Aff {nnR}

Aff

Description

The function that returns \mathsf{Aff} neural networks.

Usage

Aff(W, b)

Arguments

W

An m \times n matrix representing the weight of the affine neural network

b

An m \times 1 vector representing the bias of the affine neural network

Value

Returns the network ((W,b)) representing an affine neural network. Also denoted as \mathsf{Aff}_{W,b} See also Cpy and Sum.

References

Definition 2.3.1. Jentzen, A., Kuckuck, B., and von Wurstemberger, P. (2023). Mathematical introduction to deep learning: Methods, implementations, and theory. https://arxiv.org/abs/2310.20360

And especially:

Definition 2.8. 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

Aff(4, 5)
c(5, 6, 7, 8, 9, 10) |>
  matrix(2, 3) |>
  Aff(5)