Re-read this and perhaps identified a mis-understanding. Above you mentioned that "directed dependency labeling works better with vectors learned from PoS-tagge

Re-read this and perhaps identified a mis-understanding. Above you mentioned that "directed dependency labeling works better with vectors learned from PoS-tagged words than with PoS-tagged vectors (learned from untagged words)". The method does not pos-label vectors or words in the model. Instead, it pos-labels the text that sense2vec is trained on. In this way, you get multiple vectors for words with multiple-POS usages (as if they were different words altogether). The change to the syntactic parser was just based on using POS to select which word embedding (of the several available for each word) to use as input. Sense2vec was trained on predicted POS labels. The parser used gold standard POS tags in both normal word2vec and sense2vec for even comparison.