人工智能实战第二次作业_张绍恺

0.导航

项目	内容
这个作业属于哪个课程	人工智能实战
这个作业的要求在哪里	第二次作业 - 双变量的反向传播
我在这个课程的目标是	开拓视野，积累AI实战经验
这个作业在哪个具体方面帮助我	熟悉BP求导的具体实现过程

1.具体作业内容

• 阅读文章线性反向传播,用python程序实现具体迭代计算过程
• 思考重新计算贡献值的影响

2.具体Python代码实现展示

重新计算贡献值

z_aim = 150.0
w = 3.0
b = 4.0
z = 162.0
delta_z = z - z_aim
error_range = 1e-5
count = 0

while(abs(delta_z) > error_range):
	count += 1
	x = 2 * w + 3 * b
	y = 2 * b + 1
	z = x * y
	delta_z = z - z_aim
	delta_b = ((delta_z / 2) / (2 * x + 3 * y))
	delta_w = ((delta_z / 2) / (2 * y))
	w = w - delta_w
	b = b - delta_b
	print("Interation %d: w = %.8f, b = %.8f, z = %.8f, error = %.8f" % (count, w, b, z, abs(delta_z)))

print("")
print("Final interation:")
print("Total interation times = %d, w = %.8f, b = %.8f, z = %.8f, error = %.8f" % (count, w, b, z, abs(delta_z)))

运行结果

Interation 1: w = 2.66666667, b = 3.90476190, z = 162.00000000, error = 12.00000000
Interation 2: w = 2.66151866, b = 3.90326327, z = 150.18140590, error = 0.18140590
Interation 3: w = 2.66151740, b = 3.90326291, z = 150.00004434, error = 0.00004434
Interation 4: w = 2.66151740, b = 3.90326291, z = 150.00000000, error = 0.00000000

Final interation:
Total interation times = 4, w = 2.66151740, b = 3.90326291, z = 150.00000000, error = 0.00000000
[Finished in 0.2s]

不考虑贡献值

仅需将上述代码中的以下两行

	delta_b = ((delta_z / 2) / (2 * x + 3 * y))
	delta_w = ((delta_z / 2) / (2 * y))

替换为

	delta_b = ((delta_z / 2) / 63)
	delta_w = ((delta_z / 2) / 18)

结果如下

Interation 1: w = 2.66666667, b = 3.90476190, z = 162.00000000, error = 12.00000000
Interation 2: w = 2.66162761, b = 3.90332218, z = 150.18140590, error = 0.18140590
Interation 3: w = 2.66147411, b = 3.90327832, z = 150.00552614, error = 0.00552614
Interation 4: w = 2.66146940, b = 3.90327697, z = 150.00016964, error = 0.00016964
Interation 5: w = 2.66146925, b = 3.90327693, z = 150.00000521, error = 0.00000521

Final interation:
Total interation times = 5, w = 2.66146925, b = 3.90327693, z = 150.00000521, error = 0.00000521
[Finished in 0.1s]

3.思考和比较

在反向传播的迭代过程中，随着z的值不断变化，delta_z的值也随之变化，因此即时更新z对w和b的偏导也十分必要，既能加快收敛速度，更快得到结果，从理论上也更加符合梯度下降的实现过程。