no code implementations • 19 May 2020 • Joan Bruna, Oded Regev, Min Jae Song, Yi Tang
We introduce a continuous analogue of the Learning with Errors (LWE) problem, which we name CLWE.
no code implementations • 31 Oct 2017 • Oded Regev, Aravindan Vijayaraghavan
In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\delta$ using $poly(k, d, 1/\delta)$ samples.
no code implementations • 17 Feb 2015 • Oded Regev, Noah Stephens-Davidowitz
$ \newcommand{\R}{\ensuremath{\mathbb{R}}} \newcommand{\lat}{\mathcal{L}} \newcommand{\ensuremath}[1]{#1} $We show that for any lattice $\lat \subseteq \R^n$ and vectors $\vec{x}, \vec{y} \in \R^n$, \[ \rho(\lat + \vec{x})^2 \rho(\lat + \vec{y})^2 \leq \rho(\lat)^2 \rho(\lat + \vec{x} + \vec{y}) \rho(\lat + \vec{x} - \vec{y}) \; , \] where $\rho$ is the Gaussian measure $\rho(A) := \sum_{\vec{w} \in A} \exp(-\pi \| \vec{w} \|^2)$.
Probability Functional Analysis Number Theory