Reparameterization Gradient

Problem

With the reparameterization z = mu + sigma * eps, the pathwise derivatives of f(z) are df/dmu = f'(z) and df/dsigma = f'(z) * eps.

For f(x) = sum(coeffs[i] * x^i), evaluate f'(z) and return [df_dmu, df_dsigma].

Hint

The same derivative value scales the sigma partial by the noise sample.

case 1

in: [[0,0,1],1,2,0.5]

expected: [4,2]

case 2

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

expected: [12,-24]

case 3

in: [[0,1],0,3,1]

expected: [1,1]

case 4

in: [[5],1,1,1]

expected: [0,0]

Starter codePython

def reparameterization_grad(coeffs, mu, sigma, eps):
    # Return [df_dmu, df_dsigma]
    # Your code here
    pass

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