杂项知识点

1 激活函数

常用的激活函数包罗sigmoid + tanh + Relu + leakRelu
1.1 sigmoid

2. import torch
3. import numpy as np
4. import matplotlib.pyplot as plt
5. # sigmoid + tanh + Relu + leakRelu
6. ## 1 sigmoid
7. ### 1.1 代码复现sigmoid
8. #(1)函数
9. def sigmoid(x):
10.     return 1./(1+torch.exp(-x))
12. def sigmoid_diff(x):
13.     t = sigmoid(x)
14.     return t*(1-t)
15. #(2))检测
16. x = torch.arange(3)
17. print(sigmoid(x))
18. print(sigmoid_diff(x))
19. print("#"*10)
21. ## 1.2 用torch检测sigmoid的导数
22. for i in range(3):
23.     x = torch.tensor([i],dtype=torch.float32,requires_grad=True)
24.     y = sigmoid(x)
25.     y.backward()
26.     print(x.grad.item(),end=", ")
28. '''
29. tensor([0.5000, 0.7311, 0.8808])
30. tensor([0.2500, 0.1966, 0.1050])
31. ##########
32. 0.25， 0.1966119408607483， 0.10499356687068939
33. '''

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1.2 tanh

1. import torch
2. import numpy as np
3. import matplotlib.pyplot as plt
4. ## 2 thah
5. ### 2.1 代码复现thah
6. #(1)函数
7. def thah(x):
8.     return 1.*(torch.exp(x)-torch.exp(-x))/(torch.exp(x)+torch.exp(-x))
10. def thah_diff(x):
11.     t = torch.exp(2*x)
12.     return 4*t/(1+t)**2
13. #(2))检测
14. x = torch.arange(3)
15. print(thah(x))
16. print(thah_diff(x))
17. print("#"*10)
19. ## 2.2 用torch检测thah的导数
20. for i in range(3):
21.     x = torch.tensor([i],dtype=torch.float32,requires_grad=True)
22.     y = thah(x)
23.     y.backward()
24.     print(x.grad.item(),end=", ")
25. '''
26. tensor([0.0000, 0.7616, 0.9640])
27. tensor([1.0000, 0.4200, 0.0707])
28. ##########
29. 1.0，0.41997432708740234，0.07065081596374512
30. '''

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1.3 Relu

1. import torch
2. import numpy as np
3. import matplotlib.pyplot as plt
4. ## 3 Relu
5. ### 3.1 代码复现Relu
6. #(1)函数
7. def Relu(x):
8.     return torch.maximum(torch.tensor(0),x)
10. def Relu_diff(x):
11.     return torch.where(x>0,1,0)
12. #(2))检测
13. x = torch.arange(-2,4)
15. print(Relu(x))
16. print(Relu_diff(x))
17. print("#"*10)
19. # 3.2 用torch检测Relu的导数
20. for i in range(-2,4):
21.     x = torch.tensor([i],dtype=torch.float32,requires_grad=True)
22.     y = Relu(x)
23.     y.backward()
24.     print(x.grad.item(),end=", ")
25. '''
26. tensor([0, 0, 0, 1, 2, 3])
27. tensor([0, 0, 0, 1, 1, 1])
28. ##########
29. 0.0, 0.0, 0.5, 1.0, 1.0, 1.0,
30. '''

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1.4 leakRelu

1. import torch
2. import numpy as np
3. import matplotlib.pyplot as plt
4. ## 4 LeakRelu
5. ### 4.1 代码复现LeakRelu
6. #(1)函数
7. def LeakRelu(x,a=0.01):
8.     return torch.maximum(torch.tensor(a),x)
10. def LeakRelu_diff(x):
11.     return torch.where(x>0,1,0.01)
12. #(2))检测
13. x = torch.arange(3)
14. print(LeakRelu(x))
15. print(LeakRelu_diff(x))
16. print("#"*10)
18. ## 4.2 用torch检测LeakRelu的导数
19. for i in range(3):
20.     x = torch.tensor([i],dtype=torch.float32,requires_grad=True)
21.     y = LeakRelu(x)
22.     y.backward()
23.     print(x.grad.item(),end=", ")
25. '''
26. tensor([0.0100, 1.0000, 2.0000])
27. tensor([0.0100, 1.0000, 1.0000])
28. ##########
29. 0.0, 1.0, 1.0,
31. '''

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