Etr {nnR}

Etr

Description

The function that returns the \mathsf{Etr} networks.

Usage

Etr(n, h)

Arguments

n

number of trapezoids to make. Note this will result in a set of trapezoids. A natural number.

h

width of trapezoids. A positive real number.

Note: Upon instantiation with any continuous function this neural network must be fed with n+1 real numbers representing the values of the function being approximated at the n+1 meshpoints which are the legs of the n trapezoids as stipulated in the input parameter n..

Value

An approximation for value of the integral of a function. Must be instantiated with a list of n+1 reals

References

Definition 2.33. 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

Etr(5, 0.1)
seq(0, pi, length.out = 1000) |> sin() -> samples
Etr(1000 - 1, pi / 1000) |> inst(ReLU, samples)

seq(0, 2, length.out = 1000)^2 -> samples
Etr(1000 - 1, 2 / 1000) |> inst(Tanh, samples)