Although neural networks are only one ML model among hundreds commonly utilized in data science, they have come to dominate much of the recent literature on ML-based XRD analysis. As such, they are briefly discussed here using a diffraction pattern as an example. This example is adapted from ref 66 ch. 18. We consider XRD patterns 𝑘 = 1 … 𝑁 where each pattern is represented by intensities vector 𝑥 of length M. This dataset is represented by an N x M matrix 𝑋 where each row is an XRD pattern 𝑥 . Assume each pattern corresponds to a value 𝑦 or 𝑦 representing a majority phase identity. If the XRD patterns consist of well-defined phases with non-overlapping peaks, an optimal decision boundary plane exists that divides vectors 𝑥 … 𝑥 into two groups. The equation of this plane has the form 𝑏 + 𝑋𝑤 = 0, where 𝑤 is the 𝑀-length vector normal to the dividing plane. The goal of this problem is to solve for 𝑤. This is the basis of the single layer perceptron model with linear activation function: if 𝑦(𝑥) = 𝑏 + 𝑤𝑋 is greater than 0, we classify the pattern as 𝑦 , and otherwise 𝑦 . Consider then a more complex problem of a dataset with many phases 𝑦 … 𝑦 . A single decision boundary can only distinguish 2 phases and cannot generalize to multiple phases. However, this problem can be solved by the combination of many simple decision boundaries. This is the conceptual foundation of neural networks: that complex decisions can be made from the agglomeration and abstraction of simple computational units.