Documentation of Backpropogation function

backpropogation.py

@@ -1,10 +1,12 @@
 import numpy as np
 
-def sigmoid(z):
-return 1.0/(1.0+np.exp(-z))
+def sigmoid(z):                      #  This is funtion which gives output between 0 and 1 
+                                     #  it represents the activation of that neuron.
+    return 1.0/(1.0+np.exp(-z))
 
 def sigmoid_prime(z):
-return sigmoid(z)*(1-sigmoid(z))
+    return sigmoid(z)*(1-sigmoid(z))    # This gives the derivative of the sigmoid function
+
 #The backpropogation function 
 def backprop(net, x, y):
         '''
@@ -16,22 +18,28 @@ def backprop(net, x, y):
         '''
         nabla_b = [np.zeros(b.shape) for b in net.biases]
         nabla_w = [np.zeros(w.shape) for w in net.weights]
+        #feedforward
         activation = x
-        activations = [x] 
-        zs = [] 
+        activations = [x]  #list to store all the activations, layer by layer
+        zs = []            #list to store all z vectors, layer by layer
         for b, w in zip(net.biases, net.weights):
             z = np.dot(w, activation)+b
             zs.append(z)
             activation = sigmoid(z)
             activations.append(activation)
+        #backward pass
+        # transpose() returns the numpy array with the rows as columns and columns as rows
         delta = net.cost_derivative(activations[-1], y) * \
             sigmoid_prime(zs[-1])
         nabla_b[-1] = delta
         nabla_w[-1] = np.dot(delta, activations[-2].transpose())
+        # l = 1 means the last layer of neurons, l = 2 is the
+        # second-last layer, and so on.
         for l in range(2, net.num_layers):
             z = zs[-l]
             sp = sigmoid_prime(z)
             delta = np.dot(net.weights[-l+1].transpose(), delta) * sp
             nabla_b[-l] = delta
             nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
-        return (net,nabla_b, nabla_w)
+        return (net,nabla_b, nabla_w)                                       #Return ''(nabla_b, nabla_w)'' representing the
+                                                                            #gradient for the cost function.