Related papers: Max-Min Neural Network Operators For Approximation…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…
This paper reports a novel deep architecture referred to as Maxout network In Network (MIN), which can enhance model discriminability and facilitate the process of information abstraction within the receptive field. The proposed network…
We study the approximation rates of a class of deep neural network approximations of operators which arise as data-to-solution maps $\mathcal{S}$ of linear elliptic partial differential equations (PDEs), and act between pairs $X,Y$ of…
The main purpose of this paper is to determine the approximations of Durrmeyer modification of Szasz-Mirakjan operators, defined by Mishra et al. (Boll. Unione Mat. Ital. (2016) 8(4):297-305). We estimate the order of approximation of the…
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…
The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth…
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…
We discuss how to evaluate the proximal operator of a convex and increasing function of a nuclear norm, which forms the key computational step in several first-order optimization algorithms such as (accelerated) proximal gradient descent…
Submodular optimization with bandit feedback has recently been studied in a variety of contexts. In a number of real-world applications such as diversified recommender systems and data summarization, the submodular function exhibits…
Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the performance in tasks with complex-valued inputs, such as in…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks…
We describe a method for approximating a single-variable function $f$ using persistence diagrams of sublevel sets of $f$ from height functions in different directions. We provide algorithms for the piecewise linear case and for the smooth…
We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint…
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the $i$-th neuron in a…
The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem supports using neural networks for various applications,…
This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may vary on a large range of scales.…
We study the approximation of multivariate functions with tensor networks (TNs), providing some answers to the following two questions: ``what are the approximation capabilities of TNs for functions from classical smoothness classes?'' and…
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…