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Following the ranking stage in beam search, a selection is made based on the beam width, denoted as K. The top K candidates with the highest probabilities are kept as the output, while all other lower-probability candidates are discarded or 'pruned'. For instance, with a beam width of K=3, the top three candidates ('cute', 'on', 'sick') would form the output, and the remaining candidates ('are', '.') would be pruned.

Pruning and K-Best Output in Beam Search

In a text generation process, a set of potential next words and their calculated probabilities are ranked as follows: `{'the': 0.45, 'a': 0.25, 'his': 0.15, 'her': 0.10, 'its': 0.05}`. If the process uses a fixed width of K=3 to select the most likely candidates, which words are kept and which are discarded (pruned)?

A language model is generating a sentence completion. In one configuration (Scenario A), it considers multiple potential next words but only keeps the single most probable word to continue the sentence. In another configuration (Scenario B), it keeps the top 3 most probable words at each step. Scenario A produces the sentence 'The cat sat on the mat.' Scenario B is able to produce the more creative sentence 'The cat sat on the windowsill.' What is the primary drawback of the process used in Scenario A, and how does it relate to which candidate words are kept versus discarded at each step?

Impact of Search Width on Text Generation

In a text generation model, after evaluating potential next words for the sequence 'The cat sat on the', the following candidates and their probabilities are produced: `{'mat': 0.55, 'couch': 0.25, 'floor': 0.12, 'table': 0.06, 'rug': 0.02}`. If the model is configured with a selection width of K=3, which words are discarded (pruned) in this step? Briefly explain your reasoning.

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