To analyze the randomness from training the NN, we trained 15 different realizations of the NN 1k network discussed in the previous section using the same training dataset. In Fig. , the average MSE loss across 𝑁 versus 𝑏 for each of these realizations of the NN 1k network are shown in gray and the average of these averages in black. There is substantial variability in the performance of the 15 NN 1k networks, with the best performing NN having a MSE loss that is an order of magnitude smaller than the worst performing NN. However, even the worst performing NN 1k has a MSE loss of about 10 -9 except near 𝑏 = 0, 1 where it is still below 10 -8 . Thus all of the NN 1k realizations are able to replicate the LS method as well as interpolate between training data points with low error.