Formula

Conditional Probability Distribution of the Verification Model in Speculative Decoding

In speculative decoding, the verification model, denoted by pp, defines a conditional probability distribution used to evaluate draft tokens. The probability of a draft token y^i+t\hat{y}_{i+t} is conditioned on the original input XX, the sequence of already verified tokens YiY_{\le i}, and all preceding draft tokens from the current step, y^i+1,,y^i+t1\hat{y}_{i+1}, \ldots, \hat{y}_{i+t-1}. This distribution is formally expressed as

Prp ⁣(y^i+tX,Yi,y^i+1,,y^i+t1).\Pr_p\!\left(\hat{y}_{i+t} \mid X, Y_{\le i}, \hat{y}_{i+1}, \ldots, \hat{y}_{i+t-1}\right).

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Updated 2026-02-05

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Ch.5 Inference - Foundations of Large Language Models

Foundations of Large Language Models

Foundations of Large Language Models Course

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