Related papers: Non-Linear Interactions in Neural Network Operator…
This paper explores the asymptotic behavior of univariate neural network operators, with an emphasis on both classical and fractional differentiation over infinite domains. The analysis leverages symmetrized and perturbed hyperbolic tangent…
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…
This paper extends the classical theory of Voronovskaya-type asymptotic expansions to generalized neural network operators defined on non-Euclidean and fractal domains. We introduce and analyze smooth operators activated by modified and…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
This work introduces rigorous convergence rates for neural network operators activated by symmetrized and perturbed hyperbolic tangent functions, utilizing novel Voronovskaya-Damasclin asymptotic expansions. We analyze basic, Kantorovich,…
Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
Here, we introduce three kinds of neural network operators of convolution type which are activated by q-deformed and \b{eta}-parametrized half hyperbolic tangent function. We obtain quantitative convergence results to the identity operator…
In the present paper, we introduce three neural network operators of convolution type activated by symmetrized, deformed and parametrized B-generalized logistic function. We deal with the approximation properties of these operators to the…
This paper establishes the Quantum Voronovskaya--Damasclin (QVD) Theorem, providing a complete asymptotic characterization of Quantum Neural Network Operators in the approximation of arbitrary quantum channels. The result extends the…
We consider solving a probably infinite dimensional operator equation, where the operator is not modeled by physical laws but is specified indirectly via training pairs of the input-output relation of the operator. Neural operators have…
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…
On the one hand, the framework of mixed norm spaces has potential applications in different areas of mathematics. On the other hand, neural network (NN) operators are well established as approximators, attracting significant attention in…
This work studies operators mapping vector and scalar fields defined over a manifold $\mathcal{M}$, and which commute with its group of diffeomorphisms $\text{Diff}(\mathcal{M})$. We prove that in the case of scalar fields…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
In this paper, we develop a multivariate framework for approximation by max-min neural network operators. Building on the recent advances in approximation theory by neural network operators, particularly, the univariate max-min operators,…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of…