A significant player in the deep learning revolution is the Rectified Linear Unit or ReLU. This simple yet incredibly efficient activation function has surpassed predecessors like sigmoid or tanh. ReLU's formula, f(x) = max(0,x), shows its monotonic nature. Negative inputs yield a return of 0, while any positive value returns as is. Hence, the output range from 0 to infinity. The ReLU function now holds a dominant role in neural network applications, especially in Convolutional Neural Networks (CNNs), serving as the activation function of choice.

## Why Choose ReLU?

The simplicity of ReLU's deep learning function eliminates complex calculations and reduces processing demands. Consequently, the model can learn in less time. Furthermore, it promotes sparsity - an essential feature in neural networks. Sparsity refers to a scenario where the majority of cell entries in a matrix are zero. This property in ReLU neural networks mirrors a scenario where some of the weights are zero, leading to compact models that offer enhanced predictive capacity and minimize overfitting and noise. For example, in a model aimed at recognizing human faces in pictures, a neuron identifying eyes should not be activated if the image is of an object, not a face. The propensity of ReLU to output zero for any negative input contributes to a sparse network.

## Comparing ReLU with Other Activation Functions

Former popular activation functions like sigmoid and tanh, saturated before ReLU captured attention. As such, tanh and sigmoid snap high values to 1.0, and low ones to -1 or 0, with sensitivity restricted to mid-point changes in input, e.g., 0.5 for sigmoid and 0.0 for tanh. This results in the 'vanishing gradient problem'.

Neural networks utilize the gradient descent method for training. During gradient descent, the backward propagation phase involves the chain rule to adjust the weights to minimize loss after each epoch. It's important to note that derivatives are crucial in the weight adjustment process. Activation functions like sigmoid or tanh, which only provide decent derivative values from -2 to 2, result in continuous gradient reduction as layers increase. Consequently, the gradient value for the initial layers reduces, impeding proper learning. However, ReLU circumvents this issue with its slope not plateauing with larger inputs, enabling faster convergence of models using ReLU.

Nonetheless, ReLU has its shortcomings like an exploding gradient. This happens when large errors accumulate during training, leading to significant changes in model weights, gearing towards model instability and restrained learning from training data. Another drawback is the "dying ReLU" – a scenario where ReLU neurons become "dead" if continuously outputting 0, rendering such neurons useless for discerning input. This can lead to a significant part of your network being inactive over time. This is likely when there's a high learning rate or significant negative bias.

To mitigate this issue, learning rates are often diminished. Another solution is the Leaky ReLU – an improved ReLU activation function variant. Instead of setting all negative inputs as 0, the Leaky ReLU specifies the function as an extremely rectified linear unit of x, using the formula: Leaky ReLU = f(x) = max(0.01*x, x).