Related papers: Applications of AAA rational approximation
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
Stochastic Approximation (SA) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We show that suitably regular functions can be approximated in the $\mathcal{C}^1$-norm both with rational functions and rational neural networks, including approximation rates with respect to width and depth of the network, and degree of…
The Artificial Neural network is a functional imitation of simplified model of the biological neurons and their goal is to construct useful computers for real world problems. The ANN applications have increased dramatically in the last few…
The rapid expansion of scientific data has widened the gap between analytical capability and research intent. Existing AI-based analysis tools, ranging from AutoML frameworks to agentic research assistants, either favor automation over…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
This paper presents a novel algorithm, based on use of rational approximants of a randomly scalarized boundary integral resolvent in conjunction with an adaptive search strategy and an exponentially convergent secant-method termination…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
We introduce Iterated Integrated Attributions (IIA) - a generic method for explaining the predictions of vision models. IIA employs iterative integration across the input image, the internal representations generated by the model, and their…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
The concept of rationality is central to the field of artificial intelligence (AI). Whether we are seeking to simulate human reasoning, or trying to achieve bounded optimality, our goal is generally to make artificial agents as rational as…
The rational Landen transformations are used to produce a highly efficient numerical method for the integration of rational functions.
This article establishes a complete approximate axiomatization for the real-closed field $\mathbb{R}$ expanded with all differentially-defined functions, including special functions such as $\sin(x), \cos(x), e^x, \dots$. Every true…
Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation…
The utilization of distributed arithmetic (DA) in AF algorithms has gained significant attention in recent years due to its potential to enhance computational efficiency and reduce resource requirements. This paper presents an exploration…
Artificial Intelligence (AI) applications in automation systems are usually distributed systems whose development and integration involve several experts. Each expert uses its own domain-specific modeling language and tools to model the…
In the paper, a novel distributed stochastic approximation algorithm (DSAA) is proposed to seek roots of the sum of local functions, each of which is associated with an agent from the multiple agents connected in a network. At any time,…