def feedforward(self, x):
"""前向传播得到神经网络的输出"""
# 计算第一层神经元的输出
sum_layer_1 = self.weights_layer_1 * x + self.biases_layer_1
out_layer_1 = af.Sigmoid(sum_layer_1)
# 计算第二层神经元的输出
sum_layer_2 = self.weights_layer_2 * out_layer_1 + self.biases_layer_2
out_layer_2 = af.Sigmoid(sum_layer_2)
return out_layer_2
def backprop(self, x, y_true):
# 计算损失函数对相应参数的偏导数，优化后的整个神经网络的权重矩阵列表
nabla_w = [np.zeros(w.shape) for w in self.weights]
# 优化后的整个神经网络的偏置向量列表
nabla_b = [np.zeros(b.shape) for b in self.biases]
# 前向传播
activation = x # 输入层的输入值直接作为激活值
activation_list = [x] # 存储每个神经层的输出
wx_plus_b_list = []
# 遍历每个神经层（除了输入层）的权重矩阵和偏置向量
for w, b in zip(self.weights, self.biases):
wx_plus_b = np.dot(w, activation) + b
wx_plus_b_list.append(wx_plus_b)
activation = af.Sigmoid(wx_plus_b)
activation_list.append(activation)
# 反向传播(从输出层开始更新神经网络的参数)
# 计算输出层误差
delta = self.Deriv_Loss(y_true,activation_list[-1])*\
af.Deriv_Sigmoid(wx_plus_b_list[-1])
# 计算输出层参数的梯度
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activation_list[-2].transpose())
# 计算中间层参数的梯度
for l in range(2, self.num_layer):
delta =np.dot(self.weights[-l+1].transpose(),delta)* \
af.Deriv_Sigmoid(wx_plus_b_list[-l])
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activation_list[-l - 1].transpose())
return (nabla_w, nabla_b)
def backprop(self, x, y_true):
"""反向传播优化神经网络"""
# 计算损失函数对相应参数的偏导数，优化后的整个神经网络的权重矩阵列表
nabla_weight_layer_1 = np.zeros(self.weights_layer_1.shape)
nabla_weight_layer_2 = np.zeros(self.weights_layer_2.shape)
# 优化后的整个神经网络的偏置向量列表
nabla_biase_layer_1 = np.zeros(self.biases_layer_1.shape)
nabla_biase_layer_2 = np.zeros(self.biases_layer_2.shape)
# 前向传播
activation = x # 输入层的输出，也是中间层第一层的输入
activation_list = [x] # 存储每个神经层的输出
wx_plus_b_list = [] # 存储每个神经层未激活的值
# 将第一层神经元的输出中间结果存储进列表
wx_plus_b = np.dot(self.weights_layer_1,
activation) + self.biases_layer_1
wx_plus_b_list.append(wx_plus_b)
activation = af.Sigmoid(wx_plus_b)
activation_list.append(activation)
# 将第二层神经元的输出中间结果存储进列表
wx_plus_b = np.dot(self.weights_layer_2,
activation) + self.biases_layer_2
wx_plus_b_list.append(wx_plus_b)
activation = af.Sigmoid(wx_plus_b)
activation_list.append(activation)
# 反向传播(从输出层开始计算神经网络的参数的梯度)
# 计算输出层误差
delta = self.Deriv_Cost(
y_true, activation_list[-1]) * af.Deriv_Sigmoid(wx_plus_b_list[-1])
# 计算输出神经层各个参数的梯度
nabla_biase_layer_2 = delta
nabla_weight_layer_2 = np.dot(delta, activation_list[-2].transpose())
# 计算中间层各个参数的梯度
delta = np.dot(self.weights_layer_2.transpose(), delta) * \
af.Deriv_Sigmoid(wx_plus_b_list[-2])
nabla_biase_layer_1 = delta
nabla_weight_layer_1 = np.dot(delta, activation_list[-3].transpose())
return (nabla_biase_layer_1, nabla_biase_layer_2, nabla_weight_layer_1,
nabla_weight_layer_2)
def feedforward(self, x):
for w, b in zip(self.weights, self.biases):
x = af.Sigmoid(np.dot(w, x) + b)
return x