Related papers: Approximation by multivariate neural network opera…
Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both to accelerate…
In this paper, we modify and apply the recently introduced Mixed Newton Method, which is originally designed for minimizing real-valued functions of complex variables, to the minimization of real-valued functions of real variables by…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions. Leveraging wavelet frame theory on the spaces of…
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…
In this article, we analyse the Kantorovich type exponential sampling operators and its linear combination. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional.…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
Images of integration operators of natural orders are considered as elements of Besov and Triebel--Lizorkin spaces with local Muckenhoupt weights on $\mathbb{R}^N$. The results connect entropy and approximation numbers of embedding…
In the present article, we deal with the overconvergence of the Sz?asz-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic…
We study uniform $\epsilon-$BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of $\epsilon,$ many geometric properties like smoothness,…
Inner products of neural network feature maps arise in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It…
This article starts with the fundamental theory of stochastic type convergence and the significance of uniform integrability in the context of expectation value. A novel probabilistic sampling kantorovich (PSK-operators) is established with…
We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on…
XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can…
Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $\mathbb{R}^n$ and $X$ a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Denote by…
Invertible neural networks (INNs) represent an important class of deep neural network architectures that have been widely used in several applications. The universal approximation properties of INNs have also been established recently.…
We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias…
Computer vision researchers have been expecting that neural networks have spatial transformation ability to eliminate the interference caused by geometric distortion for a long time. Emergence of spatial transformer network makes dream come…