Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials

We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that, yes, indeed, it makes sense to talk about neural network polynomials, neural network exponentials, sine, and cosines in the sense that they do indeed approximate their real number counterparts subject to limitations on certain of their parameters, $q$, and $\varepsilon$. While doing this, we show that the parameter and …

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