In a speculative decoding process, a verification model p is evaluating a sequence of three draft tokens, {\hat{y}_{i+1}, \hat{y}_{i+2}, \hat{y}_{i+3}}, that follow an initial prefix [\mathbf{x}, \mathbf{y}_{\le i}]. How does the context used to calculate the conditional probability for the third draft token, \text{Pr}_p(\hat{y}_{i+3}|...), differ from the context used for the first draft token, \text{Pr}_p(\hat{y}_{i+1}|...)?

Conditional Probability in Verification

In a speculative decoding step, a verification model p evaluates a sequence of draft tokens {\hat{y}_{i+1}, \hat{y}_{i+2}, \hat{y}_{i+3}} following a confirmed prefix [\mathbf{x}, \mathbf{y}_{\le i}]. The conditional probability for the second draft token, \hat{y}_{i+2}, is calculated as Pr_p(\hat{y}_{i+2} | ____).