oliveira Santos, Raghavendra Tripathi, Pierre Youssef
We prove scalar and operator-valued Khintchine inequalities for mixtures of free and tensor-independent semicircle variables, interpolating between classical and free Khintchine-ty…
On the Stability of the Jacobian Matrix in Deep Neural Networks
Benjamin Dadoun, Soufiane Hayou, Hanan Salam +2
Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian.…
Central limit theorem for -independent products and higher-order tensors
Guillaume Cébron, Patrick Oliveira Santos, Pierre Youssef
We establish a central limit theorem (CLT) for families of products of -independent random variables. We utilize graphon limits to encode the evolution of independence and chara…
Intrinsic regularity in the discrete log-Sobolev inequality
Justin Salez, Pierre Youssef
The chain rule lies at the heart of the powerful Gamma calculus for Markov diffusions on manifolds, providing remarkable connections between several fundamental notions such as Bak…