The objective function is the hinge loss, For dependency labels, following (Dozat and Manning, 2017), the classifier takes head and its children as features.
we minimize the negative log probability of the correct dependency label l i for the child-parent pair (x i , h i ) implemented as cross-entropy loss: the overall loss is sum of the objectives: As our joint span is defined in a recursive way, to score the root joint span has been equally scoring all spans and dependencies in the HPSG tree.