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