Tun {nnR}

Tun: The function that returns tunneling neural networks

Description

Tun: The function that returns tunneling neural networks

Usage

Tun(n, d = 1)

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 $1$.

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 $x$.

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)