Example of Draft Token Generation in Speculative Decoding

A system uses a fast draft model to autoregressively generate a sequence of several candidate tokens from a given prefix. The model generates these candidates one by one, and for each step, it greedily selects the token with the highest probability according to its own distribution, Pr_q. If the system is in the process of generating the third candidate token in the sequence, ŷ_{i+3}, which of the following represents the correct set of information the draft model's probability distribution must be conditioned on for this specific step?

A developer is implementing the draft token generation phase of a text generation system. The system is designed to autoregressively produce a short sequence of candidate tokens at each step. The developer's code for generating the third token in a sequence, ŷ_{i+3}, incorrectly conditions the draft model's probability distribution only on the initial prefix [X, y_{≤i}] and the first candidate token ŷ_{i+1}, omitting the second candidate token ŷ_{i+2} from the context. What is the most likely consequence of this specific error?

A fast, approximate language model is tasked with generating a sequence of three candidate tokens (ŷᵢ₊₁, ŷᵢ₊₂, ŷᵢ₊₃) starting from a given text prefix P. Arrange the following actions in the correct chronological order to describe how this sequence is produced.