A neural network that approximates \(e^x\) for real \(x\) when
given appropriate \(n,q,\varepsilon\) and instnatiated with ReLU
activation at point\(x\).
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.
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