For each i, for 1 ≤ i ≤ n, the APT for w i when contextualized by its role in the dependency tree t, denoted w i ; t , is the APT that satisfies the equality: Alternatively, this can also be expressed with the equality: Note that w h ; t and t are identical.
we take the representation of the distributional semantics of a dependency tree to be the APT for the lexeme at the root of that tree that has been contextualized by the other lexemes appearing below it in the tree.