相关论文: Squareplus: A Softplus-Like Algebraic Rectifier
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
We describe a purely-multiplicative method for extending an analytic function. It calculates the value of an analytic function at a point, merely by multiplying together function values and reciprocals of function values at other points…
Transformers have improved drastically the performance of natural language processing (NLP) and computer vision applications. The computation of transformers involves matrix multiplications and non-linear activation functions such as…
Addressing the imperative need for efficient artificial intelligence in IoT and edge computing, this study presents RepAct, a re-parameterizable adaptive activation function tailored for optimizing lightweight neural networks within the…
Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
We present an extension of the AAA (adaptive Antoulas--Anderson) algorithm for periodic functions, called 'AAAtrig'. The algorithm uses the key steps of AAA approximation by (i) representing the approximant in (trigonometric) barycentric…
This paper presents a quadratic formula-based nonlinear representation for a given single-variable function f(x), $-1 \leq x \leq 1$. First, we construct the explicit polynomial coefficient functions a(x), b(x), and c(x) using a…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in…
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and…
Softmax is widely used in deep learning to map some representation to a probability distribution. As it is based on exp/log functions that are relatively expensive in multi-party computation, Mohassel and Zhang (2017) proposed a simpler…
A "blendstring" is a piecewise polynomial interpolant with high-degree two-point Hermite interpolational polynomials on each piece, analogous to a cubic spline. Blendstrings are smoother and can be more accurate than cubic splines, and can…
Incrementalization speeds up computations by avoiding unnecessary recomputations and by efficiently reusing previous results. While domain-specific techniques achieve impressive speedups, e.g., in the context of database queries, they are…
Deep neural networks yield the state-of-the-art results in many computer vision and human machine interface applications such as object detection, speech recognition etc. Since, these networks are computationally expensive, customized…
The main contribution of this thesis is the development of a new algorithm for solving convex quadratic programs. It consists in combining the method of multipliers with an infeasible active-set method. Our approach is iterative. In each…
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the…