手写BP（反向传播）算法

# 手写BP算法
import numpy as np

# 先更新参数，再继续传播
# layers：包括从输入层到输出层，每层参数为：连接权重w，阈值b，输出y。类型为np.array
# 对于输入层，w和b随便是啥，反正不用，只需y即原始输入
# 基于激活函数sigmoid
# loss为均方误差
def bp(layers,labels,lr=0.001):
#     翻转layers，反向传播
    reversed_layers=layers[::-1]
#     输出层
    output_w,output_b,output_y=reversed_layers[0]
    g=np.array([output_y[j]*(1-output_y[j])*(labels[j]-output_y[j]) for j in range(len(labels))])
#     最后一层更新较为特殊，先进行更新
    delta_w=np.empty(shape=(output_w.shape[0],output_w.shape[1]))
#     上一层输出y
    last_y=reversed_layers[1][2]
    for h in range(output_w.shape[0]):
        for j in range(output_w.shape[1]):
            delta_w[h,j]=lr*g[j]*last_y[h]
    delta_b=-lr*g
    new_w=output_w+delta_w
    new_b=output_b+delta_b
    reversed_layers[0][0]=new_w
    reversed_layers[0][1]=new_b

    #     从倒数第二层到第二层进行更新，每次取3层进行计算，由公式知，需用到上一层输出即下一层权重
    for i in range(1,len(reversed_layers)-1):
#         下一层w
        next_w=reversed_layers[i-1][0]
        out_w,out_b,out_y=reversed_layers[i]
#         上一层y
        last_y=reversed_layers[i+1][2]
#         更新辅助量，意思即上一层每个神经元的误差都由下一层所有神经元的误差反向传播，体现在这里内循环
        e=np.empty(shape=(len(out_b),1))
        for h in range(len(out_b)):
            temp=0
            for j in range(next_w.shape[1]):
                temp+=next_w[h,j]*g[j]
            e[h]=out_y[h]*(1-out_y[h])*temp
        delta_w=np.empty(shape=(out_w.shape[0],out_w.shape[1]))
        for h in range(out_w.shape[0]):
            for j in range(out_w.shape[1]):
                delta_w[h,j]=lr*e[j]*last_y[h]
        delta_b=-lr*e
        out_new_w=out_w+delta_w
        out_new_b=out_b+delta_b
        reversed_layers[i][0]=out_new_w
        reversed_layers[i][1]=out_new_b
        g=np.copy(e)
    return layers

X=[]
Y=[]
for i in range(-100,100):
    for j in range(-100,100):
        X.append([[i],[j]])
        if j>=0:
            Y.append([1])
        else:
            Y.append([0])
X=np.array(X)
Y=np.array(Y)

indexs=np.random.choice(range(40000),size=30000)

x_train=np.array([X[i] for i in indexs])
y_train=np.array([Y[i] for i in indexs])

x_val=np.array([X[i] for i in np.setdiff1d(range(40000),indexs))
y_val=np.array([Y[i] for i in np.setdiff1d(range(40000),indexs))

# 使用sigmoid激活函数
def output(input_x,w,b):
    res=0
    t=np.matmul(np.transpose(w),input_x)-b
    return 1./(1+np.power(np.e,-t))

w1=np.random.normal(size=(2,1))
b1=np.array([[0]])
for i in range(len(x_train)):
    y0=x_train[i]
    l=y_train[i]
    input_layers=[]
    w0,b0=(0,0)
    input_layers.append([w0,b0,y0])
    input_layers.append([w1,b1,output(y0,w1,b1)])
    input_layers=bp(input_layers,l)
    w1=input_layers[1][0]
    b1=input_layers[1][1]
    
# w:  [[0.11213777]
#  [1.67425498]]
# b:  [[0.0001581]]
print(‘w: ‘,w1)
print(‘b: ‘,b1)

for xx in x_val[:50]:
    print(xx.reshape((2,)),output(xx,w1,b1).reshape((1,)))

[63 68] [1.]
[-100  -99] [1.39636722e-77]
[-100  -98] [7.44936654e-77]
[63 69] [1.]
[-100  -96] [2.12011171e-75]
[-100  -94] [6.03390049e-74]
[-100  -93] [3.21897678e-73]
[63 74] [1.]
[-100  -91] [9.16130293e-72]
[63 75] [1.]
[63 76] [1.]
[63 77] [1.]
[63 78] [1.]
[-100  -86] [3.95872874e-68]
[-100  -85] [2.11191018e-67]
[63 79] [1.]
[-100  -83] [6.01055872e-66]
[-100  -82] [3.20652436e-65]
[63 82] [1.]
[-100  -80] [9.12586299e-64]
[-100  -79] [4.86848285e-63]
[63 83] [1.]
[-100  -77] [1.38558459e-61]
[-100  -76] [7.39184317e-61]
[63 89] [1.]
[-100  -74] [2.10374039e-59]
[63 91] [1.]
[-100  -72] [5.98730724e-58]
[-100  -71] [3.19412012e-57]
[-100  -70] [1.70400531e-56]
[-100  -69] [9.09056014e-56]
[-100  -68] [4.84964942e-55]
[-100  -67] [2.58720025e-54]
[-100  -66] [1.38022454e-53]
[63 99] [1.]
[-100  -64] [3.92815978e-52]
[-100  -63] [2.09560219e-51]
[  64 -100] [2.53988133e-70]
[-100  -61] [5.9641457e-50]
[ 64 -97] [3.85631522e-68]
[ 64 -96] [2.05727442e-67]
[-100  -58] [9.05539386e-48]
[ 64 -90] [4.74253371e-63]
[ 64 -89] [2.53005596e-62]
[ 64 -87] [7.20061393e-61]
[-100  -52] [2.08749548e-43]
[ 64 -84] [1.09327301e-58]
[-100  -50] [5.94107377e-42]
[ 95 -13] [1.49260907e-05]
[-100  -45] [2.56722211e-38]