Product of Sigmoids Gradient

Problem

For f(w) = product_i sigmoid(w_i), the partial derivative with respect to w_i is f(w) * (1 - sigmoid(w_i)) because d(sigmoid)/dw = sigmoid * (1 - sigmoid).

Given the weight vector, return the gradient list.

Hint

The log-derivative trick turns the product into a sum of terms.

Test cases

case 1

in: [[0,0]]

expected: [0.125,0.125]

case 2

in: [[1,2]]

expected: [0.1731752162946797,0.07675646131035557]

case 3

in: [[0,1,2]]

expected: [0.16097856497199306,0.08658760814733985,0.038378230655177786]

Starter codePython

def product_of_sigmoids_gradient(w):
    # Your code here
    pass

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