Recently for a class in Machine Translation I did another sort of manifold learning type task.
The premise of the problem was this: Using Google's Word2Vec you can take a sentence and learn "word embeddings", or N-dimensional euclidean vectors, that are supposed to encode the meaning of each word. Similar words should be embedded in similar places. What if you do this for two translations of a text? Can you use the word embeddings in one language to predict the embeddings in another?
The answer is a solid sorta.