A text generation model employs a decoding strategy where, at each step, it extends the single most probable sequence generated so far. Suppose after three steps, the sequence 'The cat sat' has been generated. In the fourth step, the model calculates probabilities for the next word and finds that 'on' is the most likely, 'under' is the second most likely, and 'by' is the third most likely. Based on this strategy, what is the composition of the candidate set of sequences immediately after this fourth step is completed?

In a text generation model that employs a greedy search decoding strategy, the size of the candidate set of sequences, denoted as |Y_i|, increases at each step i because the model considers a growing number of possible sentence completions.

Defining the Candidate Set in a Greedy Decoding Strategy