Description

In the context of artificial neural networks, the Logistic function is an activation function defined as:

where x is the input to a Artificial Neuron.

from matplotlib import pyplot as plt
import numpy as np

def sigmoid_forward(x):
    return 1 / (1 + np.exp(-x))


x = np.arange(-7,7)
y = sigmoid_forward(x)

plt.style.use('fivethirtyeight')
fig, ax = plt.subplots()
ax.plot(x, y)
ax.set_title("Plot of the Logistic function")
plt.show()

Logistic function derivative with respect to x defined as:

Logistic function presents a serious disadvantage called vanishing gradient problem. Logistic function used in computer vision and speech recognition using deep neural nets.

TensorFlow form of Logistic function:

tf.sigmoid(
    x,
    name=None
)

Pytorch form of Logistic function:

class torch.nn.Sigmoid

Forward propagation EXAMPLE

/* ANSI C89, C99, C11 compliance                                                   */
/* The following example shows the usage of Logistic function forward propagation. */
#include <stdio.h>
#include <math.h>


float logistic_forward(float x){
   return 1.0f / (1.0f + (float)exp(-x));
}

int main()  {
   float r_x, r_y;


   r_x = 0.1f;
   r_y = logistic_forward(r_x);
   printf("Logistic function forward propagation for value x: %f\n", r_y);
   return 0;
}

Backward propagation EXAMPLE

/* ANSI C89, C99, C11 compliance                                                    */
/* The following example shows the usage of Logistic function backward propagation. */
#include <stdio.h>
#include <math.h>

float logistic_backward(float x){
   float r_log = 1.0f / (1.0f + (float)exp(-x));


   return r_log * (1.0f - r_log);
}

int main()  {
   float r_x, r_y;


   r_x = 0.1f;
   r_y = logistic_backward(r_x);
   printf("Logistic function backward propagation for value x: %f\n", r_y);
   return 0;
}