Activation functions are crucial components in neural networks, as they determine the output of a neuron based on its input. Their primary purpose is to introduce non-linearity into the model, allowing the network to learn complex patterns and relationships within the data. Without activation functions, the output of a neural network would be linear, limiting its ability to model intricate functions.

There are several types of activation functions, each with its unique characteristics. Common examples include:

1. Sigmoid Function: Outputs values between 0 and 1, often used in binary classification tasks.
2. Softmax Function: Generates a probability distribution across multiple classes, ensuring that the sum of outputs equals 1.
3. Hyperbolic Tangent Function (Tanh): Outputs values between -1 and 1, providing a zero-centered output.
4. Rectified Linear Unit (ReLU): Outputs the input directly if it is positive; otherwise, it outputs zero. It is computationally efficient and widely used in hidden layers.
5. Exponential Linear Unit (ELU) and Leaky ReLU: Variants of ReLU that address some of its limitations by allowing small gradients for negative inputs.

These functions enable neural networks to capture complex relationships in data, enhancing their predictive capabilities ¹²³⁴⁵.