Watermark Detection Z-Score

Problem

Compute the green-list watermark detection statistic for a token sequence: with g green tokens out of n and a green list covering half the vocabulary, z = (g - n/2) / sqrt(n/4).

The signature is watermark_z_score(tokens, greenlist). Return the z-score.

Hint

A large positive z-score is evidence that the text was generated with the watermark.

Test cases

case 1

in: [[1,2,3,4,1],[1,2,3]]

expected: 1.3416407865

case 2

in: [[5,6],[1,2]]

expected: -1.4142135624

case 3

in: [[1,1,1,1],[1]]

expected: 2

case 4

in: [[1,2,3,4],[1,2]]

expected: 0

Starter codePython

import math
def watermark_z_score(tokens, greenlist):
    # Your code here
    pass

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