nnR (version 0.1.0)

Tun: Tun: The function that returns tunneling neural networks

Description

Tun: The function that returns tunneling neural networks

Usage

Tun(n, d = 1)

Value

A tunnel neural network of depth n. A tunneling neural network is defined as the neural network \(\mathsf{Aff}_{1,0}\) for \(n=1\), the neural network \(\mathsf{Id}_1\) for \(n=1\) and the neural network \(\bullet^{n-2}\mathsf{Id}_1\) for \(n >2\). For this to work we must provide an appropriate \(n\) and instantiate with ReLU at some real number \(x\).

Arguments

n

The depth of the tunnel network where \(n \in \mathbb{N} \cap [1,\infty)\).

d

The dimension of the tunneling network. By default it is assumed to be \(1\).

References

Definition 2.17. 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

Tun(4)
Tun(4, 3) |> view_nn()

Tun(5)
Tun(5, 3)