Csn {nnR}

Csn

Description

The function that returns $\mathsf{Csn}$.

Usage

Csn(n, q, eps)

Arguments

n

The number of Taylor iterations. Accuracy as well as computation time increases as $n$ increases

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

Note: In practice for most desktop uses $q < 2.05$ and $\varepsilon< 0.05$ tends to cause problems in "too long a vector", atleaast as tested on my computer.

Value

A neural network that approximates $\cos$ under instantiation with ReLU activation. See also Sne.

References

Definition 2.29 in 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

Csn(2, 2.5, 0.5) # this may take some time

Csn(2, 2.5, 0.5) |> inst(ReLU, 1.50)