It's actually not asymmetric embeddings, but rather asymmetric searches. This is referring to the case where the query and documents being search against are no

It's actually not asymmetric embeddings, but rather asymmetric searches. This is referring to the case where the query and documents being search against are not interchangeable. If the query and documents are interchangeable, then that's symmetric search. It has implications for retrieval. There are embeddings models that are optimized for the symmetric search use case, and then there are models optimized for asymmetric search. You have to use the appropriate model for the task. Furthermore, you can use a LLM to transform your query into the same class as the docs being retrieved, to turn asymmetric search into symmetric search.