We calculate the approximate gradient as: In contrast to our n-best technique, the past work has calculated equation (2) using a beam search approximation of the full inside-outside algorithm (Zettlemoyer and Collins, 2005;Kwiatkowski et al., 2010;Liang et al., 2011).
since the conditional probability of t given r does not factorize, a standard chart parser would need to maintain the full logical form (i.e.