4 papers · 1 filter
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…
On measures strongly log-concave on a subspace
Pierre Bizeul
In this work we study the concentration properties of log-concave measures that are curved only on a subspace of directions. Proofs uses an adapted version of the stochastic locali…
The slicing conjecture via small ball estimates
Pierre Bizeul
Bourgain's slicing conjecture was recently resolved by Joseph Lehec and Bo'az Klartag. We present an alternative proof by establishing small ball probability estimates for isotropi…