ParameticUMAP does not separate classes in supervised regime, while UMAP does

Hello, I have a peculiar situation with ParametricUMAP. I have 12000 kind-of 8x8 images, which I want to reduce to 2 dimensions. Each image has a class label (0 or 1). The two classes are perfectly separated if I use regular UMAP in a supervised mode, however, applying the transform to new data points is painfully slow. It takes ca. 5 seconds for a single 8x8 image. My data comes in batches of 1 sample and thus I cannot combine multiple images into a single batch to speed up processing.

So I decided to try ParametricUMAP, which should help me to speed up the inference. But when applying ParametricUMAP to my data I completely lose class separation and the result looks very much like unsupervised UMAP.
Here is how it looks for supervised parametric

and unsupervised regular UMAP

I tried setting target_weight to 0.9 and it didn't change a thing.
Any idea what's causing such behavior?

Thank you.

Start by reproducing the supervised ParametricUMAP behavior with the 8x8 images, binary labels, and target_weight=0.9 described in the issue, then compare it with supervised regular UMAP and unsupervised UMAP. Done means identifying why class separation is lost or documenting the relevant limitation while preserving the intended faster inference for single-sample batches.