I have a neural network that maps my data samples to a 64-dimensional embedding. I wish to visualize a few of these embeddings (between 30 and 600) through a 2-dimensional projection, and I plan to use umap to do that. Would providing more embeddings sampled from the dataset along with the ones I want to project help the algorithm to identify the manifold and improve the quality of projection?
Yes, more data will improve the quality of the embedding UMAP can produce. While UMAP is somewhat robust/stable under subsampling in general you will get significantly better results with more data. It is also worth noting that most UMAP implementations are not designed for very small datasets (they make some optimization choices that assume a a reasonable dataset size). In practice it is probably best not to use UMAP with less than 100 or so data samples.