http://iamtrask.github.io/2015/07/12/basic-python-network/

X = np.array([ [0,0,1],[0,1,1],[1,0,1],[1,1,1] ])
y = np.array([[0,1,1,0]]).T
syn0 = 2*np.random.random((3,4)) - 1
syn1 = 2*np.random.random((4,1)) - 1
for j in xrange(60000):
l1 = 1/(1+np.exp(-(np.dot(X,syn0))))
l2 = 1/(1+np.exp(-(np.dot(l1,syn1))))
l2_delta = (y - l2)*(l2*(1-l2))
l1_delta = l2_delta.dot(syn1.T) * (l1 * (1-l1))
syn1 += l1.T.dot(l2_delta)
syn0 += X.T.dot(l1_delta)