And (if I'm understanding correctly) vectors that are near each other (in a mathematical sense) represent inputs that are "near" each other (in a conceptual sense).
So... a vector database can be organized to quickly retrieve objects with particular characteristics, without rigidly defining what those characteristics are.
Yup I think you got it perfectly. Just a small note: yes one isn’t rigidly defining what those characteristics are while finding similar embeddings (aka nearest vectors using some distance metric), but those characteristics are implicitly encoded in the model that creates the embeddings depending on how the model is trained.
So... a vector database can be organized to quickly retrieve objects with particular characteristics, without rigidly defining what those characteristics are.
Have I got it?