sigmoid function

def nonlin(x,deriv=False):
    if(deriv==True):
        return x*(1-x)
    return 1/(1+np.exp(-x))

input dataset

X = np.array([  [0,0,1],
                [0,1,1],
                [1,0,1],
                [1,1,1] ])

output dataset

y = np.array([[0,0,1,1]]).T

seed random numbers to make calculation deterministic (just a good practice)

np.random.seed(1)

initialize weights randomly with mean 0

syn0 = 2*np.random.random((3,1)) - 1
print(syn0)

## [[-0.16595599]
##  [ 0.44064899]
##  [-0.99977125]]

• variables
  • l0 is input layer
  • l1 is hidden layer
  • l1_error is the loss function
  • l1_delta is the gradient descent function for calculating the back-propagation
  • syn0 are synapses, weights between l0 and l1, and also how the weights are updated are shown.

for iter in range(100000):
# forward propagation
    l0 = X
    l1 = nonlin(np.dot(l0,syn0))
# how much did we miss 
    l1_error = y - l1
# multiply how much we missed by the 
# slope of the sigmoid at the values in l1
    l1_delta = l1_error * nonlin(l1,True)
# update weights
    syn0 += np.dot(l0.T,l1_delta)

check l1, which is output layer:

print("Output After Training:")

## Output After Training:

print(l1)

## [[0.00301758]
##  [0.00246109]
##  [0.99799161]
##  [0.99753723]]