Tanh Activation Function

Kajal Pawar

a year ago

Tanh is also known as hyperbolic tangent function. The curves of tanh function and sigmoid function are relatively similar as we can see from the image below.
hyperbolic tangent function
hyperbolic tangent function
Let ’s compares both of them. When the input is large or small, the output is almost smooth and the gradient is small, which is not conducive to weight update. The difference is the output interval.
The output interval of tanh is 1, and the whole function is 0-centric, which is better than sigmoid.
In general, binary classification problems, the tanh function is used for the hidden layer and the sigmoid function is used for the output layer. However, these are not static, and the specific activation function to be used must be analyzed according to the specific problem, or it depends on different experiments.
The equation of the tanh function id given by:
equation of the tanh function
equation of the tanh function
                                                                             Or
equation of the tanh function
equation of the tanh function
The graph of the tanh function and its derivative can be shown as:
graph of the tanh function and its derivative
graph of the tanh function and its derivative

How to write a tanh function and its derivative in python?

So, writing a tanh function and its derivative is quite easy. Simply we have to define a function for the formula. It is implemented as shown below:
tanh function
def tanh_function(z):
    return (np.exp(z) - np.exp(-z)) / (np.exp(z) + np.exp(-z))
tanh function derivative
def tanh_prime_function(z):
    return 1 - np.power(tanh_function(z),2)

Tanh and Sigmoid activation function:

  • Tanh is quite similar to the Y=X function in the vicinity of the origin. When the value of the activation function is low, the matrix operation can be directly performed which makes the training process relatively easier. Both tanh and sigmoid activation functions are fired which makes the neural network heavier.
  • Sigmoid function ranges from 0 to 1, but there might be a case where we would like to introduce a negative sign to the output of the artificial neuron. This is where Tanh (hyperbolic tangent function) becomes very useful. Tanh function is almost similar to sigmoid function but the only the main difference is that its output varies from +1 to -1 and Tanh function is centred at zero.

When will can use tanh function:

Most of the times Tanh function is usually used in hidden layers of a neural network because its values lies between -1 to 1 that’s why the mean for the hidden layer comes out be 0 or its very close to 0, hence tanh functions helps in centering the data by bringing mean close to 0 which makes learning for the next layer much easier. So, tanh function is useful.

Advantages of tanh function

  • For tanh activation function the gradient is stronger as compared to sigmoid function.

Disadvantages of tanh function

  • Tanh also has the vanishing gradient problem similar to the sigmoid function.

A simple implementation of tanh activation function in python

# import libraries
import matplotlib.pyplot as plt
import numpy as np

#creating a tanh function
def tanh(x):
    a=(np.exp(x)-np.exp(-x))/(np.exp(x)+np.exp(-x))
    dt=1-t**2
    return a,da
b=np.arange(-4,4,0.01)
tanh(b)[0].size,tanh(b)[1].size
# Setup centered axes
fig, ax = plt.subplots(figsize=(9, 5))
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
# Create and show plot
ax.plot(b,tanh(b)[0], color="#307EC7", linewidth=3, label="tanh")
ax.plot(b,tanh(b)[1], color="#9621E2", linewidth=3, label="derivative")
ax.legend(loc="upper right", frameon=false)
fig.show()
Output:
The plot shown below is the output of the above code which plots the tanh and its derivative function.
utput of the above code which plots the tanh and its derivative function
utput of the above code which plots the tanh and its derivative function
I hope you enjoyed reading this article and finally, you came to know about Tanh Activation Function and its implementation using python.
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Thanks for reading…
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