In the field of machine learning, the universal approximation theorems state that neural networks with a certain structure can, in principle, approximate...

{\displaystyle k} input units. Theorem. (Theorem 3.1.1): The parity function is conjunctively local of order n {\displaystyle n} . Theorem. (Section 5.5): The connectedness...

In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous...

interpreted in terms of the universal approximation theorem or probabilistic inference. The classic universal approximation theorem concerns the capacity of...

architecture to finite-dimensional neural networks, similar universal approximation theorems have been proven for neural operators. In particular, it has...

Time hierarchy theorem (computational complexity theory) Toda's theorem (computational complexity theory) Universal approximation theorem (artificial neural...

of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is the de Moivre–Laplace theorem. Let { X...

field of scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep...

and infrastructure protection. He is known for proving the universal approximation theorem for artificial neural networks with sigmoid activation functions...

Concepts and Theorems of Mathematical Statistics. New York: Springer-Verlag. ISBN 0-387-96186-0. Serfling, Robert J. (1980). Approximation Theorems of Mathematical...

enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange...

innovation. The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive...

neural network can be proven to be a universal function approximator. This is known as the Universal Approximation Theorem. The identity activation function...

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate...

 467–474), Nilsson (1998, chpt. 3.3) Universal approximation theorem: Russell & Norvig (2021, p. 752) The theorem: Cybenko (1988), Hornik, Stinchcombe...

translates to a much more lightweight network. According to the universal approximation theorem, provided adequate learning, sufficient number of hidden units...

differentiable activation functions, such that the conditions for the universal approximation theorem holds. It is shown that this method provides a strongly consistent...

theory of rough paths. Together with Patrick Kidger he proved a universal approximation theorem for neural networks of arbitrary depth. Lyons obtained his...

continuous function on compact subsets of Rn as shown by the universal approximation theorem, thus it can have an arbitrary decision boundary. In particular...

K} letters of that proof. The PCP theorem is the cornerstone of the theory of computational hardness of approximation, which investigates the inherent...

topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional...

Williams to learn internal representations. 1988 Discovery Universal approximation theorem Kurt Hornik [de] proves that standard multilayer feedforward...

^{2n+1}} , proved by combining Whitney embedding theorem for manifolds and the universal approximation theorem for neural networks. To regularize the flow...

set, with no bound on its length. So, the Solovay–Kitaev theorem shows that this approximation can be made surprisingly efficient, thereby justifying that...

& Tarjan (1980) observed that the separator theorem may be used to obtain polynomial time approximation schemes for NP-hard optimization problems on...

1975 and is sometimes known as Voronin's universality theorem. A mathematically precise statement of universality for the Riemann zeta function  ζ(s)  follows...

self-Avoiding, Simple, and Self-similar curves) can be thought of as finite approximations of a certain type of space-filling curves. Intuitively, a curve in two...

Cybenko, known for proving one of the first versions of the universal approximation theorem of neural networks. The magazine is interdisciplinary and covers...

(2021-03-18). "Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators". Nature Machine Intelligence. 3 (3): 218–229...

relativity, but the universality of the gravitational constant is intact and the law still continues to be used as an excellent approximation of the effects...