Sqr {nnR}

Sqr

Description

A function that returns the $\mathsf{Sqr}$ neural networks.

Usage

Sqr(q, eps)

Arguments

q

a real number in $(2,\infty)$. Accuracy as well as computation time increases as $q$ gets closer to $2$ increases

eps

a real number in $(0,\infty)$. ccuracy as well as computation time increases as $\varepsilon$ gets closer to $0$ increases

Value

A neural network that approximates the square of a real number.when provided appropriate $q,\varepsilon$ and upon instantiation with ReLU, and a real number $x$

References

Proposition 3.4. Grohs, P., Hornung, F., Jentzen, A. et al. Space-time error estimates for deep neural network approximations for differential equations. (2019). https://arxiv.org/abs/1908.03833

#' @references Definition 2.24. Rafi S., Padgett, J.L., Nakarmi, U. (2024) Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials https://arxiv.org/abs/2402.01058

Examples

Sqr(2.5, 0.1)
Sqr(2.5, 0.1) |> inst(ReLU, 4)