神经网络与深度学习笔记（三）python 实现反向传播算法

1、BP方程式

2、计算步骤

3、代码

def backprop(self, x, y):"""Return a tuple "(nabla_b, nabla_w)" representing thegradient for the cost function C_x. "nabla_b" and"nabla_w" are layer-by-layer lists of numpy arrays, similarto "self.biases" and "self.weights"."""    # 分配 w 、b 的空间    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 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)        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)