Related papers: The universal approximation theorem for complex-va…
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…
The universal approximation theorem asserts that a single hidden layer neural network approximates continuous functions with any desired precision on compact sets. As an existential result, the universal approximation theorem supports the…
Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation…
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,…
We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functions $\varrho:\mathbb{C}\to \mathbb{C}$ that have the property…
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…
This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These neural networks are simple because they are designed with a…
The classical Universal Approximation Theorem holds for neural networks of arbitrary width and bounded depth. Here we consider the natural `dual' scenario for networks of bounded width and arbitrary depth. Precisely, let $n$ be the number…
This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approximation within weighted $C^k$-spaces and weighted Sobolev…
The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studied in many papers. Such networks can…
The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby…
Complex-valued neural networks have attracted increasing attention in recent years, while it remains open on the advantages of complex-valued neural networks in comparison with real-valued networks. This work takes one step on this…
The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb{R}^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden…
In this paper, we explain the universal approximation capabilities of deep residual neural networks through geometric nonlinear control. Inspired by recent work establishing links between residual networks and control systems, we provide a…
We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more.…
We study shallow and deep neural networks whose inputs range over a general topological space. The model is built from a prescribed family of continuous feature maps and reduces to multilayer feedforward networks in the Euclidean case. We…
We present the Input-Connected Multilayer Perceptron (IC-MLP), a feedforward neural network architecture in which each hidden neuron receives, in addition to the outputs of the preceding layer, a direct affine connection from the raw input.…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…
Feedforward neural networks have wide applicability in various disciplines of science due to their universal approximation property. Some authors have shown that single hidden layer feedforward neural networks (SLFNs) with fixed weights…