Top: Cross-entropy loss for one-hidden-layer instance of Parametric UMAP versus a neural network trained to predict nonparametric embeddings using MSE on MNIST. The same network architectures are used in each case. The $x$-axis varies the number of neurons in the network's single hidden layer layer. The dashed gray line is the loss for the nonparametric embedding. Bottom: Projections corresponding to the losses shown in the panel above.