Gradient Penalty (Finite Difference)

Problem

Estimate the WGAN gradient penalty with a central finite difference: g_i = (d_plus_i - d_minus_i) / (2 * epsilon), then return the mean of g_i^2 over all i.

The signature is gradient_penalty_finite_difference(d_plus, d_minus, epsilon). d_plus and d_minus are critic scores at perturbed points.

Hint

The penalty pushes the critic's gradient norm toward 1, so the squared slopes are averaged.

Test cases

case 1

in: [[1,0],[0,0],0.1]

expected: 12.5

case 2

in: [[0.5,0.5],[0.5,0.5],0.05]

expected: 0

case 3

in: [[1,2],[0.5,1.5],0.5]

expected: 0.25

case 4

in: [[3,1],[1,3],0.25]

expected: 16

Starter codePython

def gradient_penalty_finite_difference(d_plus, d_minus, epsilon):
    # Your code here
    pass

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