Xpn {nnR}

The Xpn function

Description

The Xpn function

Usage

Xpn(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 e^x for real x when given appropriate n,q,\varepsilon and instnatiated with ReLU activation at pointx.

References

Definition 2.28 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

Xpn(3, 2.25, 0.25) # this may take some time

Xpn(3, 2.2, 0.2) |> inst(ReLU, 1.5) # this may take some time