nnR (version 0.1.0)

MC: The MC neural network

Description

This function implements the 1-D approximation scheme outlined in the References.

Note: Only 1-D interpolation is implemented.

Usage

MC(X, y, L)

Value

A neural network that gives the maximum convolution approximation of a function whose outputs is \(y\) at \(n\) sample points given by each row of \(X\), when instantiated with ReLU.

Arguments

X

a list of samples from the functions domain.

y

the function applied componentwise to each point in the domain.

L

the Lipschitz constant for the function. Not necessarily global, but could be an absolute upper limit of slope, over the domain.

References

Lemma 4.2.9. Jentzen, A., Kuckuck, B., and von Wurstemberger, P. (2023). Mathematical introduction to deep learning: Methods, implementations, and theory. https://arxiv.org/abs/2310.20360.

Examples

seq(0, 3.1416, length.out = 200) -> X
sin(X) -> y
MC(X, y, 1) |> inst(ReLU, 0.25) # compare to sin(0.25)