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The vector of skills vs. vector of job properties thing could be a coherent idea. I'd argue it's not a good idea (and I have created joint-embedding models for multi-modal text and image nearest neighbor search systems). But it could be a coherent idea.

In deep learning anyway, it's a very similar idea in spirit to something like word2vec. In word2vec you learn how to create some arbitrary vector of real numbers, let's say a 256-component vector, that represents words. The components of the vector for each word are learned by forcing the model to solve a prediction task, like predicting whether two words were truly seen in the same context in a given document or not. The model updates the 256-vector of each word such that this prediction task (which can be based on the inner product of those 256-vectors for sets of words) gets better and better. By the end of this, you can in some sense claim a word's mapping into its 256-vector "represents" some "context" intrinsic to that word. And that 256-dimensional "space of context" where the vectors reside is known as an embedding space. So the 256-vector of a word is often called that word's embedding.

For more generic problem, you aren't learning just one type of embedding, but possibly many. In TripleByte's case, I'm guessing they are inputting text characteristics of candidate resumes, self-descriptions, GitHub repos, Stack Overflow profiles, LinkedIn pages, etc. etc., and treating a candidate like a bag-of-words from all those…

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