Related papers: On the representation of bent functions by bent re…
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
Categorical data plays an important part in machine learning research and appears in a variety of applications. Models that can express large classes of real-valued functions on the Boolean cube are useful for problems involving…
It has been a long-standing goal in machine learning, as well as in AI more generally, to develop life-long learning systems that learn many different tasks over time, and reuse insights from tasks learned, "learning to learn" as they do…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
We develop representation theory approach to the study of special functions associated with toric varieties. In particular we show that the corresponding special functions are given by matrix elements of certain non-reductive Lie algebras
The Walsh--Hadamard spectrum of a bent function uniquely determines a dual function. The dual of a bent function is also bent. A bent function that is equal to its dual is called a self-dual function. The Hamming distance between a bent…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
Hypergraph Horn functions were introduced as a subclass of Horn functions that can be represented by a collection of circular implication rules. These functions possess distinguished structural and computational properties. In particular,…
We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational "rate function" representation.
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
Two classes of ternary bent functions of degree four with two and three terms in the univariate representation that belong to the completed Maiorana-McFarland class are found. Binomials are mappings $\F_{3^{4k}}\mapsto\fthree$ given by…
While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…