A Parametric UMAP's sampling and effective loss function In Parametric UMAP [

The loss is computed for this mini-batch and then the parameters of the neural network are updated via stochastic gradient descent. UMAP: First, since automatic differentiation is used, not only the head of a negative sample edge is repelled from the tail but both repel each other. Second, the same number of edges are sampled in each epoch. This leads to a different repulsive weight for Parametric UMAP as described in Theorem A.1. Parametric UMAP's negative sampling is uniform from a batch that is itself sampled Since UMAP's implementation considers a point its first nearest neighbor, but the C Computing the expected gradient of UMAP's optimization procedure In this appendix, we show that the expected update in UMAP's optimization scheme does not It is continuously differentiable unless two embedding points coincide.