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We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {-1,1}^n. This result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the…
Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved…
We describe an implementation of a genetic algorithm on partially commutative groups and apply it to the double coset search problem on a subclass of groups. This transforms a combinatorial group theory problem to a problem of combinatorial…
Low-light image enhancement remains an open problem, and the new wave of artificial intelligence is at the center of this problem. This work describes the use of genetic algorithms for optimizing analytical models that can improve the…
Solving an optimization task in any domain is a very challenging problem, especially when dealing with nonlinear problems and non-convex functions. Many meta-heuristic algorithms are very efficient when solving nonlinear functions. A…
We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the…
Learning-based binary hashing has become a powerful paradigm for fast search and retrieval in massive databases. However, due to the requirement of discrete outputs for the hash functions, learning such functions is known to be very…
Zero-free based algorithm is a major technique for deterministic approximate counting. In Barvinok's original framework[Bar17], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
The Function Field Sieve algorithm is dedicated to computing discrete logarithms in a finite field GF(q^n), where q is small an prime power. The scope of this article is to select good polynomials for this algorithm by defining and…
Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of…
Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth,…
The generalized quadratic assignment problem (GQAP) is one of the hardest problems to solve in the operations research area. The GQAP addressed in this work is defined as the task of minimizing the assignment and transportation costs of…
Recent work has shown the surprising power of low-degree sandwiching polynomial approximators in the context of challenging learning settings such as learning with distribution shift, testable learning, and learning with contamination. A…
In this paper, we consider the problem of finding perfectly balanced Boolean functions with high non-linearity values. Such functions have extensive applications in domains such as cryptography and error-correcting coding theory. We provide…
We introduce Probabilistic Gaussian Homotopy (PGH), a probability-space continuation framework for nonconvex optimization. Unlike classical Gaussian homotopy, which smooths the objective and uniformly averages gradients, PGH deforms the…
Functions of chemical composition are complex and discrete in nature making it impossible to optimize them with gradient methods. Genetic algorithms, which do not use derivative information, are used to maximize the thermal conductivity of…
Here we present some revised arguments to a randomized algorithm proposed by Sudan to find the polynomials of bounded degree agreeing on a dense fraction of a set of points in $\mathbb{F}^{2}$ for some field $\mathbb{F}$.