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For example, you can create an embedding for an image using a neural net that has been trained to receive an image and output a vector of 1024 floats, which represent the content of the image. This vector is a lossy compressed version of the image.

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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.

Have I got it?

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.

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