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Univariate polynomial root-finding has been studied for four millennia and very intensively in the last decades. Our new near-optimal root-finders approximate all zeros of a polynomial p almost as fast as one accesses its coefficients with…
Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…
We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a…
In this paper, an original reduction algorithm for solving simultaneous multivariate polynomial equations is presented. The algorithm is exponential in complexity, but the well-known algorithms, such as the extended Euclidean algorithm and…
The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…
We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…
Blackbox algorithms for linear algebra problems start with projection of the sequence of powers of a matrix to a sequence of vectors (Lanczos), a sequence of scalars (Wiedemann) or a sequence of smaller matrices (block methods). Such…
Let $\Omega$ be a finite set of finitary operation symbols. An $\Omega$-expanded group is a group (written additively and called the additive group of the $\Omega$-expanded group) with an $\Omega$-algebra structure. We use the black-box…
We present a symbolic perturbation scheme for arbitrary polynomial geometric predicates which combines the benefits of Emiris and Canny's simple randomized linear perturbation scheme with Yap's multiple infinitesimal scheme for general…
We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the…
[PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian groups and finite meta-cyclic groups. We prove that for a dense set of positive integers $n$, isomorphism testing for abelian groups of black-box type of order $n$…
We present a deterministic algorithm which computes the multilinear factors of multivariate lacunary polynomials over number fields. Its complexity is polynomial in $\ell^n$ where $\ell$ is the lacunary size of the input polynomial and $n$…
Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…
Weakly supervised text classification methods typically train a deep neural classifier based on pseudo-labels. The quality of pseudo-labels is crucial to final performance but they are inevitably noisy due to their heuristic nature, so…
We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample…
We present a meta-algorithm for learning a posterior-inference algorithm for restricted probabilistic programs. Our meta-algorithm takes a training set of probabilistic programs that describe models with observations, and attempts to learn…
The paper examines hierarchies for nondeterministic and deterministic ordered read-$k$-times Branching programs. The currently known hierarchies for deterministic $k$-OBDD models of Branching programs for $ k=o(n^{1/2}/\log^{3/2}n)$ are…