comp

%comp%

The function that takes the composition of two neural
networks assuming they are compatible, i.e., given
\(\nu_1, \nu_2 \in \mathsf{NN}\), it must be the case that
\(\mathsf{I}(\nu)_1 = \mathsf{O}(\nu_2)\).

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

comp function

<dl><dt>phi_1</dt>
<dd>first neural network to be composed, goes on the left</dd>
<dt>phi_2</dt>
<dd>second neural network to be composed, goes on right</dd></dl>

Arguments

comp — comp

<dl>

<dt>phi_1</dt>
<dd>first neural network to be composed, goes on the left</dd>


<dt>phi_2</dt>
<dd>second neural network to be composed, goes on right</dd>

</dl>

comp: comp

Description

Usage

Value

Arguments

References

Examples