nnR (version 0.1.0)

Mxm: Mxm

Description

The function that returns the \(\mathsf{Mxm}\) neural networks.

Note: Because of certain quirks of R we will have split into five cases. We add an extra case for \(d = 3\). Unlike the paper we will simply reverse engineer the appropriate d.

Usage

Mxm(d)

Value

The neural network that will ouput the maximum of a vector of size \(d\) when activated with the ReLU function.

For a specific definition, see:

Arguments

d

The dimension of the input vector on instantiation.

References

Lemma 4.2.4. 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

Mxm(1) |> inst(ReLU, -5)
Mxm(3) |> inst(ReLU, c(4, 5, 1))
Mxm(5) |> inst(ReLU, c(5, 3, -1, 6, 6))