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