There has been plenty of work on alignment of embeddings, a lot of it cited in the paper. This paper solves the problem of translation, where (unlike in word alignment) there isn't already a set of candidate vectors in the target embedding space. It's generation, not matching.
The problem solved in this paper is strictly harder than alignment. Alignment works with multiple, unmatched representations of the same inputs (e.g, different embeddings of the same words). The goal is to match them up.
The goal here is harder: given an embedding of an unknown text in one space, generate a vector in another space that's close to the embedding of the same text -- but, unlike in the word alignment problem, the texts are not known in advance.
Neither unsupervised transport, nor optimal alignment can solve this problem. Their input sets must be embeddings of the same texts. The input sets here are embeddings of different texts.
FWIW, this is all explained in the paper, including even the abstract. The comparisons with optimal assignment explicitly note that this is an idealized pseudo-baseline, and in reality OA cannot used for embedding translation (as opposed to matching, alignment, correspondence, etc.)
For example, broken SSL in Amazon FPS allows a MITM
attacker to forge instant payment notifications and
defraud merchants who use vulnerable SDKs. This
is a real vulnerability, acknowledged by Amazon.
Oh thanks, I think that FAQ is exactly what I was looking for. I realize we might not be your target audience, but it seems like it'd be worth including those impact analysis statements in the paper itself, since they're short and do really help to clarify the situation.
I'll have to take a second look at the instant payment notification forgery. Last I used FPS, I remember the transaction notifications being signed. Maybe "instant payments" are a new thing.
