Activation functions in PyTorch (4)

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*Memos:

• My post explains GELU() and Mish().
• My post explains SiLU() and Softplus().
• My post explains Step function, Identity and ReLU.
• My post explains Leaky ReLU, PReLU and FReLU.
• My post explains ELU, SELU and CELU.
• My post explains Tanh, Softsign, Sigmoid and Softmax.
• My post explains Vanishing Gradient Problem, Exploding Gradient Problem and Dying ReLU Problem.
• My post explains layers in PyTorch.
• My post explains loss functions in PyTorch.
• My post explains optimizers in PyTorch.

(1) GELU(Gaussian Error Linear Unit):

• can convert an input value(x) to an output value by the input value's probability under a Gaussian distribution with optional Tanh. *0 is exclusive except when x = 0.
• 's formula is. *Both of them get the almost same results: Or:
• is GELU() in PyTorch.
• is used in:
  • Transformer. *Transformer() in PyTorch.
  • NLP(Natural Language Processing) based on Transformer such as ChatGPT, BERT(Bidirectional Encoder Representations from Transformers), etc. *Strictly speaking, ChatGPT and BERT are based on Large Language Model(LLM) which is based on Transformer.
• '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 computationally expensive because of complex operation including Erf(Error function) or Tanh.
• 's graph in Desmos:

(2) Mish:

• can convert an input value(x) to an output value by x * Tanh(Softplus(x)). *0 is exclusive except when x = 0.
• 's formula is:
• is Mish() in PyTorch.
• '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 computationally expensive because of Tanh and Softplus operation.
• 's graph in Desmos:

(3) SiLU(Sigmoid-Weighted Linear Units):

• can convert an input value(x) to an output value by x * Sigmoid(x). *0 is exclusive except when x = 0.
• 's formula is y = x / (1 + e^-x).
• is also called Swish.
• is SiLU() in PyTorch.
• '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 computationally expensive because of Sigmoid.
• 's graph in Desmos:

(4) Softplus:

• can convert an input value(x) to the output value between 0 and ∞. *0 is exclusive.
• 's formula is y = log(1+e^x).
• is Softplus() in PyTorch.
• 's pros:
  • It normalizes input values.
  • The convergence is stable.
  • It mitigates Vanishing Gradient Problem.
  • It mitigates Exploding Gradient Problem.
  • It avoids Dying ReLU Problem.
• 's cons:
  • It's computationally expensive because of log and exponential operation.
• 's graph in Desmos: