The activation functions in PyTorch (5)

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*Memos:

• My post explains Tanh() and Softsign().
• My post explains Sigmoid() and Softmax().
• 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 GELU, Mish, SiLU and Softplus.
• My post explains Vanishing Gradient Problem, Exploding Gradient Problem and Dying ReLU Problem.

(1) Tanh:

• can convert an input value(x) to the output value between -1 and 1. *0 and 1 are exclusive.
• 's formula is y = (e^x - e^-x) / (e^x + e^-x).
• is also called Hyperbolic Tangent Function.
• is Tanh() in PyTorch.
• is used in:
  • RNN(Recurrent Neural Network). *RNN in PyTorch.
  • LSTM(Long Short-Term Memory). *LSTM() in PyTorch.
  • GRU(Gated Recurrent Unit). *GRU() in PyTorch.
  • GAN(Generative Adversarial Network).
• s'pros:
  • It normalizes input values.
  • The convergence is stable.
  • It mitigates Exploding 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 causes Vanishing Gradient Problem.
  • It's computationally expensive because of exponential and complex operation.
• 's graph in Desmos:

(2) Softsign:

• can convert an input value(x) to the output value between 1 and -1. *1 and -1 are exclusive.
• 's formula is y = x / (1 + |x|).
• is Softsign() in PyTorch.
• 's pros:
  • It normalizes input values.
  • The convergence is stable.
  • It mitigates Exploding 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 causes Vanishing Gradient Problem.
• 's graph in Desmos:

(3) Sigmoid:

• can convert an input value(x) to the output value between 0 and 1. *0 and 1 are exclusive.
• 's formula is y = 1 / (1 + e^-x).
• is Sigmoid() in PyTorch.
• is used in:
  • Binary Classification Model.
  • Logistic Regression.
  • LSTM.
  • GRU.
  • GAN.
• 's pros:
  • It normalizes input values.
  • The convergence is stable.
  • It mitigates Exploding Gradient Problem.
  • It avoids Dying ReLU Problem.
• 's cons:
  • It causes Vanishing Gradient Problem.
  • It's computationally expensive because of exponential operation.
• 's graph in Desmos:

(4) Softmax:

• can convert input values(xs) to the output values between 0 and 1 each and whose sum is 1(100%): *Memos:
  • *0 and 1 are exclusive.
  • If input values are [5, 4, -1], then the output values are [0.730, 0.268, 0.002] which is 0.730(73%) + 0.268(26.8%) + 0.002(0.2%) = 1(100%). *Sometimes, approximately 100%.
• 's formula is:
• is Softmax() in PyTorch.
• is used in:
  • Multi-Class Classification Model.
• 's pros:
  • It normalizes input values.
  • The convergence is stable.
  • It mitigates Exploding Gradient Problem.
  • It avoids Dying ReLU Problem.
• 's cons:
  • It causes Vanishing Gradient Problem.
  • It's computationally expensive because of exponential and complex operation.
• 's graph in Desmos:

• 's code from scratch in PyTorch. *dim=0 must be set for sum() otherwise different values are returned for a different D(Dimensional) tensor.

import torch

def softmax(input):
    e_i = torch.exp(input)
    return e_i / e_i.sum(dim=0)
                       # ↑↑↑↑↑ Must be set.

my_tensor = torch.tensor([8., -3., 0., 1.])

print(softmax(my_tensor))
# tensor([9.9874e-01, 1.6681e-05, 3.3504e-04, 9.1073e-04])

my_tensor = torch.tensor([[8., -3.], [0., 1.]])

print(softmax(my_tensor))
# tensor([[9.9966e-01, 1.7986e-02],
#         [3.3535e-04, 9.8201e-01]])

my_tensor = torch.tensor([[[8.], [-3.]], [[0.], [1.]]])

print(softmax(my_tensor))
# tensor([[[9.9966e-01],
#          [1.7986e-02]],
#         [[3.3535e-04],
#          [9.8201e-01]]])