for gs point proton rms radius. The optimum number of neurons in the hidden layer was obtained according to a trial and error process.

![Topological structure of the designed ANN.[]{data-label="fig:ANN_architecture"}](ANN_architecture-eps-converted-to.pdf){width="\linewidth"}

The *activation* function employed for the hidden layer was a widely-used form, the *hyperbolic tangent sigmoid* function $$\label{eq:tansig}
    f(x) = tansig(x) = \frac{2}{(1 + e^{-2x})} - 1,$$ where $x$ is the input value of the hidden neuron and $f(x)$ is the output of the hidden neuron. $tansig$ is mathematically equivalent to the *hyperbolic tangent function*, $tanh$, but it improves network functionality because it runs faster than $tanh$. It has been proven that one hidden layer and *sigmoid*-like *activation* function in this layer are sufficient to approximate any continuous real function, given sufficient number of neurons in the hidden layer [@CYBENKO:1989]. MATLAB software v9.2.0 (R2017a) with *Neural Network Toolbox* was used for the implementation of this work. As mentioned before in Section \[sec:Introduction\], the data set for $^6\mathrm{Li}$ was taken from the ab initio NCSM calculations with the MFDn code using the Daejeon16 NN interaction [@SHIROKOV:2016] and basis spaces up through $N_{\rm max} = 18$. However, only the data with even $N_{\rm max}$ values corresponding to “natural" parity states and up 