Sigmoid Activation Function

Shashank Shanu

17 hours ago

Sigmoid Activation Function
Sigmoid Activation Function
Table of Content
  • What is a Sigmoid Function?
  • Advantages of Sigmoid Function: -
  • Disadvantages of Sigmoid functions:
  • How to write a sigmoid function and its derivative in python?
  • Simple implementation of the sigmoid activation function in python
        As we discussed earlier in the previous article what is activation functions and types of activation function briefly. In this article I will try to explain you in detail about one the activation function which is Sigmoid Activation function.
So, let’s start
Most of you I think are already familiar about the activation functions if not I would recommend you to through my previous article first and then come back to this article to get better understanding.

What is a Sigmoid Function?

       The Sigmoid function is the most frequently widely used activation function in the beginning of deep learning. It is a smoothing function that is easy to derive and implement.
The name Sigmoidal is derived from the Greek letter Sigma, and when it is plotted, appears as a sloping “S” across the Y-axis.
A sigmoidal function is a logistic function which purely refers to any function that retains the “S” shape, for example tanh(x). Where a traditional sigmoidal function exists between 0 and 1, tanh(x) follows a similar shape, but exists between 1 and -1. On its own, a sigmoidal function is also differentiable, we can easily find the slope of the sigmoid curve, at any given two points.
In the sigmoid function, we can see that its output lies in between the open interval (0,1). We can think of probability, but in the strict sense, don't treat it as probability. The sigmoid function was once more popular. It can be thought of as the firing rate of a neuron. In the middle where the slope is relatively large, it is the sensitive area of the neuron. On the sides where the slope is very gentle, it is the neuron's inhibitory area.
The equation of the Sigmoid function is given by:
Equation of Sigmoid function
Equation of Sigmoid function
And, the graph of the sigmoid function can be represented as:
Graph of the sigmoid function
Graph of the sigmoid function
Sigmoid function itself contains some defects.
1) When the input is slightly away from the coordinate origin, the gradient of the function becomes very small, almost zero. In the process of neural network backpropagation, we all use the chain rule of differential to calculate the differential of each weight w. When the backpropagation passes through the sigmoid function, the differential on this chain is very small. Moreover, it may pass through many sigmoid functions, which will eventually cause the weight(w) to have little effect on the loss function, which is not conducive to the optimization of the weight. This problem is called gradient saturation or gradient dispersion.
2) The function output is not centred on 0, which will reduce the efficiency of the weight update.
3) The sigmoid function performs exponential operations, which is slower for computers.
Some of the advantages and disadvantages of Sigmoid functions are mentioned below:

Advantages of Sigmoid Function: -

  • It provides Smooth gradient which helps us in preventing “jumps” in output values.
  • Output values bound between 0 and 1, normalizing the output of each neuron.
  • It provides clear predictions, i.e. very close to 1 or 0 which helps us to improve model performance.

Disadvantages of Sigmoid functions:

  • It is most prone to gradient vanishing problem.
  • Function output is not zero-centred.
  • Power operations are relatively time-consuming which increases model complexity.

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

So, writing a sigmoid function and its derivative is quite easy. Simply we have to define a function for the formula. It is implemented as shown below:
Sigmoid function
def sigmoid(z):
   return 1.0 / (1 + np.exp(-z))
Sigmoid function derivative
def sigmoid_prime(z):
return sigmoid(z) * (1-sigmoid(z))

Simple implementation of the sigmoid activation function in python

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

#creating sigmoid function
def sigmoid(x):
    s=1/(1+np.exp(-x))
    ds=s*(1-s)  
    return s,ds
a=np.arange(-6,6,0.01)
sigmoid(x)
# Setup centered axes
fig, ax = plt.subplots(figsize=(9, 5))
ax.spines['left'].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(a,sigmoid(x)[0], color="#307EC7", linewidth=3, label="sigmoid")
ax.plot(a,sigmoid(x)[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 sigmoid and its derivative function
output of graph of sigmod function
output of graph of sigmod function
I hope you enjoyed reading this article and finally, you came to know about Sigmoid Activation Function and how we can implement it in python. 
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Thanks for reading…
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