Sigmoid Gradient

Problem Statement

Compute the derivative of the Sigmoid function given the activation output.

The Sigmoid function is defined as: $\sigma(z) = \frac{1}{1 + e^{-z}}$

A useful property is that its derivative can be computed directly from the output:

This makes backpropagation efficient since we already have the sigmoid output from the forward pass.

Write a function sigmoid_derivative(sigmoid_output) that returns the gradient values for each element.

Return a list of floats representing the derivatives. Round each value to 4 decimal places.

Input:

sigmoid_output=[0.5, 0.8]

Output:

[0.25, 0.16]

Reasoning:

For 0.5: 0.5 × (1 - 0.5) = 0. $5 \times 0$ .5 = 0.25. For 0.8: 0.8 × (1 - 0.8) = 0. $8 \times 0$ .2 = 0.16.