Answers.Body: <blockquote>
  <p>intuitively it seems like having a negative gradient when the input is very negative should be even worse than having a zero gradient, since the gradient update steps would go the wrong way.</p>
  </blockquote>
  <p>Gradient update steps go in the opposite direction of the gradient. It's gradient descent, not ascent. If the input is very negative and the gradient is negative, then gradient descent will move in the positive direction, towards 0. That's the &quot;right&quot; way.</p>
  <p>Gradient descent can work with practically any activation function. It would work fine if the activation was f(x) = min(x, 0), in which the &quot;problem&quot; you describe is magnified. It will go the right way and be functionally the same as ReLU.</p>
  
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Answers.Body: <p>It does not matter the sign of the gradient. Activations are universal approximation even if flipped:</p>
  <p><span class="math-container">$$
  W \sigma(Wx + b) + b\\
  -W (-\sigma(Wx + b)) + b
  $$</span>
  say <span class="math-container">$\sigma$</span> is the sigmoid, in the second case, the gradient is always negative, yet you are still an universal approximator, since you just need to flip the sign of the second layer <span class="math-container">$W$</span> matrix</p>
  <p>The take home message is: the sign of the activation is not that important. The reason why SiLU works better, has nothing to do with the gradient not being 0, otherwise sigmoid, tanh, leaky relu and so on, would be a possible solution</p>
  
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Answers.Body: <p>Due to the definition of <a href="https://en.wikipedia.org/wiki/Swish_function" rel="noreferrer">SiLU</a> activation function, only slightly negative gradients in regions near <span class="math-container">$0$</span>-valued input can cause weight updates that seem to be moving in the &quot;wrong&quot; direction.</p>
  <p>However, due to their generally small magnitudes, intuitively these updates are usually not large enough to drastically impact the optimization process. Moreover, the usual SGD optimization introduces a lot of noise into the gradient updates where the above occasional small wrong updates are usually overwhelmed by the noise and the model continues to learn effectively.</p>
  <p>Additionally with batch normalization techniques, inputs are more likely to hover around zero, and the distribution of positive and negative gradients is balanced. This balance minimizes the negative impact of slightly negative gradients together with its everywhere-smooth property and increased computational cost compared to ReLU.</p>
  <p>Finally some level of oscillation in parameter updates can actually act as a form of (implicit) regularization, preventing the model from overfitting to a specific direction in the gradient landscape. This can help the model explore a broader region of the parameter space. In modern deep learning, overparameterization helps to absorb slight perturbations caused by negative gradients whose flexibility allows it to learn complex patterns even when some updates are counter-intuitive.</p>
  
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Body: <p>Unlike ReLU, the derivative of SiLU is non-zero everywhere except at the global minimum. However, intuitively it seems like having a negative gradient when the input is very negative should be even worse than having a zero gradient, since the gradient update steps would go the wrong way. Why is this not a problem in practice?</p>
  
Tags: <training><activation-functions>
Title: Why doesn't SiLU suffer from a worse version of a "dying ReLU" problem?
UserDisplayName: llllvvuu
ThreadText: # Why doesn't SiLU suffer from a worse version of a "dying ReLU" problem?
  
  (Asked by: username_0 on 2024-09-10)
  
  Unlike ReLU, the derivative of SiLU is non-zero everywhere except at the global minimum. However, intuitively it seems like having a negative gradient when the input is very negative should be even worse than having a zero gradient, since the gradient update steps would go the wrong way. Why is this not a problem in practice?
  
  **Tags:** training, activation-functions
  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_3 on 2024-09-10. Score: 5 | Accepted answer
  
  Due to the definition of [SiLU](https://en.wikipedia.org/wiki/Swish_function) activation function, only slightly negative gradients in regions near $0$-valued input can cause weight updates that seem to be moving in the "wrong" direction.
  
  However, due to their generally small magnitudes, intuitively these updates are usually not large enough to drastically impact the optimization process. Moreover, the usual SGD optimization introduces a lot of noise into the gradient updates where the above occasional small wrong updates are usually overwhelmed by the noise and the model continues to learn effectively.
  
  Additionally with batch normalization techniques, inputs are more likely to hover around zero, and the distribution of positive and negative gradients is balanced. This balance minimizes the negative impact of slightly negative gradients together with its everywhere-smooth property and increased computational cost compared to ReLU.
  
  Finally some level of oscillation in parameter updates can actually act as a form of (implicit) regularization, preventing the model from overfitting to a specific direction in the gradient landscape. This can help the model explore a broader region of the parameter space. In modern deep learning, overparameterization helps to absorb slight perturbations caused by negative gradients whose flexibility allows it to learn complex patterns even when some updates are counter-intuitive.
  
  
  ---
  
  ### Answer by username_1 on 2024-09-11. Score: 3
  
  > intuitively it seems like having a negative gradient when the input is very negative should be even worse than having a zero gradient, since the gradient update steps would go the wrong way.
  
  Gradient update steps go in the opposite direction of the gradient. It's gradient descent, not ascent. If the input is very negative and the gradient is negative, then gradient descent will move in the positive direction, towards 0. That's the "right" way.
  
  Gradient descent can work with practically any activation function. It would work fine if the activation was f(x) = min(x, 0), in which the "problem" you describe is magnified. It will go the right way and be functionally the same as ReLU.
  
  
  ---
  
  ### Answer by username_2 on 2024-09-11. Score: 1
  
  It does not matter the sign of the gradient. Activations are universal approximation even if flipped:
  
  $$
  W \sigma(Wx + b) + b\\
  -W (-\sigma(Wx + b)) + b
  $$
  say $\sigma$ is the sigmoid, in the second case, the gradient is always negative, yet you are still an universal approximator, since you just need to flip the sign of the second layer $W$ matrix
  
  The take home message is: the sign of the activation is not that important. The reason why SiLU works better, has nothing to do with the gradient not being 0, otherwise sigmoid, tanh, leaky relu and so on, would be a possible solution
  
  
  ---
  
  