神经网络前向传播和反向传播算法（作业4）

前向传播推导过程

反向传播推导过程是根据以上正向传播推导出的，利用求导的链式法则，这里将所搭建的神经网络的代码放上。求完正向传播和反向传播之后再利用梯度下降算法减小误差。这里将每个参数按照以上规则进行计算。每个神经元与下一个神经元的连接都有权重值和偏置项

import numpy as npdef sigmoid(x):return 1 / (1 + np.exp(-x))def sigmoidD(x):return x * (1 - x)x1s = np.array([])
x2s = np.array([])
x3s = np.array([])y1s = np.array([])
y2s = np.array([])
# 参数定义
# 第一层神经元
#   第一个神经元
w11_1 = np.random.rand()
b11_1 = np.random.rand()w21_1 = np.random.rand()
b21_1 = np.random.rand()w31_1 = np.random.rand()
b31_1 = np.random.rand()#   第二个神经元
w12_1 = np.random.rand()
b12_1 = np.random.rand()w22_1 = np.random.rand()
b22_1 = np.random.rand()w32_1 = np.random.rand()
b32_1 = np.random.rand()#   第三个神经元
w13_1 = np.random.rand()
b13_1 = np.random.rand()w23_1 = np.random.rand()
b23_1 = np.random.rand()w33_1 = np.random.rand()
b33_1 = np.random.rand()#   第四个神经元
w14_1 = np.random.rand()
b14_1 = np.random.rand()w24_1 = np.random.rand()
b24_1 = np.random.rand()w34_1 = np.random.rand()
b34_1 = np.random.rand()# 第二层神经元
#   第一个神经元
w11_2 = np.random.rand()
b11_2 = np.random.rand()
w21_2 = np.random.rand()
b21_2 = np.random.rand()
w31_2 = np.random.rand()
b31_2 = np.random.rand()
w41_2 = np.random.rand()
b41_2 = np.random.rand()#   第二个神经元
w12_2 = np.random.rand()
b12_2 = np.random.rand()
w22_2 = np.random.rand()
b22_2 = np.random.rand()
w32_2 = np.random.rand()
b32_2 = np.random.rand()
w42_2 = np.random.rand()
b42_2 = np.random.rand()# 前向传播
def forward_propgation(x1s, x2s, x3s):# 第一层z1_1 = w11_1 * x1s + b11_1 + w21_1 * x2s + b21_1 + w31_1 * x3s + b31_1a1_1 = sigmoid(z1_1)z2_1 = w12_1 * x1s + b12_1 + w22_1 * x2s + b22_1 + w32_1 * x3s + b32_1a2_1 = sigmoid(z2_1)z3_1 = w13_1 * x1s + b13_1 + w23_1 * x2s + b23_1 + w33_1 * x3s + b33_1a3_1 = sigmoid(z3_1)z4_1 = w14_1 * x1s + b14_1 + w24_1 * x2s + b24_1 + w34_1 * x3s + b34_1a4_1 = sigmoid(z4_1)# 第二层z1_2 = w11_2 * a1_1 + b11_2 + w21_2 * a2_1 + b21_2 + w31_2 * a3_1 + b31_2 + w41_2 * a4_1 + b41_2a1_2 = sigmoid(z1_2)z2_2 = w12_2 * a1_1 + b12_2 + w22_2 * a2_1 + b22_2 + w32_2 * a3_1 + b32_2 + w42_2 * a4_1 + b42_2a2_2 = sigmoid(z2_2)return a2_2, z2_2, a1_2, z1_2, a4_1, z4_1, a3_1, z3_1, a2_1, z2_1, a1_1, z1_1a2_2, z2_2, a1_2, z1_2, a4_1, z4_1, a3_1, z3_1, a2_1, z2_1, a1_1, z1_1 = forward_propgation(x1s, x2s, x3s)for _ in range(5000):for i in range(100):x1 = x1s[i]x2 = x2s[i]x3 = x3s[i]y1 = y1s[i]y2 = y2s[i]# 先完成一次前向传播a2_2, z2_2, a1_2, z1_2, a4_1, z4_1, a3_1, z3_1, a2_1, z2_1, a1_1, z1_1 = forward_propgation(x1s, x2s, x3s)# 误差代价函数e1 = (y1 - a1_2) ** 2e2 = (y2 - a2_2) ** 2# 求w11_2 b11_2 w21_2 b21_2 w31_2 b31_2 w41_2 b41_2# 求w11_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw11_2 = a1_1de1dw11_2 = de1da1_2 * da1_2dz1_2 * dz1_2dw11_2# 求b11_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db11_2 = 1de1db11_2 = de1da1_2 * da1_2dz1_2 * dz1_2db11_2# 求w21_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw21_2 = a2_1de1dw21_2 = de1da1_2 * da1_2dz1_2 * dz1_2dw21_2# 求b21_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db21_2 = 1de1db21_2 = de1da1_2 * da1_2dz1_2 * dz1_2db21_2# 求w31_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw31_2 = a3_1de1dw31_2 = de1da1_2 * da1_2dz1_2 * dz1_2dw31_2# 求b31_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db31_2 = 1de1db31_2 = de1da1_2 * da1_2dz1_2 * dz1_2db31_2# 求w41_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw41_2 = a4_1de1dw41_2 = de1da1_2 * da1_2dz1_2 * dz1_2dw41_2# 求b41_2de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db41_2 = 1de1db41_2 = de1da1_2 * da1_2dz1_2 * dz1_2db41_2# 求w12_2 b12_2 w22_2 b22_2 w32_2 