Training these quantized word vectors has to be done in full precision (so no memory gains during training the word vectors).

But when you save them to disk every value is either -1/3 or +1/3 so one could encode the word vectors in binary. This can lead to reducing memory usage during application time if you kept the word vectors in this compressed format (though you'd need to write a decode function in tensorflow or pytorch to take a sequence of bits corresponding to a word and convert it into a vector of -1/3s and +1/3s)