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I have seen word vectors, word representations and vector embedding in those papers (and in a few other places):

What's the difference between word vectors, word representations and vector embeddings?

I would say that a word vector is a kind of word representation, but how about vector embeddings?

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    Before going to the trouble of (trying to) read all three papers, I will say that there are a lot of meanings in use for word, especially in differing fields, like linguistics and AI. Hence, what one person means by word vector may be quite different from what somebody else understands by it. – jlawler Jun 9 '14 at 3:59
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  • Word vectors are the same as word embeddings. (2)
  • A word representation is a mathematical object associated with each word, often a vector (1). Word vectors/embeddings are one type of word representations, amongst others. Word vectors are one the most common types of word representation in the current NLP literature nowadays.

(1): Turian, Joseph, Lev Ratinov, and Yoshua Bengio. "Word representations: a simple and general method for semi-supervised learning." Proceedings of the 48th annual meeting of the association for computational linguistics. Association for Computational Linguistics, 2010.

(2): https://youtu.be/MRH9ABxCUZ0?t=28m30s

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