Sne {nnR}R Documentation

Sne

Description

Returns the Sne\mathsf{Sne} neural networks

Usage

Sne(n, q, eps)

Arguments

n

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

q

a real number in (2,)(2,\infty). Accuracy as well as computation time increases as qq gets closer to 22 increases

eps

a real number in (0,)(0,\infty). ccuracy as well as computation time increases as ε\varepsilon gets closer to 00 increases

Note: In practice for most desktop uses q<2.05q < 2.05 and ε<0.05\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\sin when given an appropriate n,q,εn,q,\varepsilon and instantiated with ReLU activation and given value xx.

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

[Package nnR version 0.1.0 Index]