Expert Capacity Drop Rate

Problem

Compute the fraction of tokens dropped by expert capacity limits. Capacity per expert = ceil(num_tokens * capacity_factor / num_experts); tokens beyond capacity are dropped.

The signature is expert_capacity_drop(expert_counts, num_tokens, capacity_factor). Return the drop rate.

Hint

Tiny capacity factors drop tokens; large ones waste compute on padding.

Test cases

case 1

in: [[10,10,10,10],40,1]

expected: 0

case 2

in: [[20,0,0,0],20,1]

expected: 0.75

case 3

in: [[5,5,5,5],20,0.5]

expected: 0.4

case 4

in: [[7,3],10,1]

expected: 0.2

Starter codePython

import math
def expert_capacity_drop(expert_counts, num_tokens, capacity_factor):
    # Your code here
    pass

4 test cases · run your code against them in the editor