Related papers: Identity Testing and Lower Bounds for Read-$k$ Obl…

A number of recent works have studied algorithms for entrywise $\ell_p$-low rank approximation, namely, algorithms which given an $n \times d$ matrix $A$ (with $n \geq d$), output a rank-$k$ matrix $B$ minimizing…

Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…

Let $A$ be an $(m \times n)$ integral matrix, and let $P=\{ x : A x \leq b\}$ be an $n$-dimensional polytope. The width of $P$ is defined as $ w(P)=min\{ x\in \mathbb{Z}^n\setminus\{0\} :\: max_{x \in P} x^\top u - min_{x \in P} x^\top v…

We study Online Linear Programming (OLP) with batching. The planning horizon is cut into $K$ batches, and the decisions on customers arriving within a batch can be delayed to the end of their associated batch. Compared with OLP without…

We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…

We address complexity issues for linear differential equations in characteristic $p>0$: resolution and computation of the $p$-curvature. For these tasks, our main focus is on algorithms whose complexity behaves well with respect to $p$. We…

The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…

We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given…

In this paper we show that the black-box polynomial identity testing for noncommutative polynomials $f\in\mathbb{F}\langle z_1,z_2,\cdots,z_n \rangle$ of degree $D$ and sparsity $t$, can be done in randomized $\poly(n,\log t,\log D)$ time.…

Nisan showed in 1991 that the width of a smallest noncommutative single-(source,sink) algebraic branching program (ABP) to compute a noncommutative polynomial is given by the ranks of specific matrices. This means that the set of…

We study exact active learning of binary and multiclass classifiers with margin. Given an $n$-point set $X \subset \mathbb{R}^m$, we want to learn any unknown classifier on $X$ whose classes have finite strong convex hull margin, a new…

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…

We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is $O(\log^2 n)$, where $n$ is the length of the branching…

$ \newcommand{\inparen}[1]{\left( #1 \right)} \newcommand{\pfrac}[2]{\inparen{\frac{1}{2}}} \newcommand{\ilog}[1]{\log^{\circ #1}} \newcommand{\F}{\mathbb{F}} $The Polynomial Identity Lemma (also called the "Schwartz--Zippel lemma") states…

A covering integer program (CIP) is a mathematical program of the form: min {c^T x : Ax >= 1, 0 <= x <= u, x integer}, where A is an m x n matrix, and c and u are n-dimensional vectors, all having non-negative entries. In the online…

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum…

We introduce the problem of constructing explicit variety evasive subspace families. Given a family $\mathcal{F}$ of subvarieties of a projective or affine space, a collection $\mathcal{H}$ of projective or affine $k$-subspaces is…

We study the problem of efficient PAC active learning of homogeneous linear classifiers (halfspaces) in $\mathbb{R}^d$, where the goal is to learn a halfspace with low error using as few label queries as possible. Under the extra assumption…

The Rotary Position Embedding (RoPE) mechanism has become a powerful enhancement to the Transformer architecture, which enables models to capture token relationships when encoding positional information. However, the RoPE mechanisms make…

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…