Sne {nnR}

Sne

Description

Returns the $\mathsf{Sne}$ neural networks

Usage

Sne(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 $\sin$ when given an appropriate $n,q,\varepsilon$ and instantiated with ReLU activation and given value $x$.

References

Definition 2.30. 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

Sne(2, 2.3, 0.3) # this may take some time, click only once and wait

Sne(2, 2.3, 0.3) |> inst(ReLU, 1.57) # this may take some time, click only once and wait