  Modern methods in dimensionality reduction are dominated by nonlinear
attraction-repulsion force-based methods (this includes t-SNE, UMAP,
ForceAtlas2, LargeVis, and many more). The purpose of this paper is to
demonstrate that all such methods, by design, come with an additional feature
that is being automatically computed along the way, namely the vector field
associated with these forces. We show how this vector field gives additional
high-quality information and propose a general refinement strategy based on
ideas from Morse theory. The efficiency of these ideas is illustrated
specifically using t-SNE on synthetic and real-life data sets.
