THE SPECULATIVE-DECODING ACCEPTANCE
Intermediate
Difficulty: Medium Tags: LLM Inference, Speculative Decoding, Sampling
Story
A speculative decoding engine proposes tokens using a draft distribution and verifies them against the target distribution. For one proposed token, compute the acceptance probability specified by the standard rejection rule. This isolates one position and does not simulate replacement sampling.
The Math
For proposed token x, draft probability q(x) > 0, and target
probability p(x), the acceptance probability is:
a(x) = min(1, p(x)/q(x))
If q(x) == 0, the input is invalid and will not occur.
Input Format
p (float), q (float).
Output Format
Acceptance probability (6 decimal places).
Constraints
0 <= p <= 1,0 < q <= 1.- Time limit: 1.0 second.
Example
Input
p = 0.12, q = 0.3
Output
0.400000
Explanation: The ratio is 0.12/0.3 = 0.4, below one.
Keywords
llm-inferencespeculative-decodingsampling
Python
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