Surrogate Gradient

Problem

Spiking neural networks replace the derivative of the Heaviside spike with a smooth surrogate. A common choice is the derivative of arctan(k*x):

g(x) = k / (1 + (k*x)^2)

Given x and the sharpness k > 0, return g(x).

Hint

The surrogate is symmetric and peaks at x = 0 with value k.

case 1

in: [0,5]

expected: 5

case 2

in: [0.1,5]

expected: 4

case 3

in: [-0.1,5]

expected: 4

case 4

in: [1,1]

expected: 0.5

case 5

in: [0.5,2]

expected: 1

Starter codePython

def surrogate_gradient(x, scale):
    # Your code here
    pass

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