We study learning algorithms for two sparse variants of the classical learning parity with
noise (LPN) problem. We provide a new algorithmic framework that improves the state of the …

The exponent $\sigma (T) $ of a tensor $ T\in\mathbb {F}^ d\otimes\mathbb {F}^
d\otimes\mathbb {F}^ d $ over a field $\mathbb {F} $ captures the base of the exponential …

We study the average-case version of the Orthogonal Vectors problem, in which one is given
as input n vectors from {0, 1} d which are chosen randomly so that each coordinate is 1 …

Abstract The Johnson-Lindenstrauss family of transforms constitutes a key algorithmic tool
for reducing the dimensionality of a Euclidean space with low distortion of distances …

We study the algorithmic problem of sparse mean estimation in the presence of adversarial
outliers. Specifically, the algorithm observes a\emph {corrupted} set of samples from …

We present an $ O^*(|\mathbb {F}|^{\min\left\{R,\\sum_ {d\ge 2} n_d\right\}+(R-n_0)(\sum_
{d\ne 0} n_d)}) $-time algorithm for determining whether the rank of a concise tensor …

We present an $ O^*\left (|\mathbb {F}|^{(R-n_*)\left (\sum_d n_d\right)+ n_*}\right) $-time
algorithm for determining whether a tensor of shape $ n_0\times\dots\times n_ {D-1} $ over a …

The light bulb problem aims to distinguishing correlated vectors among random vectors. In
this report, we summarize existing algorithms and explore a novel sequential formulation of …