The activation functions in PyTorch (3)

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*Memos:

• My post explains PReLU() and ELU().
• My post explains SELU() and CELU().
• My post explains Step function, Identity and ReLU.
• My post explains Leaky ReLU, PReLU and FReLU.
• 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) ELU(Exponential Linear Unit):

• can convert an input value(x) to the output value between aex - a and x: *Memos:
  • If x < 0, then aex - a while if 0 <= x, then x.
  • a is 1.0 by default basically.
• is ELU() in PyTorch.
• 's pros:
  • It normalizes negative input values.
  • The convergence with negative input values is stable.
  • 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 computationally expensive because of exponential operation.
  • It's non-differentiable at x = 0 if a is not 1.
• 's graph in Desmos:

(2) SELU(Scaled Exponential Linear Unit):

• can convert an input value(x) to the output value between λ(ae^x - a) and λx: *Memos:
  • If x < 0, then λ(aex - a) while if 0 <= x, then λx.
  • λ=1.0507009873554804934193349852946
  • α=1.6732632423543772848170429916717
• is SELU() in PyTorch.
• 's pros:
  • It normalises negative input values.
  • The convergence with negative input values is stable.
  • 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 may cause Exploding Gradient Problem because a positive input value is increased by the multiplication with λ.
  • It's computationally expensive because of exponential operation.
  • It's non-differentiable at x = 0 if a is not 1.
• 's graph in Desmos:

(3) CELU(Continuously Differentiable Exponential Linear Unit):

• is improved ELU, being able to differentiate at x = 0 even if a is not 1.
• can convert an input value(x) to the output value between ae^x/a - a and x: *Memos:
  • If x < 0, then aex/a - a while if 0 <= x, then x.
  • a is 1.0 by default basically.
• 's formula is:
• is CELU() in PyTorch.
• 's pros:
  • It normalises negative input values.
  • The convergence with negative input values is stable.
  • 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 computationally expensive because of exponential operation.
• 's graph in Desmos: