Although we have focused on the MSE loss as a measure of the accuracy of a NN to this point, the number of black-white interfaces can also be used to characterize the degree of mixing that each NN realization produces . Each mixing step should create two additional black-white interfaces, although the creation of additional interfaces does not necessarily indicate that the NN is matching the LS method. To demonstrate this, a single NN 1k network is tasked with mixing the 10 000 evenly spaced (with respect to 𝑏) validation initial conditions for 31 steps. The number of interfaces for each of the 10 000 validation set initial conditions as it is mixed by NN 1k is shown in Fig. (a) as a function of the mixing step (𝑁 ). The diagonal line with slope 2 represents the optimal interface generation of two additional interfaces per step. Horizontal lines indicate that the NN does not create configurations with new interfaces at the step where the horizontal line departs from the diagonal line, which only happens when the NN erroneously places all three cut locations in the same color. The numbers at the right side of the figure indicate the number of validation configurations (out of 10 000) at 𝑁 = 31 have reached a particular number of interfaces. The majority of validation configurations, 8 590 out of 10 000, successfully create states that have 64 black-white interfaces at 𝑁 = 31, the maximum amount possible given the structure of the data. The remainder get stuck for 𝑁 < 31, even as early as 𝑁 = 1 in a small number of cases. Note that there are cases where the NN successfully adds a pair of interfaces even after several steps of non-mixing, evident as diagonal lines off the main diagonal.