b32_2 w42_2 b42_2# 求w12_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw12_2 = a1_1de2dw12_2 = de2da2_2 * da2_2dz2_2 * dz2_2dw12_2# 求b12_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db12_2 = 1de2db12_2 = de2da2_2 * da2_2dz2_2 * dz2_2db12_2# 求w22_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw22_2 = a2_1de2dw12_2 = de2da2_2 * da2_2dz2_2 * dz2_2dw22_2# 求b22_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db22_2 = 1de2db22_2 = de2da2_2 * da2_2dz2_2 * dz2_2db22_2# 求w32_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw32_2 = a3_1de2dw32_2 = de2da2_2 * da2_2dz2_2 * dz2_2dw32_2# 求b32_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db32_2 = 1de2db32_2 = de2da2_2 * da2_2dz2_2 * dz2_2db32_2# 求w42_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw42_2 = a4_1de2dw42_2 = de2da2_2 * da2_2dz2_2 * dz2_2dw42_2# 求b42_2de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db42_2 = 1de2db42_2 = de2da2_2 * da2_2dz2_2 * dz2_2db42_2# 求w11_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw11_1 = x1de1dw11_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1dw11_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw11_1 = x1de2dw11_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1dw11_1dedw11_1 = de1dw11_1 + de2dw11_1  # 求误差对w11_1的和# 求b11_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db1_1 = 1de1db11_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1db1_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db11_1 = 1de2db11_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1db11_1dedb11_1 = de1db11_1 + de2db11_1  # 求误差对b11_1的和# 求w21_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw21_1 = x2de1dw21_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1dw21_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw21_1 = x2de2dw21_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1dw21_1dedw21_1 = de1dw21_1 + de2dw21_1  # 求误差对w21_1的和# 求b21_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db2_1 = 1de1db21_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1db2_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db21_1 = 1de2db21_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1db21_1dedb21_1 = de1db21_1 + de2db21_1  # 求误差对b21_1的和# 求w31_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw31_1 = x3de1dw31_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1dw31_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw31_1 = x3de2dw31_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1dw31_1dedw31_1 = de1dw31_1 + de2dw31_1  # 求误差对w31_1的和# 求b31_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db3_1 = 1de1db31_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1db3_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db31_1 = 1de2db31_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1db31_1dedb31_1 = de1db31_1 + de2db31_1  # 求误差对b31_1的和# 求w12_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da2_1 = w21_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1dw12_1 = x1de1dw12_1 = de1da1_2 * da1_2dz1_2 * dz1_2da2_1 * da2_1dz2_1 * dz2_1dw12_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da2_1 = w22_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1dw12_1 = x1de2dw12_1 = de2da2_2 * da2_2dz2_2 * dz2_2da2_1 * da2_1dz2_1 * dz2_1dw12_1dedw12_1 = de1dw12_1 + de2dw12_1  # 求误差对w12_1的和# 求b12_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da2_1 = w21_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1db12_1 = 1de1db12_1 = de1da1_2 * da1_2dz1_2 * dz1_2da2_1 * da2_1dz2_1 * dz2_1db12_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da2_1 = w22_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1db12_1 = 1de2db12_1 = de2da2_2 * da2_2dz2_2 * dz2_2da2_1 * da2_1dz2_1 * dz2_1db12_1dedb12_1 = de1db12_1 + de2db12_1  # 求误差对b12_1的和# 求w22_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da2_1 = w21_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1dw22_1 = x2de1dw22_1 = de1da1_2 * da1_2dz1_2 * dz1_2da2_1 * da2_1dz2_1 * dz2_1dw22_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da2_1 = w22_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1dw22_1 = x2de2dw22_1 = de2da2_2 * da2_2dz2_2 * dz2_2da2_1 * da2_1dz2_1 * dz2_1dw22_1dedw22_1 = de1dw22_1 + de2dw22_1  # 求误差对w22_1的和# 求b22_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da2_1 = w21_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1db22_1 = 1de1db22_1 = de1da1_2 * da1_2dz1_2 * dz1_2da2_1 * da2_1dz2_1 * dz2_1db22_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da2_1 = w22_2da2_1dz2_1 = sigmoidD(a2_1)dz2_1db22_1 = 1de2db22_1 = de2da2_2 * da2_2dz2_2 * dz2_2da2_1 * da2_1dz2_1 * dz2_1db22_1dedb22_1 = de1db22_1 + de2db22_1  # 求误差对b22_1的和# 求w32_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw32_1 = x3de1dw32_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1dw32_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1dw32_1 = x3de2dw32_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1dw32_1dedw32_1 = de1dw32_1 + de2dw32_1  # 求误差对w32_1的和# 求b32_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da1_1 = w11_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db32_1 = 1de1db32_1 = de1da1_2 * da1_2dz1_2 * dz1_2da1_1 * da1_1dz1_1 * dz1_1db32_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da1_1 = w12_2da1_1dz1_1 = sigmoidD(a1_1)dz1_1db32_1 = 1de2db32_1 = de2da2_2 * da2_2dz2_2 * dz2_2da1_1 * da1_1dz1_1 * dz1_1db32_1dedb32_1 = de1db32_1 + de2db32_1  # 求误差对b32_1的和# 求w13_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da3_1 = w31_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1dw13_1 = x1de1dw13_1 = de1da1_2 * da1_2dz1_2 * dz1_2da3_1 * da3_1dz3_1 * dz3_1dw13_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da3_1 = w32_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1dw13_1 = x1de2dw13_1 = de2da2_2 * da2_2dz2_2 * dz2_2da3_1 * da3_1dz3_1 * dz3_1dw13_1dedw13_1 = de1dw13_1 + de2dw13_1  # 求误差对w13_1的和# 求b13_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da3_1 = w31_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1db13_1 = 1de1db13_1 = de1da1_2 * da1_2dz1_2 * dz1_2da3_1 * da3_1dz3_1 * dz3_1db13_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da3_1 = w32_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1db13_1 = 1de2db13_1 = de2da2_2 * da2_2dz2_2 * dz2_2da3_1 * da3_1dz3_1 * dz3_1db13_1dedb13_1 = de1db13_1 + de2db13_1  # 求误差对b13_1的和# 求w23_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da3_1 = w31_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1dw23_1 = x2de1dw23_1 = de1da1_2 * da1_2dz1_2 * dz1_2da3_1 * da3_1dz3_1 * dz3_1dw23_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da3_1 = w32_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1dw23_1 = x2de2dw23_1 = de2da2_2 * da2_2dz2_2 * dz2_2da3_1 * da3_1dz3_1 * dz3_1dw23_1dedw23_1 = de1dw23_1 + de2dw23_1  # 求误差对w23_1的和# 求b23_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da3_1 = w31_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1db23_1 = 1de1db23_1 = de1da1_2 * da1_2dz1_2 * dz1_2da3_1 * da3_1dz3_1 * dz3_1db23_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da3_1 = w32_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1db23_1 = 1de2db23_1 = de2da2_2 * da2_2dz2_2 * dz2_2da3_1 * da3_1dz3_1 * dz3_1db23_1dedb23_1 = de1db23_1 + de2db23_1  # 求误差对b23_1的和# 求w33_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da3_1 = w31_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1dw33_1 = x3de1dw33_1 = de1da1_2 * da1_2dz1_2 * dz1_2da3_1 * da3_1dz3_1 * dz3_1dw33_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da3_1 = w32_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1dw33_1 = x3de2dw33_1 = de2da2_2 * da2_2dz2_2 * dz2_2da3_1 * da3_1dz3_1 * dz3_1dw33_1dedw33_1 = de1dw33_1 + de2dw33_1  # 求误差对w33_1的和# 求b23_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da3_1 = w31_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1db33_1 = 1de1db33_1 = de1da1_2 * da1_2dz1_2 * dz1_2da3_1 * da3_1dz3_1 * dz3_1db33_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da3_1 = w32_2da3_1dz3_1 = sigmoidD(a3_1)dz3_1db33_1 = 1de2db33_1 = de2da2_2 * da2_2dz2_2 * dz2_2da3_1 * da3_1dz3_1 * dz3_1db33_1dedb33_1 = de1db33_1 + de2db33_1  # 求误差对b33_1的和# 求w14_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da4_1 = w41_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1dw14_1 = x1de1dw14_1 = de1da1_2 * da1_2dz1_2 * dz1_2da4_1 * da4_1dz4_1 * dz4_1dw14_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da4_1 = w42_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1dw14_1 = x1de2dw14_1 = de2da2_2 * da2_2dz2_2 * dz2_2da4_1 * da4_1dz4_1 * dz4_1dw14_1dedw14_1 = de1dw14_1 + de2dw14_1  # 求误差对w14_1的和# 求b14_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da4_1 = w41_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1db14_1 = 1de1db14_1 = de1da1_2 * da1_2dz1_2 * dz1_2da4_1 * da4_1dz4_1 * dz4_1db14_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da4_1 = w42_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1db14_1 = 1de2db14_1 = de2da2_2 * da2_2dz2_2 * dz2_2da4_1 * da4_1dz4_1 * dz4_1db14_1dedb14_1 = de1db14_1 + de2db14_1  # 求误差对b14_1的和# 求w24_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da4_1 = w41_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1dw24_1 = x2de1dw24_1 = de1da1_2 * da1_2dz1_2 * dz1_2da4_1 * da4_1dz4_1 * dz4_1dw24_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da4_1 = w42_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1dw24_1 = x2de2dw24_1 = de2da2_2 * da2_2dz2_2 * dz2_2da4_1 * da4_1dz4_1 * dz4_1dw24_1dedw24_1 = de1dw24_1 + de2dw24_1  # 求误差对w24_1的和# 求b24_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da4_1 = w41_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1db24_1 = 1de1db24_1 = de1da1_2 * da1_2dz1_2 * dz1_2da4_1 * da4_1dz4_1 * dz4_1db24_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da4_1 = w42_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1db24_1 = 1de2db24_1 = de2da2_2 * da2_2dz2_2 * dz2_2da4_1 * da4_1dz4_1 * dz4_1db24_1dedb24_1 = de1db24_1 + de2db24_1  # 求误差对b24_1的和# 求w34_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da4_1 = w41_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1dw34_1 = x3de1dw34_1 = de1da1_2 * da1_2dz1_2 * dz1_2da4_1 * da4_1dz4_1 * dz4_1dw34_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da4_1 = w42_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1dw34_1 = x3de2dw34_1 = de2da2_2 * da2_2dz2_2 * dz2_2da4_1 * da4_1dz4_1 * dz4_1dw34_1dedw34_1 = de1dw34_1 + de2dw34_1  # 求误差对w34_1的和# 求b34_1de1da1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2da4_1 = w41_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1db34_1 = 1de1db34_1 = de1da1_2 * da1_2dz1_2 * dz1_2da4_1 * da4_1dz4_1 * dz4_1db34_1de2da2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2da4_1 = w42_2da4_1dz4_1 = sigmoidD(a4_1)dz4_1db34_1 = 1de2db34_1 = de2da2_2 * da2_2dz2_2 * dz2_2da4_1 * da4_1dz4_1 * dz4_1db34_1dedb34_1 = de1db34_1 + de2db34_1  # 求误差对b34_1的和deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw11_2 = a1_1dedw11_2 = deda1_2 * da1_2dz1_2 * dz1_2dw11_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db11_2 = 1dedb11_2 = deda1_2 * da1_2dz1_2 * dz1_2db11_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw21_2 = a2_1dedw21_2 = deda1_2 * da1_2dz1_2 * dz1_2dw21_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db21_2 = 1dedb21_2 = deda1_2 * da1_2dz1_2 * dz1_2db21_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw31_2 = a3_1dedw31_2 = deda1_2 * da1_2dz1_2 * dz1_2dw31_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db31_2 = 1dedb31_2 = deda1_2 * da1_2dz1_2 * dz1_2db31_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2dw41_2 = a4_1dedw41_2 = deda1_2 * da1_2dz1_2 * dz1_2dw41_2deda1_2 = -2 * (y1 - a1_2)da1_2dz1_2 = sigmoidD(a1_2)dz1_2db41_2 = 1dedb41_2 = deda1_2 * da1_2dz1_2 * dz1_2db41_2# 第二层，第二个神经元deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw12_2 = a1_1dedw12_2 = deda2_2 * da2_2dz2_2 * dz2_2dw12_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db12_2 = 1dedb12_2 = deda2_2 * da2_2dz2_2 * dz2_2db12_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw22_2 = a2_1dedw22_2 = deda2_2 * da2_2dz2_2 * dz2_2dw22_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db22_2 = 1dedb22_2 = deda2_2 * da2_2dz2_2 * dz2_2db22_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw32_2 = a3_1dedw32_2 = deda2_2 * da2_2dz2_2 * dz2_2dw32_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db32_2 = 1dedb32_2 = deda2_2 * da2_2dz2_2 * dz2_2db32_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2dw42_2 = a4_1dedw42_2 = deda2_2 * da2_2dz2_2 * dz2_2dw42_2deda2_2 = -2 * (y2 - a2_2)da2_2dz2_2 = sigmoidD(a2_2)dz2_2db42_2 = 1dedb42_2 = deda2_2 * da2_2dz2_2 * dz2_2db42_2# 实行梯度下降alpha = 0.02w11_1 = w11_1 - alpha * dedw11_1b11_1 = b11_1 - alpha * dedb11_1w21_1 = w21_1 - alpha * dedw21_1b21_1 = b21_1 - alpha * dedb21_1w31_1 = w31_1 - alpha * dedw31_1b31_1 = b31_1 - alpha * dedb31_1#   第二个神经元w12_1 = w12_1 - alpha * dedw12_1b12_1 = b12_1 - alpha * dedb12_1w22_1 = w22_1 - alpha * dedw22_1b22_1 = b22_1 - alpha * dedb22_1w32_1 = w32_2 - alpha * dedw32_1b32_1 = b32_1 - alpha * dedb32_1#   第三个神经元w13_1 = w13_1 - alpha * dedw13_1b13_1 = b13_1 - alpha * dedb13_1w23_1 = w23_1 - alpha * dedw23_1b23_1 = b23_1 - alpha * dedb23_1w33_1 = w33_1 - alpha * dedw33_1b33_1 = b33_1 - alpha * dedb33_1#   第四个神经元w14_1 = w14_1 - alpha * dedw14_1b14_1 = b14_1 - alpha * dedb14_1w24_1 = w24_1 - alpha * dedw24_1b24_1 = b24_1 - alpha * dedb24_1w34_1 = w34_1 - alpha * dedw34_1b34_1 = b34_1 - alpha * dedb34_1# 第二层神经元#   第一个神经元w11_2 = w11_2 - alpha * dedw11_2b11_2 = b11_2 - alpha * dedb11_2w21_2 = w21_2 - alpha * dedw21_2b21_2 = b21_2 - alpha * dedb21_2w31_2 = w31_2 - alpha * dedw32_2b31_2 = b31_2 - alpha * dedb31_2w41_2 = w41_2 - alpha * dedw41_2b41_2 = b41_2 - alpha * dedb41_2#   第二个神经元w12_2 = w12_2 - alpha * dedw12_2b12_2 = b12_2 - alpha * dedb12_2w22_2 = w22_2 - alpha * dedw22_2b22_2 = b22_2 - alpha * dedb22_2w32_2 = w32_2 - alpha * dedw32_2b32_2 = b32_2 - alpha * dedb32_2w42_2 = w42_2 - alpha * dedw42_2b42_2 = b42_2 - alpha * dedb42_2

神经网络前向传播和反向传播算法（作业4）相关推荐

（二十四）手推BP神经网络的前向传播和反向传播
手推BP神经网络的前向传播和反向传播一.基本术语 1.监督学习与非监督学习 Supervised Learning有监督式学习: 输入的数据被称为训练数据,一个模型需要通过一个训练过程,在这个过程中 ...
