I use word2vec a lot, and things like it, and I've always found it overstated to say that it "learns the relationships between things".
You say, as many people do, that the operation "king - man + woman = queen" indicates that it understands that the relation between "king" and "queen" is the relation between "man" and "woman". But there is something much simpler going on.
What you're asking it for, in particular, is to find the vector represented by "king - man + woman", and find the vector Q with the highest dot product with to this synthetic vector, out of a restricted vocabulary.
The dot product is distributive, so distribute it: you want to find the maximum value of (king * Q) - (man * Q) + (woman * Q).
So you want to find a vector that is like "king" and "woman", and not like "man", and is part of the extremely limited vocabulary that you use for the traditional word2vec analogy evaluation, but not one of the three words you used in the question. (All of these constraints are relevant.) Big surprise, the word that fits the bill is "queen".
(I am not the first to do this analysis, but I've heard it from enough people that I don't know who to credit.)
It's cool that you can use sums of similarities between words to get the right answer to some selected analogy problems. Really, it is. It's a great thing to show to people who wouldn't otherwise understand why we care so much about similarities between words.
But this is not the same thing as "solving analogies" or "understanding relationships". It's a trick where you make a system so good at recognizing similarities that it doesn't have to solve analogies or understand relationships to solve the very easy analogy questions we give it.
You say, as many people do, that the operation "king - man + woman = queen" indicates that it understands that the relation between "king" and "queen" is the relation between "man" and "woman". But there is something much simpler going on.
What you're asking it for, in particular, is to find the vector represented by "king - man + woman", and find the vector Q with the highest dot product with to this synthetic vector, out of a restricted vocabulary.
The dot product is distributive, so distribute it: you want to find the maximum value of (king * Q) - (man * Q) + (woman * Q).
So you want to find a vector that is like "king" and "woman", and not like "man", and is part of the extremely limited vocabulary that you use for the traditional word2vec analogy evaluation, but not one of the three words you used in the question. (All of these constraints are relevant.) Big surprise, the word that fits the bill is "queen".
(I am not the first to do this analysis, but I've heard it from enough people that I don't know who to credit.)
It's cool that you can use sums of similarities between words to get the right answer to some selected analogy problems. Really, it is. It's a great thing to show to people who wouldn't otherwise understand why we care so much about similarities between words.
But this is not the same thing as "solving analogies" or "understanding relationships". It's a trick where you make a system so good at recognizing similarities that it doesn't have to solve analogies or understand relationships to solve the very easy analogy questions we give it.