A very common workflow is to index some data based on its embeddings and then given a new query embedding retrieve the most similar examples with k-Nearest Neighbor search. For example, you can imagine embedding a large collection of papers by their abstracts and then given a new paper of interest retrieve the most similar papers to it.
TLDR in my experience it ~always works better to use an SVM instead of kNN, if you can afford the slight computational hit
P. Pantel, и D. Lin. Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining, стр. 613--619. New York, NY, USA, ACM, (2002)