What is the derivative of the sigmoid function?

What is the derivative of the sigmoid function?

The derivative of the sigmoid function, which is defined as ( S(x) = \frac{1}{1 + e^{-x}} ), is ( S'(x) = S(x)(1 - S(x)) ). This means it can be expressed in terms of the sigmoid function itself.

Can you explain why the derivative is expressed that way?

Certainly! The derivative ( S'(x) = S(x)(1 - S(x)) ) shows how the output of the sigmoid function changes with respect to its input. It highlights that the slope is highest when the output is around 0.5, which is where the function is most sensitive.

What are some applications of the sigmoid function in machine learning?

The sigmoid function is commonly used in logistic regression, neural networks, and as an activation function. It helps model probabilities and can squash outputs to a range between 0 and 1.

Are there other activation functions I should know about?

Yes, besides the sigmoid function, other popular activation functions include ReLU (Rectified Linear Unit), tanh (hyperbolic tangent), and softmax, each with its own advantages depending on the context.