is_nn

Function to create a list of lists for neural network layers

Do algebraic operations on neural networks. We seek here to implement
in R, operations on neural networks and their resulting approximations. Our operations derive
their descriptions mainly from
Rafi S., Padgett, J.L., and Nakarmi, U. (2024), "Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials", <doi:10.48550/arXiv.2402.01058>,
Grohs P., Hornung, F., Jentzen, A. et al. (2023), "Space-time error estimates for deep neural network approximations for differential equations", <doi:10.1007/s10444-022-09970-2>,
Jentzen A., Kuckuck B., von Wurstemberger, P. (2023), "Mathematical Introduction to Deep Learning Methods, Implementations, and Theory" <doi:10.48550/arXiv.2310.20360>.
Our implementation is meant mainly as a pedagogical tool, and proof of concept. Faster implementations with
deeper vectorizations may be made in future versions.

Shakil Rafi

Neural Networks Made Algebraic

Joshua Lee Padgett

Ukash Nakarmi

is_nn function

<dl><dt>nn</dt>
<dd>A neural network. Neural networks are defined to be an ordered
list of ordered pairs of \((W,b)\). Where \(W\) is the matrix
representing the weight matrix \(W\) at that layer and \(b\) the bias vector.</dd></dl>

Arguments

is_nn — is_nn

<dl>

<dt>nn</dt>
<dd>A neural network. Neural networks are defined to be an ordered
list of ordered pairs of \((W,b)\). Where \(W\) is the matrix
representing the weight matrix \(W\) at that layer and \(b\) the bias vector.</dd>

</dl>

is_nn: is_nn

Description

Usage

Value

Arguments

References

Examples