Related papers: Max-Min Neural Network Operators For Approximation…

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results…

In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution…

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator and on…

The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions $\sigma$, then a standard feedforward neural network with one hidden layer is able to approximate any…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

In this paper, we investigate the approximation behavior of both one and multidimensional neural network type operators for functions in $L^p(I^d,\rho)$, where $1\leq p<\infty$, associated with a general measure $\rho$ defined over a…

We present a probabilistic variant of the recently introduced maxout unit. The success of deep neural networks utilizing maxout can partly be attributed to favorable performance under dropout, when compared to rectified linear units. It…

Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…

In this paper we study the theory of the so-called Kantorovich max-product neural network operators in the setting of Orlicz spaces $L^{\varphi}$. The results here proved, extend those given by Costarelli and Vinti in Result Math., 2016, to…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…

We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…

In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized…

This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…

In this paper we introduce and study a class of structured set-valued operators which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued…

Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…

This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…

Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood,…

The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.).…

Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…