Activation functions play a crucial role in neural networks as they introduce non-linearity to the network's output. They are applied to the weighted sum of the inputs and biases at each neuron, allowing the network to learn complex patterns and make predictions.

  The primary role of activation functions is to introduce non-linearity into the network. Without activation functions, the neural network would be limited to learning linear relationships between the input and the output. This means that the network would only be able to approximate simple functions, failing to capture the complexity of real-world data.

  Activation functions also determine the output range of a neuron. They map the input values to a specified range, typically bounded between 0 and 1 or -1 and 1. This normalization helps in ensuring that the output of each neuron in the network falls within a suitable range, making it easier for subsequent layers or the final output layer to process the information.

  Furthermore, activation functions enable the network to model complex, non-linear data distributions. By introducing non-linearity, they allow the network to approximate any arbitrary function to a desired degree, making it more flexible and expressive in capturing and representing complex patterns from the input data.

  There are various activation functions used in neural networks, each with its advantages and limitations. Some commonly used activation functions include sigmoid, tanh, ReLU (Rectified Linear Unit), and softmax.

  In conclusion, activation functions are essential in neural networks because they add non-linearity, determine the output range of a neuron, and enable the network to learn and represent complex patterns from the input data. Their choice significantly influences the network's learning capacity and performance.