New points

A fitted model places new points in two ways.

Y_new = model.transform(X_new)
Y_opt = model.transform_opt(X_new, steps=200, lr=0.05)

transform

transform runs the new points through the trained flow once and keeps the first coordinates. It is fast, deterministic and part of the bijection, so the full latent of the same points from transform_latent decodes back exactly.

The forward pass places new points well relative to the global arrangement of the layout but finds their nearest neighbours poorly. On held-out MNIST points, 7% of the 15 nearest neighbours in the input were among the 15 nearest in the layout, against 35% with transform_opt.

transform_opt

transform_opt starts from the forward pass and then moves each new point, for steps Adam steps at rate lr, towards the layout positions of its 15 nearest training points in the input. The training layout stays fixed. This is the same kind of placement that UMAP's transform does, and it takes about two seconds for 50,000 points on a GPU.

The positions it returns are no longer outputs of the flow. inverse_transform decodes them like any other position, but they have no residual for inverse_latent.

Which to use

Use transform_opt when the neighbours of new points matter, for example to label them by their neighbours. Use transform when you need the map itself, for example to compare new points with the training data in the latent space or to decode them exactly.