comp {nnR}

comp

Description

The function that takes the composition of two neural networks assuming they are compatible, i.e., given \nu_1, \nu_2 \in \mathsf{NN}, it must be the case that \mathsf{I}(\nu)_1 = \mathsf{O}(\nu_2).

Usage

comp(phi_1, phi_2)

phi_1 %comp% phi_2

Arguments

phi_1

first neural network to be composed, goes on the left

phi_2

second neural network to be composed, goes on right

Value

The composed neural network. See also dep.

Our definition derive specifically from:

References

Definition 2.1.1. Jentzen, A., Kuckuck, B., and von Wurstemberger, P. (2023). Mathematical introduction to deep learning: Methods, implementations, and theory. https://arxiv.org/abs/2310.20360

Remark: We have two versions of this function, an infix version for close resemblance to mathematical notation and prefix version.

Examples

create_nn(c(5, 4, 6, 7)) |> comp(create_nn(c(4, 1, 5)))