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What is the “dead ReLU” problem and, why is it an issue in Neural Network training?

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The problem of “dead ReLU” or “dying ReLU” refers to a situation in neural networks where certain neurons using the Rectified Linear Unit (ReLU) activation function become inactive during training and never recover. Such neurons always output zero and do not contribute to the learning process. This phenomenon can hinder the performance and training of deep neural networks.

ReLU formula

Dying ReLU occurs when the weights associated with a ReLU neuron are updated in such a way that the neuron always produces negative values for all inputs during training. Since ReLU sets negative values to zero, the neuron effectively becomes inactive, and its gradient becomes zero. As a result, the weights associated with this neuron no longer receive updates, and the neuron remains “dead” throughout the training process.

Title: Explaining how negative inputs to neurons leads to dying ReLU problem
Source:  Andrej Karpathy blog titled “Yes you should understand backprop”
(further annotated by Research for better illustration)

Reasons leading to Dead ReLU problem

  • Weights initialization
    If weights are initialized in a way that biases the ReLU neurons toward producing negative activations for most inputs, these neurons are at risk of becoming “dead” or inactive.
Zooming into a neuron
Title: Zooming into a neuron (where, x: input features, w: weights, b: bias, f: activation function (think ReLU for this scenario))
  • High negative bias
    Since bias serves as an input to an activation function along with weights, a high negative bias can push the output towards 0 for the ReLU activation

  • High Learning rate
    If the learning rate is too high, it can cause weights to be updated in such a way that pushes the ReLU neuron’s activations into the negative regime

  • Incompatible Data Normalization
    Data preprocessing, such as normalization or standardization, can also impact the occurrence of the Dying ReLU problem. Improper data scaling might lead to situations where many ReLU neurons are initially biased towards producing negative activations, increasing the chances of dying ReLUs

Why is Dying ReLU a problem

If a majority of neurons do not fire in neural network training, or are dead neurons (over 40%), it can severely impact the neural network training process. There are two key consequences:

  • Reduced Model Capacity: Dying ReLU neurons limit the representational capacity of the neural network, potentially preventing it from learning complex patterns or features in the data
  • Slower Convergence: When a significant number of ReLU neurons die, the training process can become slower, as there are fewer active neurons actively learning from the data

How to deal with the Dying ReLU problem?

ReLU is one of the most preferred activation functions in neural network training as it is simple to use, computationally efficient and avoids the vanishing gradient problem. However, dead ReLU is a hinderance in the training process due to the issues stated above. In order to mitigate the dying ReLU problem, the following techniques are employed:

  • Random initialization
    Use of proper weight initialization techniques can help reduce the chances of neurons dying during training. Eg: He initialization, Xavier initialization
  • ReLU Variants
    One common solution is to use ReLU variants such as Leaky ReLU or Parametric ReLU (PReLU), or ELU. These activation functions allow a small gradient for negative inputs, preventing neurons from becoming completely inactive
Title: Illustration of ReLU vs Leaky ReLU vs ELU
Source: Aditi Shenoy’s Master’s thesis
  • Batch Normalization
    Batch normalization can also mitigate the dying ReLU problem by normalizing activations within a layer and reducing the likelihood of a large portion of neurons becoming inactive
  • Low Learning Rate
    A very high learning rate can push the neurons to an inactive state, therefore experiment with lower learning rates for weight updates to find an optimal point

Video Explanation

  • In this Stanford lecture by Andrej Karpathy, he talks about ReLU activation function in detail, the problem of “dead ReLU” and the different variants of ReLU to deal with the “dead ReLU” problem. (starting at 20:55 mins) (Runtime: 10 mins)
ReLU activation function and the Dying ReLU problem by Andrej Karpathy, Stanford

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