Prd {nnR}

Prd

Description

A function that returns the $\mathsf{Prd}$ neural networks that approximates the product of two real numbers when given an appropriate $q$, $\varepsilon$, a real number $x$ and instantiation with ReLU. activation.

Usage

Prd(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 takes in $x$ and $y$ and approximately returns $xy$ when instantiated with ReLU activation, and given a list c(x,y), the two numbers to be multiplied.

Note that this must be instantiated with a tuple c(x,y)

References

Proposition 3.5. 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

Definition 2.25. 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

Prd(2.1, 0.1) |> inst(ReLU, c(4, 5)) # This may take some time, please only click once