DCI Disentanglement

Problem

Return the DCI disentanglement score of an importance matrix. Rows are ground-truth factors and columns are learned generators. For each factor, normalize its row into a distribution over generators, take the Shannon entropy in bits, then return

1 - mean(entropy) / log2(num_generators)

A score of 1 means every factor is controlled by a single generator.

Hint

Entangled factors spread their importance across several generators.

Test cases

case 1

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

expected: 1

case 2

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

expected: 0

case 3

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

expected: 1

case 4

in: [[[1,0,0],[0,2,0],[1,1,0]]]

expected: 0.7896900821428475

Starter codePython

import math
def dci_disentanglement(importance):
    # Your code here
    pass

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