Is every vector an embedding?
No. A vector is any ordered collection of numbers. Embeddings are a particular kind of representation, usually learned to capture relationships useful for a task.
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The dimension is the number of numerical components in the vector. More dimensions allow a different representation capacity but do not automatically guarantee better results.
A model interprets each position according to its training setup. Swapping positions can turn a word count into a link count and produce incorrect behavior.
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