import numpy as np
alphas = [0.001,0.01,0.1,1,10,100,1000]
# compute sigmoid nonlinearity
def sigmoid(x):
output = 1/(1+np.exp(-x))
return output
# convert output of sigmoid function to its derivative
def sigmoid_output_to_derivative(output):
return output*(1-output)
X = np.array([[0,0,1],
[0,1,1],
[1,0,1],
[1,1,1]])
y = np.array([[0],
[1],
[1],
[0]])
for alpha in alphas:
print "\nTraining With Alpha:" + str(alpha)
np.random.seed(1)
# randomly initialize our weights with mean 0
synapse_0 = 2*np.random.random((3,4)) - 1
synapse_1 = 2*np.random.random((4,1)) - 1
for j in xrange(60000):
# Feed forward through layers 0, 1, and 2
layer_0 = X
layer_1 = sigmoid(np.dot(layer_0,synapse_0))
layer_2 = sigmoid(np.dot(layer_1,synapse_1))
# how much did we miss the target value?
layer_2_error = layer_2 - y
if (j% 10000) == 0:
print "Error after "+str(j)+" iterations:" + str(np.mean(np.abs(layer_2_error)))
# in what direction is the target value?
# were we really sure? if so, don't change too much.
layer_2_delta = layer_2_error*sigmoid_output_to_derivative(layer_2)
# how much did each l1 value contribute to the l2 error (according to the weights)?
layer_1_error = layer_2_delta.dot(synapse_1.T)
# in what direction is the target l1?
# were we really sure? if so, don't change too much.
layer_1_delta = layer_1_error * sigmoid_output_to_derivative(layer_1)
synapse_1 -= alpha * (layer_1.T.dot(layer_2_delta))
synapse_0 -= alpha * (layer_0.T.dot(layer_1_delta))