There's several use-cases listed where Markdown could be used for, such as paper writing, presentation etc (I'm not sure I am going to use it for the later in the near future...).
That's pretty much correct.
You would typically calculate a vector for "King-Man+Woman" and then do a query on this based on a cosine distance (or similar measure) over the entire vocabulary.
The query would give you a ranked list of the closest word vectors with scores that indicate how good the match is.
I would also agree with you that it is fine to add additional rules to improve the outcome, but than it shouldn't be made clear in the way the result is presented (as you say, that rarely happens in intro-level tutorials/courses).
Your last point sounds like a cool idea! Using those more in-depth metrics to find weaknesses and see if other, complementary algorithms can fill the gap.
Good point!
I would see this rather as yet another argument for why you should simply give the actual output of the NLP algorithm.
So if people actually do the calculation King-Man+Woman and it comes closest to King, than they should report "King-Man+Woman~=King" and not "King-Man+Woman=Queen" (only because that's what they expected).
Exactly! I think that was part of the problem for many of the examples that turn out to not-really-work.
People pretend they let the work do by an algorithm, but then hand-pick from a list of somewhat close candidates. Which of course happens with a hypothesis (and thereby desired outcome) in mind.
I'm fine with the free lunch thing. But here the cheating is done on the level of how people present the capabilities of the tool.
If you ask the algorithm how "SHE is to LOVELY as HE is to X", the reported answer (Bolukbasi 2016) was "BRILLIANT", which in this case suggests a heavy gender-bias. But what the algorithm actually gives for X is: "LOVELY". The authors justed picked the 10th example in the list without clearly stating it.