nnR - Neural Networks Made Algebraic

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.