I may be wrong, having just heard of self-organizing maps... But they do seem related, in that it’s arguing the data can always be (mostly) accurately represen

I may be wrong, having just heard of self-organizing maps... But they do seem related, in that it’s arguing the data can always be (mostly) accurately represented by a map projecting onto a lower-dimension manifold. The recent paper on topological covers along with the self-organizing maps wiki seem to indicate that nothing should be harmed by doing this in a discrete setting. Essentially, a self-organizing map projecting to the R^n slices, and then learning the shape of the manifold generated by that atlas of projections.