Sum {nnR}

Sum

Description

The function that returns $\mathsf{Sum}$ neural networks.

These are neural networks defined as such

$\mathsf{Aff}_{\left[ \mathbb{I}_k \: \mathbb{I}_k \: \cdots \: \mathbb{I}_k\right],0_{k}}$

Usage

Sum(n, k)

Arguments

n

number of copies of a certain vector to be summed.

k

the size of the summation vector.

Value

An affine neural network that will take a vector of size $n \times k$ and return the summation vector that is of length $k$. See also Aff and Cpy.

References

Definition 2.10. 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