Positioning the black segment on the left and then cutting the leftmost segment of each color as in Fig. is necessary because the general IET mixing problem allows significant freedom in choosing which possible cut locations are used to perform the LS cut-and-shuffle. For states with several equivalent or nearly equivalent options for placing cuts, such as 𝑁 = 1 in Fig. , which has two equal length black segments and two equal length white segments, there are multiple sets of cut locations that are equally valid with respect to the principles of the LS method. The existence of multiple (nearly) equivalent mixing cut location options makes the problem too broad for the NN to learn in a general way without specifying additional criteria for the cut locations. Therefore, we add the criterion that the LS method should place cuts in the leftmost longest segment of each color, which specifies a left-to-right pattern that the NN can learn. 3 An NN is termed deep if there are more than three layers. A layer is termed densely connected if each neuron is connected to every neuron in the adjacent layers. The input to the NN, layer (a) in Fig. , is the 64element vector of segment endpoints representing the domain to be mixed. The output of the neural network, layer (f) in Fig. , is a set of three cut locations (indicated by blue triangles), 𝜒 𝑖 ∈ (0, 1), ordered such that, with respect to the LS method, 𝜒 1 is the center of the longest black segment, 𝜒 2 is the center of the longest white segment, and 𝜒 3 is the right edge of longest black segment. Although NNs can approximate any continuous function , the LS method is only piecewise linear. The LS method is not, for general configurations, a continuous function of its inputs, but the aforementioned left-to-right pattern in the training data allows for a wellbehaved continuous approximation to exist throughout the training data distribution, removing discontinuous behavior from the training data.