Related papers: Approximation by Steklov Neural Network Operators
For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim(N\ge1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the…
Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of these methods often depend on traditional eigensolvers, which…
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…
A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…
A class of algorithms comprised by certain semismooth Newton and active-set methods is able to solve convex minimization problems involving sparsity-inducing regularizers very rapidly; the speed advantage of methods from this class is a…
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…
In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradient descent algorithm on a submanifold of the Stiefel…
We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the…
Neural operators serve as universal approximators for general continuous operators. In this paper, we derive the approximation rate of solution operators for the nonlinear parabolic partial differential equations (PDEs), contributing to the…
Time series, spatial data, and images are natural applications of Neural Processes. However, when such data exhibit strong periodicity and quasi-periodicity, existing methods often suffer from underfitting and generalise poorly beyond the…
In the present paper, the authors introduce and investigate new sequences of positive linear operators which include some well known operators as special cases. Here we estimate the rate of convergence for functions having derivatives of…
The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and $A$-statistical convergence are established. Our results are based on a $\rho$ function. These results include the…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer the problem of uniform approximation of continuous functions on closed bounded interval and the problem of…
The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the…
Current state-of-the-art analyses on the convergence of gradient descent for training neural networks focus on characterizing properties of the loss landscape, such as the Polyak-Lojaciewicz (PL) condition and the restricted strong…
In this Master Thesis, we study the approximation capabilities of Neural Networks in the context of numerical resolution of elliptic PDEs and Approximation Theory. First of all, in Chapter 1, we introduce the mathematical definition of…