Activation functions are crucial components in neural networks, playing a vital role in determining the output of each neuron. They introduce non-linear properties to the network, allowing it to learn complex patterns from data.

Types of Activation Functions

  1. Sigmoid

    • The sigmoid function maps any real-valued number into the (0, 1) interval.
    • It is defined as ( \sigma(x) = \frac{1}{1 + e^{-x}} ).
    • Sigmoid Function Plot

  2. Tanh

    • The hyperbolic tangent function maps any real-valued number into the (-1, 1) interval.
    • It is defined as ( \tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} ).
    • Tanh Function Plot

  3. ReLU (Rectified Linear Unit)

    • The ReLU function is defined as ( f(x) = \max(0, x) ).
    • It is widely used due to its simplicity and effectiveness in deep networks.
    • ReLU Function Plot

  4. Leaky ReLU

    • Leaky ReLU is a variant of ReLU that addresses the dead neurons problem of ReLU.
    • It allows a small gradient when the input is negative, preventing neurons from dying.
    • Leaky ReLU Function Plot

  5. Softmax

    • The softmax function is commonly used in the output layer of a neural network for multi-class classification.
    • It converts the output of the network into probabilities.
    • Softmax Function Plot

Choosing the Right Activation Function

Choosing the right activation function depends on the specific problem and the architecture of the neural network. Each function has its advantages and disadvantages, and it is essential to experiment and evaluate their performance.

For further reading on activation functions, you can explore our Deep Learning Basics tutorial.