ziyubiti

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]    # idx0:30*1; idx1:10*1
        nabla_w = [np.zeros(w.shape) for w in self.weights]   # idx0:30*784; idx1:10*30
        for x, y in mini_batch:                              # loop 10, BP calc  and update gradient 10 times
            delta_nabla_b, delta_nabla_w = self.backprop(x, y)        # delta b,delta w , their dimension is same as b,w
            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]  # bj:zip two column vector, but list output row by row
            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)]     # update w, sum the average 10 changes
        self.biases = [b-(eta/len(mini_batch))*nb
                       for b, nb in zip(self.biases, nabla_b)]       # update b,
    def backprop(self, x, y):
        """Return a tuple ``(nabla_b, nabla_w)`` representing the
        gradient for the cost function C_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)                              # middle variable z before sigmoid, z1,z2
            activation = sigmoid(z)
            activations.append(activation)            # activation output, x, s1,s2
        # backward pass
        delta = self.cost_derivative(activations[-1], y) * \                # C=1/2 *(s2-y).^2, so dc/ds=(s2-y)
            sigmoid_prime(zs[-1])                                            # delta 10*1
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())           # s1: 30*1, s1':1*30; delta:10*1, dot:10*30
        # Note that the variable l in the loop below is used a little
        # differently to the notation in Chapter 2 of the book.  Here,
        # l = 1 means the last layer of neurons, l = 2 is the
        # second-last layer, and so on.  It's a renumbering of the
        # scheme in the book, used here to take advantage of the fact
        # that Python can use negative indices in lists.
        for l in xrange(2, self.num_layers):
            z = zs[-l]                                                         
            sp = sigmoid_prime(z)                                           #sp1: dz1, 30*1
            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp       # w[1]: 10*30;  delta update to 30*1 
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())      # delta 30*1, l=2, s0=x,784*1, ze w[-2]=w[0]=30*784 
        return (nabla_b, nabla_w)
    def cost_derivative(self, output_activations, y):
        """Return the vector of partial derivatives \partial C_x /
        \partial a for the output activations."""
        return (output_activations-y)