As our exploration method does not directly samples K individual derivations but clusters the K particles on a smaller number of derivations with the recurrence (1).
we reformulate (8) not directly as (7) but rather as: we approximate the sum on the full set of parses Y(x i ) by the sum of the set of parses found in the beamỸ(x i ) and sampled with the importance distribution P * (x, y).