Which activation function is known for its simplicity and is commonly used in neural networks?

The activation function known for its simplicity and widespread use in neural networks is the rectified linear unit (ReLU). ReLU is defined mathematically as ( f(x) = \max(0, x) ). This function outputs zero for any negative input and the input itself for any positive input.

One of the primary reasons for ReLU's popularity is its computational efficiency; it allows models to converge faster compared to other activation functions. This is because, during backpropagation, it has a simple derivative that is either 0 (for negative inputs) or 1 (for positive inputs), meaning that it doesn’t require complex calculations.

Additionally, ReLU helps to mitigate the vanishing gradient problem, which can occur with activation functions that squash inputs to a range, such as sigmoid and tanh, especially in deep networks. While other activation functions have their advantages in specific scenarios, ReLU's straightforward implementation and superior performance in many types of neural networks have made it a standard choice in the field.