The Sigmoid function, also known as the logistic function, is an activation function used in neural networks. It converts any real-valued number into a value between 0 and 1.

In the video, as the red circle moves, the blue circle follows, showing the corresponding value of sigma of x, or sigmoid of x. The Sigmoid function is calculated as e to the power x divided by 1 plus e to the power x.

This results in an 'S-shaped' curve that’s commonly used to convert outputs into probabilities.

When x is zero, the value of sigmoid of x is exactly 0.5, right in the middle of the curve. This is useful for binary classification tasks, where we want to interpret model predictions as probabilities—whether something belongs to one class or the other.

As x becomes more positive, sigma of x approaches 1. Similarly, when x becomes more negative, sigma x approaches 0. This is why the Sigmoid function is perfect for binary classification tasks where the output needs to be between 0 and 1.

This smooth gradient of the Sigmoid function also helps during training, as the gradient can be calculated at any point on the curve, which is essential for backpropagation in neural networks.

If you enjoyed this visualization of the Sigmoid function, be sure to check out the code linked below:
github.com/mshossain/Simple_NN/blob/main/SigmoidVi…

The full sigmoid function theory video is here:    • Sigmoid Function -- When to use it as...  


Dr. Shahriar Hossain
computing4all.com/