Related papers: Limitations of Sums of Bounded-Read Formulas
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
The paper proves sum-of-square-of-rational-function based representations (shortly, sosrf-based representations) of polynomial matrices that are positive semidefinite on some special sets: $\mathbb{R}^n;$ $\mathbb{R}$ and its intervals…
Determining I/O lower bounds is a crucial step in obtaining communication-efficient parallel algorithms, both across the memory hierarchy and between processors. Current approaches either study specific algorithms individually, disallow…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
Expansive polynomials (whose roots are greater than 1 in modulus) often arise in dynamical systems and other computational problems. This paper examines the expansivity gap (the gap between 1 and the smallest modulus of the roots) of these…
We obtain sharp upper bounds for three-term segments of a bounded power series. Along the way we show that the Taylor polynomials of a certain algebraic function do not vanish in the unit disk.
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training,…
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…
The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of general non-conservative systems of hyperbolic balance laws can be rewritten as a finite-volume-type formula, also known as flux-differencing formula, if…
In this paper, we present some explicit exponents in the estimates for the volumes of sub-level sets of polynomials on bounded sets, and applications to the decay of oscillatory integrals and the convergent of singular integrals.
In this paper, we study the distribution of difference of multiplicative and additive characters modulo $p$ at consecutive polynomial values. More precisely, for an interval $I$ over finite field and $0<m<1$, we investigate the following…
The joint spectral radius of a bounded set of $d \times d$ real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn…