2025.3.11 tanh関数

NumPy版

code:p1.py

import matplotlib.pyplot as plt

import numpy as np

x = np.linspace(-5, 5)

y = np.tanh(x)

plt.plot(x, y)

plt.grid()

plt.show()

PyTorch版

code:p1.py

import matplotlib.pyplot as plt

import torch as pt

x = pt.linspace(-5, 5, 50)

y = pt.tanh(x)

plt.plot(x, y)

plt.grid()

plt.show()

シグモイド関数との比較

code:p1.py

import matplotlib.pyplot as plt

import torch as pt

x = pt.linspace(-5, 5, 50)

y1 = pt.tanh(x)

y2 = pt.sigmoid(x)

plt.plot(x, y1, label='tanh')

plt.plot(x, y2, label='$\sigma$')

plt.grid()

plt.legend()

plt.show()

https://scrapbox.io/files/67cfe7bac4d8e2eb4702bd1d.png

シグモイド関数をtanhに変形する

$ 2\sigma(2x)-1 = \tanh(x)

code:p1.py

import matplotlib.pyplot as plt

import torch as pt

x = pt.linspace(-5, 5, 50)

y1 = pt.tanh(x)

y2 = pt.sigmoid(x*2)*2-1

plt.plot(x, y1, label='$tanh$')

plt.plot(x, y2, label='$2\sigma(2x)-1$')

plt.grid()

plt.legend()

plt.show()

https://scrapbox.io/files/67cfe5e2552b27c0a8fc4975.png

tanhをシグモイド関数に変形する

$ \frac{1}{2} \left(\tanh(\frac{x}{2})+1\right) = \sigma(x)

code:p1.py

import matplotlib.pyplot as plt

import torch as pt

x = pt.linspace(-5, 5, 50)

y1 = (1/2)*(pt.tanh(x/2)+1)

y2 = pt.sigmoid(x)

plt.plot(x, y1, label='$0.5( tanh (x/2)+1)$')

plt.plot(x, y2, label='$\sigma(x)$')

plt.grid()

plt.legend()

plt.show()

https://scrapbox.io/files/67cfe76e6d7413e2a56a22c0.png