Understanding how stem cells organize to form early tissue layers remains an important open question in developmental biology. Helpful in understanding this process are biomarkers or features that signal when a significant transition or decision occurs. We show such features from the spatial layout of the cells in a colony are sufficient to train neural networks to classify stem cell colonies according to differentiation protocol treatments each colony has received. We use topological data analysis to derive input information about the cells' positions to a four-layer feedforward neural network. We find that despite the simplicity of this approach, such a network has performance similar to the traditional image classifier ResNet. We also find that network performance may reveal the time window during which differentiation occurs across multiple conditions.