What are the advantages of ReLU over sigmoid?

1. Mitigates the Vanishing Gradient Problem 

• ReLU: The gradient of ReLU is 1 for positive inputs, and 0 for negative inputs. For  positive values, the gradient does not vanish, which helps in maintaining the magnitude  of gradients during backpropagation. This avoids the issue where gradients become  very small as they are propagated backward through many layers, which can slow down  or halt learning in deep networks. 

• Sigmoid: The gradient of the sigmoid function can be very small for large positive or  negative values of input. This can lead to the vanishing gradient problem, where  gradients become extremely small during backpropagation, causing slow or stalled  training for early layers. 

2. Faster Training 

• ReLU: The computation involved in ReLU is simple and efficient, as it only requires a  threshold operation. This makes it faster to compute compared to sigmoid, which  involves exponential calculations. 

ReLU(x) = max(0,x). 

• Sigmoid: Computing the sigmoid function involves an exponential function. This is  more computationally expensive than the ReLU operation 

Sigmoid(x) = ! 

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3. Sparsity 

• ReLU: It introduces sparsity in the activations because it outputs zero for all negative  inputs. This sparsity can be beneficial for neural network performance, as it can lead to  more efficient computations and a more compact representation. 

• Sigmoid: The sigmoid function does not introduce sparsity, as it always outputs values  between 0 and 1. All neurons are activated to some degree, which can lead to less  efficient computation in practice. 

4. Improved Convergence 

• ReLU: Because of its properties, ReLU can often lead to faster convergence during  training. The ability to maintain gradients effectively helps in speeding up the learning  process and achieving better performance in less time. 

• Sigmoid: Due to the vanishing gradient problem and computational overhead, networks  using sigmoid activation functions may converge more slowly and require more epochs  to train effectively. 

These advantages make ReLU a preferred choice in many deep learning architectures,  especially in convolutional and fully connected neural networks. However, it’s also important  to consider that ReLU has its own drawbacks (e.g., dead neurons), and variants like Leaky  ReLU, Parametric ReLU, and ELU can address some of these issues. 

ReLU

What is the problem with ReLU activation?

The Rectified Linear Unit (ReLU) activation function is widely used in neural networks due to its simplicity and effectiveness. However, it does have some limitations:

1. Zero Gradient for Negative Inputs:

   
   

   • ReLU sets all negative input values to zero. While this sparsity property helps with training speed, it can cause issues during backpropagation. Specifically, when the gradient of the ReLU function is zero (for negative inputs), the corresponding weights do not get updated during training. This phenomenon is known as the “dying ReLU” problem12.

     
     

   • Essentially, some neurons become “inactive” and contribute nothing to learning because their output remains zero for all inputs.

     
     

2. Exploding Gradient:

   
   

   • ReLU can lead to the exploding gradient problem. When gradients are large, weight updates during training become excessively large, causing instability and slow convergence.

     
     

   • Although ReLU mitigates the vanishing gradient problem (which occurs with sigmoid and tanh activations), it introduces the risk of exploding gradients.

     
     

3. Dead Neurons:

   
   

   • Neurons that consistently output zero (due to negative inputs) are considered “dead.” These dead neurons do not contribute to the network’s learning process.

     
     

   • Dead neurons can occur if the initial weights are set such that the neuron’s output is always negative.