Candidate Set in Sampling-Based Decoding

In an autoregressive text generation process, the sequence generated up to a certain point is The dog chased the. At the current step, the model generates and selects the token ball. What is the new, extended sequence that will be used as the basis for generating the subsequent token?

An autoregressive model is generating a sequence. It begins with the single token y_1 = 'The'. In the next step, it samples the token ȳ_2 = 'cat'. Following that, it samples the token ȳ_3 = 'sat'. What is the resulting sequence that is formed after these two sampling steps?

Formal Representation of Sequence Extension