前馈神经网络--前向传播与反向传播计算过程
目录 2.多层感知机(前馈神经网络) 2.1 定义 2.2 神经元 2.3 激活函数 2.3.1 sigmoid函数 2.3.2 tanh函数 2.3.3 relu函数 2.4 计算 2.4.1 前向 ...
LSTM前向传播与反向传播算法推导（非常详细）
1.长短期记忆网络LSTM LSTM(Long short-term memory)通过刻意的设计来避免长期依赖问题,是一种特殊的RNN.长时间记住信息实际上是 LSTM 的默认行为,而不是需要努力学 ...
神经网络的前向传播和反向传播
本博客是对Michael Nielsen所著的<Neural Network and Deep Learning>第2章内容的解读,有兴趣的朋友可以直接阅读原文http://neuraln ...
花书+吴恩达深度学习（十三）卷积神经网络 CNN 之运算过程（前向传播、反向传播）
目录 0. 前言 1. 单层卷积网络 2. 各参数维度 3. CNN 前向传播反向传播如果这篇文章对你有一点小小的帮助,请给个关注,点个赞喔~我会非常开心的~ 花书+吴恩达深度学习(十)卷积神经网络 ...
神经网络的前向传播与反向传播
神经网络的前向传播和反向传播相信一开始,大家可能都对神经网络的前向传播和反向传播很头疼,我之前也是一样,后来慢慢懂了,现在深感知识传递的重要性.因此现在我就把我的一点点对两者的理解表达一下,希望能帮 ...
神经网络理解：前向传播与反向传播
文章目录参考资料神经网络前向传播 1. 输入层->隐含层 2. 隐含层->输出层反向传播 1. 计算总误差 2. 隐藏层与输出层之间的权重更新 3. 输入层与隐藏层之间的权重更新 ...
对于CNN卷积神经网络的前向传播和反向传播的理解
对于CNN卷积神经网络的前向传播和反向传播的理解前向传播示意图: 咋一看这张图,作为初学者可能会不知所云(￣ω￣=)?但是想要很好的理解前向传播的原理,我们得从这张图细说. 文章目录对于CNN ...
神经网络前向传播和反向传播公式推导（公式+图解）
以如下的预测是否是猫的双层神经网络为例进行公式推导: 符号注解: n_x : 输入特征的数量 n_h : 隐藏层的节点数量 n_y : 输出层的节点数量 m : 样本数量 W :权重矩阵 b :偏置 ...
详解+推导神经网络中的前向传播和反向传播公式（神经网络中的梯度下降）
文章目录线性回归快速回忆逻辑回归中的正向传播与反向传播逻辑回归中的正向传播与反向传播-代码实战神经网络的正向传播与反向传播参考资料线性回归快速回忆在线性回归(y=ax+by=ax+by= ...

神经网络前向传播和反向传播算法（作业4）

神经网络前向传播和反向传播算法（作业4）相关推荐

最新文章

热门文章