For graph-based dependency parsing, it is not straightforward to extend the linear models to the more powerful nonlinear neural network, because we need to figure out the scores for the factors of the tree, which are not specified in the original treebank.
we only know which factors are in the correct parsing tree, but there are no natural ways to indicate how they are scored; the only intuition is to give high scores to the right factors and low scores to the wrong ones.