What are activation functions in neural networks and why are they important?

Activation functions are mathematical equations that determine the output of a neural network node, or neuron, based on its input. They introduce non-linearity into the model, enabling it to learn complex patterns in data. Without activation functions, a neural network would simply perform linear transformations, limiting its capability. Common activation functions include ReLU (Rectified Linear Unit), sigmoid, and tanh, each having distinct characteristics and use cases, such as ReLU being favored for deep networks due to its performance benefits.