classNetwork(object):
...
def backprop(self,x,y):
"""Return a tuple "(nabla_b,nabla_w)" representing the
gradient for the cost function L_x. "nabla_b" and
"nabla_w" are layer-by-layer lists of numpy arrays, similar
to "self.biases" and "self.weights"."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# Feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation) + b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# Backward pass
delta = self.cost_derivative(activations[-1],y)∗sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable "l" is used as follows:
# l = 1 means the last layer of neurons,
# l = 2 is the second-last layer,and so on.
# We take advantage that Python
# can use negative indices in lists.
for l in xrange(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(),delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta,activations[-l-1].transpose())
return (nabla_b,nabla_w)
...
def cost_derivative(self,output_activations,y):
"""Return the vector of partial derivatives \partial{L_x} /
\partial{a} for the output activations."""
return (output_activations - y)
def sigmoid(z):
"""The sigmoid function."""
return 1.0 / (1.0 + np.exp(-z))
def sigmoid_prime(z):
"""Derivative of thesigmoid function."""
return sigmoid(z) * (1-sigmoid(z))complete this code with python 3 update
class Network(object):
...
def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying
gradient descent using backpropagation to a single mini batch.
The "mini_batch" is a list of tuples "(x, y)", and "eta"
is the learning rate."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]