For selectional branching, the margin threshold m and the beam size I) need to be tuned (Section 3.3).

For this development set, the beam size of 64 and 80 gave the exact same result, so we kept the one with a larger beam size (I) = 80).

Figure 3: Parsing accuracies with respect to margins and beam sizes on the English development set.

Thus, it is preferred if the beam size is not fixed but proportional to the number of low confidence predictions that a greedy parser makes, in which case, fewer transition sequences need to be explored to produce the same or similar parse output.

Thus, it is preferred if the beam size is not fixed but proportional to the number of low confidence predictions made for the one-best sequence.

The selectional branching method presented here performs at most d - t — 6 transitions, where t is the maximum number of transitions performed to generate a transition sequence, d = min(b, |A|+1), bis the beam size , |A| is the number of low confidence predictions made for the one-best sequence, and e = @.

Compared to beam search that always performs b - t transitions, selectional branching is guaranteed to perform fewer transitions given the same beam size because d g b and e > 0 except for d = 1, in which case, no branching happens.

Figure 6 shows the training curves of the averaged perceptron with respect to the performance on the development set when the beam size is 4.

4.4 Impact of beam size

The beam size is an important hyper parameter in both training and test.

In Section 4.5 we will show that the standard perceptron introduces many invalid updates especially with smaller beam sizes , also observed by Huang et al.

Then the K -best partial configurations are selected to the beam, assuming the beam size is K.

K: Beam size .

We have some parameters to tune: parsing feature weight 0p, beam size , and training epoch.

In this experiment, the external dictionaries are not used, and the beam size of 32 is used.

Table 3 shows the performance and speed of the full joint model (with no dictionaries) on CTB-Sc-l with respect to the beam size .

length, comparing with top-down, 2nd-MST and shift-reduce parsers ( beam size : 8, pred size: 5)

During training, we fixed the prediction size and beam size to 5 and 16, respectively, judged by pre-

After 25 iterations of perceptron training, we achieved 92.94 unlabeled accuracy for top-down parser with the FIRST function and 93.01 unlabeled accuracy for shift-reduce parser on development data by setting the beam size to 8 for both parsers and the prediction size to 5 in top-down parser.

The complexity becomes 0(n2 >x< b) where b is the beam size .

Figure 6: Accuracies against the training epoch for joint segmentation and tagging as well as joint phrase-structure parsing using beam sizes 1, 4, l6 and 64, respectively.

Figure 6 shows the accuracies of our model using different beam sizes with respect to the training epoch.

The performance of our model increases as the beam size increases.

With linear-time complexity, our parser is highly efficient, processing over 30 sentences per second with a beam size of 16.

The results for W-DITG are listed in Table l. Tests 1 and 2 show that with the same beam size (i.e.

To enable TTT achieving similar F-score or F-score upper bound, the beam size has to be doubled and the time cost is more than twice the original (c.f.

This also explains (in Tables 2 and 3) why DPDI with beam size 10 leads to higher Bleu than TTT with beam size 20, even though both pruning methods lead to roughly the same alignment F-score

The third type of pruning is equivalent to minimizing the beam size of alignment hypotheses in each hypernode.

Note that the beam size (max number of E-spans) for each F-span is 10.

Unless otherwise stated we use 25 iterations of perceptron training and a beam size of 20.

The subset of size k (the beam size ) of the highest scoring expansions are retained and put back into the agenda for the next step.

Algorithm 2 Beam search and early update Input: Data set D, epochs T, beam size k: Output: weight vector to a 1: w = 0 2: fort 6 LT do

Input: Data set D, iterations T, beam size k: Output: weight vector to 1: w = 6) 2: fort 6 LT do ~ for <M¢,Ai,¢4¢> E D do Agendaa = Agendap = Aacc : 6) lossacc = 0 for j 6 Ln do ~ Agendaa = EXPAND(AgendaG, Aj, mj, k) Agendap = EXPAND(Agendap, Aj, mj, k) if fl CONTAINsCORRECT(Agendap) then 3] = EXTRACTBEST(AgendaG) g = EXTRACTBEST(Agendap) Aacc = Aacc + _ lossacc = lossacc + LOSS(jI]) Agendap = Agendaa g = EXTRACTBEST(Agendap) if fl CORRECTQQ) then g = EXTRACTBEST(AgendaG) Aace = Aacc + _ lossacc = lossacc + LOSS(:IQ) if A... 7e 6’ then update w.r.t.

the English development set as a function of number of training iterations with two different beam sizes , 20 and 100, over the local and nonlocal feature sets.

HHMM was run with beam size of 2000.

HHMM parser beam sizes are indicated for the syntactic LM.

Figure 9: Results for Ur—En devtest (only sentences with 1-20 words) with HHMM beam size of 2000 and Moses settings of distortion limit 10, stack size 200, and ttable_limit 20.

We used a default beam size 1:: = 10.

Table 1 shows the results of our full model using beam size 1:: = 10, as well as model variants.

As detailed, only a set of top scoring tuples of size 1:: ( beam size ) is maintained per relation 7“ E T during candidate generation.

The beam size 1:: allows controlling the tradeoff between performance and cost.

Beam size is fixed at 2000.4 Sentence compressions are evaluated by a 5-gram language model trained on Gigaword (Graff, 2003) by SRILM (Stolcke, 2002).

4We looked at various beam sizes on the heldout data, and observed that the performance peaks around this value.

postorder) as a sequence of nodes in T, the set L of possible node labels, a scoring function 8 for evaluating each sentence compression hypothesis, and a beam size N. Specifically, O is a permutation on the set {0, l, .

Om, L ={RET, REM, PAR}, hypothesis scorer S, beam size N

By default, the beam size of 20 is used for all decoders in the experiments.

For partial hypothesis re-ranking, obtaining more top-ranked results requires increasing the beam size , which is not affordable for large numbers in experiments.

We work around this issue by approximating beam sizes larger than 20 by only enlarging the beam size for the span covering the entire source sentence.

The lower bound can be initialized to the best sequence score using a beam search (with beam size being 1).

The search is similar to the beam search with beam size being 1.

We initialize the lower bound lb with the k-th best score from beam search (with beam size being 11:) at line 1.

As the performance of our KB-QA system relies heavily on the k-best beam approximation, we evaluate the impact of the beam size and list the comparison results in Figure 6.

Figure 6: Impacts of beam size on accuracy.

We can see that using a small k can achieve better results than baseline, where the beam size is set to be 200.

k: beam size .

In general a larger beam size can yield better performance but increase training and decoding time.

As a tradeoff, we set the beam size as 8 throughout the experiments.

We set the beam size k to 16, which brings a good balance between efficiency and accuracy.

Input: A word-segmented sentence, beam size k. Output: A constituent parse tree.

Input: A POS-tagged sentence, beam size k. Output: A constituent parse tree.