【人工智能导论：模型与算法】慕课笔记1 误差反向传播 CODE

目标值 与 误差值，反了。

迭代后，目标值趋近于 零，误差趋近于 目标值 1.73 。

没发现原因 ~ 

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 跟LiuHB讨论，发现是对 梯度 理解的不够深刻。继续研究。

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 例子的原文：

https://www.cnblogs.com/hbuwyg/p/15550275.html

带Python代码

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y = 0.2 ； 梯度 取正方向；程序完美：error趋于0，目标值趋于0.2

y = 0.5 ； 梯度 取负方向；error取反；程序完美：error趋于0，目标值趋于0.5

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说明这个程序的迭代，跟初值有很大关系。

原有的初值是：x0= -1；x1=-2。 y=1/(1+exp(-(-w0-2w1+w2)))=1/(1+exp(w0-+w1-w2))

当 w0 = 2；w1 = -3；w2 = -3 时：y= 1 / (1 + exp( -((2x0) -3x1 -3)))   

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import math
def back_propagation(x0,x1,w0,w1,w2,y,N):
#     y = 1 / (1 + math.exp( -((x0 * w0)  + (x1 * w1) + w2)))   
    print("\n=============================NO",N,"=============================")
    N = N-1
    f1 = x0 * w0
    f2 = x1 * w1
    f3 = f1 + f2
    f4 = f3 + w2
    f5 = -f4
    f6= math.exp(f5)
    f7 = 1 + f6
    f8 = 1/f7
     # MSE 
#     error = 0.5 * math.pow((y - f8),2)   
    error = y - f8
    print("RESULT,               ERROR\n" ,f8, error)    
#     print("----------------END---Forward-------------------------")
    bp1 = -(1/math.pow(f7,2)) * error
    bp2 = 1 * bp1
    bp3 = math.exp(f5) * bp2
    bp4 = -bp3
    bp5 = bp4
    bp6 = bp5
    bp_w1 = bp6 * x1
#     bp_x1 = bp6 * w1
    bp_w0 = bp6 * x0
#     bp_x0 = bp6 * w0
    bp_w2 = bp5
    w0 = w0 - bp_w0
    w1 = w1 - bp_w1
    w2 = w2 - bp_w2
#     print(bp1,bp2,bp3)
#     print(bp4,bp5,bp6)
    print("----------------END---BP----Update w---------------------")
    print("x0:" , x0,"x1:" , x1,"y:" , y) 
#     print("bp_w0:" , bp_w0,"bp_w1:" , bp_w1,"bp_w2:" , bp_w2) 
    print("w0:" , w0,"w1:" , w1,"w2:" , w2)
    if (N > 0):
        back_propagation(x0,x1,w0,w1,w2,y,N)
    return 

x0 = -1
x1 = -2
w0 = 2
w1 = -3
w2 = -3
y = 1.73
N = 10
back_propagation(x0,x1,w0,w1,w2,y,N)

=============================NO 10 =============================
RESULT,               ERROR
 0.7310585786300049 0.9989414213699951
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.1964038040505485 w1: -2.607192391898903 w2: -3.1964038040505485

=============================NO 9 =============================
RESULT,               ERROR
 0.45551225254229843 1.2744877474577017
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.5125033261603766 w1: -1.9749933476792467 w2: -3.5125033261603766

=============================NO 8 =============================
RESULT,               ERROR
 0.11154856232322807 1.618451437676772
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.6729007336654407 w1: -1.6541985326691184 w2: -3.6729007336654407

=============================NO 7 =============================
RESULT,               ERROR
 0.045764387022953316 1.6842356129770466
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.7464513161952797 w1: -1.50709736760944 w2: -3.7464513161952797

=============================NO 6 =============================
RESULT,               ERROR
 0.02992416510794365 1.7000758348920564
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.7958023236502387 w1: -1.4083953526995214 w2: -3.7958023236502387

=============================NO 5 =============================
RESULT,               ERROR
 0.022426856120331854 1.7075731438796682
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.833238973256924 w1: -1.3335220534861503 w2: -3.833238973256924

=============================NO 4 =============================
RESULT,               ERROR
 0.0179962126173677 1.7120037873826324
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.863494101589214 w1: -1.2730117968215704 w2: -3.863494101589214

=============================NO 3 =============================
RESULT,               ERROR
 0.015053680787498781 1.7149463192125012
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.8889217263926086 w1: -1.222156547214781 w2: -3.8889217263926086

=============================NO 2 =============================
RESULT,               ERROR
 0.012951208624576063 1.717048791375424
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.9108715763814192 w1: -1.1782568472371597 w2: -3.9108715763814192

=============================NO 1 =============================
RESULT,               ERROR
 0.01137126330526271 1.7186287366947373
----------------END---BP----Update w---------------------
x0: -1 x1: -2 y: 1.73
w0: 2.9301923279002793 w1: -1.1396153441994392 w2: -3.9301923279002793