Related papers: Efficient implementation of elementary functions i…
Intermediate task fine-tuning has been shown to culminate in large transfer gains across many NLP tasks. With an abundance of candidate datasets as well as pre-trained language models, it has become infeasible to run the cross-product of…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…
This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor…
The Median of Medians (also known as BFPRT) algorithm, although a landmark theoretical achievement, is seldom used in practice because it and its variants are slower than simple approaches based on sampling. The main contribution of this…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
In 2013, Henn proposed a special basis for a certain class of master integrals, which are expressible in terms of iterated integrals. In this basis, the master integrals obey a differential equation, where the right hand side is…
We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield exact limits and often give rise to…
In this paper we use Python to implement two efficient modular exponentiation methods: the adaptive m-ary method and the adaptive sliding-window method of window size k, where both m's are adaptively chosen based on the length of exponent.…
With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL). In this paper, we propose a general framework that unifies model-based and…
We count algebraic points of bounded height and degree on the graphs of certain functions analytic on the unit disk, obtaining a bound which is polynomial in the degree and in the logarithm of the multiplicative height. We combine this work…
In this paper we obtain several informative error bounds on function approximation for the policy evaluation algorithm proposed by Basu et al. when the aim is to find the risk-sensitive cost represented using exponential utility. The main…
The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
Large language models (LLMs) have revolutionized AI applications, yet their enormous computational demands severely limit deployment and real-time performance. Quantization methods can help reduce computational costs, however, attaining the…
The growing demands of the worldwide IT infrastructure stress the need for reduced power consumption, which is addressed in so-called transprecision computing by improving energy efficiency at the expense of precision. For example, reducing…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
We revisit the widely used bss eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by…
In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and…