What are the primary benefits and drawbacks of using ReLU versus Sigmoid activation functions in a deep neural network?

ReLU (Rectified Linear Unit) and Sigmoid are common activation functions used in deep neural networks, each with its own benefits and drawbacks. A primary benefit of ReLU is its ability to alleviate the vanishing gradient problem, which can hinder the training of deep networks. The derivative of ReLU is either 0 or 1, meaning gradients are less likely to be squashed as they propagate through the layers. This allows for faster and more effective training, especially in deep networks. Sigmoid, on the other hand, has a derivative that ranges from 0 to 0.25, which can lead to vanishing gradients, especially in deep networks. Another benefit of ReLU is its computational efficiency. ReLU involves a simple thresholding operation (outputting 0 for negative inputs and the input value for positive inputs), which is faster than the exponential calculations required by Sigmoid. This can significantly speed up the training process. A drawback of ReLU is the 'dying ReLU' problem. If a ReLU neuron's weights are updated such that it always receives negative inputs, it will become inactive, always outputting 0. This neuron will effectively 'die' and stop contributing to the learning process. Sigmoid does not suffer from this problem, as it always produces a non-zero output. A primary drawback of Sigmoid is that its output is not zero-centered, which can slow down training. Because the outputs of Sigmoid are always positive, the gradients during backpropagation can have consistent signs, leading to inefficient weight updates. ReLU, with its zero-centered output for negative inputs, can mitigate this issue. In summary, ReLU offers faster training and alleviates the vanishing gradient problem, but is susceptible to the dying ReLU problem. Sigmoid, while less prone to dying neurons, suffers from vanishing gradients and slower training due to its non-zero-centered output and computational complexity.