The activation functions in PyTorch (2)

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*Memos:

• My post explains ReLU() and LeakyReLU().
• My post explains PReLU() and ELU().
• My post explains Step function, Identity and ReLU.
• My post explains ELU, SELU and CELU.
• My post explains GELU, Mish, SiLU and Softplus.
• My post explains Tanh, Softsign, Sigmoid and Softmax.
• My post explains Vanishing Gradient Problem, Exploding Gradient Problem and Dying ReLU Problem.

(1) Leaky ReLU(Leaky Rectified Linear Unit):

• is improved ReLU, being able to mitigate Dying ReLU Problem.
• can convert an input value(x) to the output value between ax and x. *Memos:
  • If x < 0, then ax while if 0 <= x, then x.
  • a is 0.01 by default basically.
• 's formula is y = max(ax, x).
• is also called LReLU.
• is LeakyReLU() in PyTorch.
• is used in:
  • GAN.
• 's pros:
  • It mitigates Vanishing Gradient Problem.
  • It mitigates Dying ReLU Problem. *0 is still produced for the input value 0 so Dying ReLU Problem is not completely avoided.
• 's cons:
  • It's non-differentiable at x = 0.
• 's graph in Desmos:

(2) PReLU(Parametric Rectified Linear Unit):

• is improved Leaky ReLU, having the 0 or more learnable parameters which are changing(adjusting) during training to improve a model's accuracy and convergence.
• can convert an input value(x) to the output value between ax and x: *Memos:
  • If x < 0, then ax while if 0 <= x, then x.
  • a is 0.25 by default basically. *a is the initial value for 0 or more learnable parameters.
• 's formula is y = max(ax, x).
• is PReLU() in PyTorch.
• is used in:
  • SRGAN(Super-Resolution Generative Adversarial Network). *SRGAN is a type of GAN(Generative Adversarial Network).
• 's pros:
  • It mitigates Vanishing Gradient Problem.
  • It mitigates Dying ReLU Problem. *0 is still produced for the input value 0 so Dying ReLU Problem is not completely avoided.
• 's cons:
  • It's non-differentiable at x = 0. *The gradient for step function doesn't exist at x = 0 during Backpropagation which does differential to calculate and get a gradient.
• 's graph in Desmos:

(3) FReLU(Flexible Rectified Linear Unit):

• is improved ReLU, having the 0 or more learnable bias parameters which are changing(adjusting) during training to improve a model's accuracy and convergence.
• 's formula is y = ReLU(x) + b. *b is the initial value for 0 or more learnable bias parameters.
• is also called Funnel Activation.
• isn't in PyTorch so you can use frelu.pytorch or FunnelAct_Pytorch.
• 's pros:
  • It mitigates Vanishing Gradient Problem.
  • It avoid Dying ReLU Problem when b < 0 or 0 < b.
• 's cons:
  • It causes Dying ReLU Problem when b = 0.
  • It causes Exploding Gradient Problem when b is greater and greater than 0.
  • It's non-differentiable at the angle. *The gradient for FReLU doesn't exist at the angle during Backpropagation which does differential to calculate and get a gradient.
• 's graph in Desmos: