8 papers
Optimal bounds for convex bodies
Pierre Bizeul
Let be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequal…
Distances between non-symmetric convex bodies: optimal bounds up to polylog
Pierre Bizeul, Boaz Klartag
In this paper we determine, up to polylogarithmic factors, the diameter of the Banach--Mazur compactum of -dimensional convex bodies without symmetry assumptions. We prove that…
Minimum Norm Interpolation via the Local Theory of Banach Spaces: The Role of -Uniform Convexity
Gil Kur, Pierre Bizeul
The minimum-norm interpolator (MNI) framework has recently attracted considerable attention as a tool for understanding generalization in overparameterized models, such as neural n…
On the Log-Sobolev Constant of Log-Concave Vectors
Pierre Bizeul
It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whethe…
Entropy and Learning of Lipschitz Functions under Log-Concave Measures
Pierre Bizeul, Boaz Klartag
We study regression of -Lipschitz functions under a log-concave measure on . We focus on the high-dimensional regime where the sample size is subexponenti…
Polynomial Approximation in of the Double Exponential via Complex Analysis
Pierre Bizeul, Boaz Klartag
We study the polynomial approximation problem in where . We show that for any absolutely continuous function , $$ \sum_{k=1}^{\infty} \log^…