Question about acceptance length and rate metrics

[llsj14]

Hello,

Following my previous question (#148) about the sampling technique, I now have some questions related to the metrics discussed in your paper. I would greatly appreciate your help in understanding the paper.

1. Regarding the acceptance rate, I understand that tree structures were not considered when calculating this metric. Based on this, would the following example be correct for computing the average acceptance rate?

• 0-a: 2/2
• 1-a: 3/4
• 2-a: 3/4
  

2. The average acceptance length 𝑇 can generally be calculated in speculative decoding using the following formula if we assume each step is independent of prior steps.

• 𝑇 = average acceptance length = 1 + p + p^2 + ... p^K = (1-p^(K+1)) / (1 - p)

Here, 𝐾 represents the number of speculative tokens, and 𝑝 is the average acceptance rate. Using this formula, I derived the following table:

However, in Table 3 of your paper, the average acceptance rate is approximately 0.65, yet the average acceptance length is reported as 3.25. This is significantly higher than the values (2.3–2.7) predicted by the formula-based table above.

Could this discrepancy be explained by the fact that tree structures are not considered when calculating the acceptance rate but are accounted for when calculating the acceptance length?

3. I'm curious about the number of candidate tokens used in the tree structure experiments in the EAGLE paper. For example, MEDUSA sets 64 or 256 candidates, which corresponds to the number of leaf nodes in the trees for a single batch. (I could only find the settings mentioned in Appendix 2 of the EAGLE paper, which describe 60 draft tokens with a depth of 6 and 10 nodes during the expansion phase. Would it be similar to EAGLE v1?)

Thank you