python里反向傳播算法詳解

更新時(shí)間：2020年11月22日 11:24:41 作者：十一

在本篇文章了小編給大家整理的是一篇關(guān)于python里反向傳播算法詳解內(nèi)容，有興趣的朋友們可以學(xué)習(xí)下。

反向傳播的目的是計(jì)算成本函數(shù)C對(duì)網(wǎng)絡(luò)中任意w或b的偏導(dǎo)數(shù)。一旦我們有了這些偏導(dǎo)數(shù)，我們將通過一些常數(shù) α的乘積和該數(shù)量相對(duì)于成本函數(shù)的偏導(dǎo)數(shù)來更新網(wǎng)絡(luò)中的權(quán)重和偏差。這是流行的梯度下降算法。而偏導(dǎo)數(shù)給出了最大上升的方向。因此，關(guān)于反向傳播算法，我們繼續(xù)查看下文。

我們向相反的方向邁出了一小步——最大下降的方向，也就是將我們帶到成本函數(shù)的局部最小值的方向。

圖示演示:

反向傳播算法中Sigmoid函數(shù)代碼演示：

# 實(shí)現(xiàn) sigmoid 函數(shù)
return 1 / (1 + np.exp(-x))
def sigmoid_derivative(x):
# sigmoid 導(dǎo)數(shù)的計(jì)算
return sigmoid(x)*(1-sigmoid(x))

反向傳播算法中ReLU 函數(shù)導(dǎo)數(shù)函數(shù)代碼演示：

def relu_derivative(x): # ReLU 函數(shù)的導(dǎo)數(shù)
d = np.array(x, copy=True) # 用于保存梯度的張量
d[x < 0] = 0 # 元素為負(fù)的導(dǎo)數(shù)為 0
d[x >= 0] = 1 # 元素為正的導(dǎo)數(shù)為 1
return d

實(shí)例擴(kuò)展：

BP反向傳播算法Python簡(jiǎn)單實(shí)現(xiàn)

import numpy as np

# "pd" 偏導(dǎo)
def sigmoid(x):
  return 1 / (1 + np.exp(-x))

def sigmoidDerivationx(y):
  return y * (1 - y)


if __name__ == "__main__":
  #初始化
  bias = [0.35, 0.60]
  weight = [0.15, 0.2, 0.25, 0.3, 0.4, 0.45, 0.5, 0.55]
  output_layer_weights = [0.4, 0.45, 0.5, 0.55]
  i1 = 0.05
  i2 = 0.10
  target1 = 0.01
  target2 = 0.99
  alpha = 0.5 #學(xué)習(xí)速率
  numIter = 10000 #迭代次數(shù)
  for i in range(numIter):
    #正向傳播
    neth1 = i1*weight[1-1] + i2*weight[2-1] + bias[0]
    neth2 = i1*weight[3-1] + i2*weight[4-1] + bias[0]
    outh1 = sigmoid(neth1)
    outh2 = sigmoid(neth2)
    neto1 = outh1*weight[5-1] + outh2*weight[6-1] + bias[1]
    neto2 = outh2*weight[7-1] + outh2*weight[8-1] + bias[1]
    outo1 = sigmoid(neto1)
    outo2 = sigmoid(neto2)
    print(str(i) + ", target1 : " + str(target1-outo1) + ", target2 : " + str(target2-outo2))
    if i == numIter-1:
      print("lastst result : " + str(outo1) + " " + str(outo2))
    #反向傳播
    #計(jì)算w5-w8(輸出層權(quán)重)的誤差
    pdEOuto1 = - (target1 - outo1)
    pdOuto1Neto1 = sigmoidDerivationx(outo1)
    pdNeto1W5 = outh1
    pdEW5 = pdEOuto1 * pdOuto1Neto1 * pdNeto1W5
    pdNeto1W6 = outh2
    pdEW6 = pdEOuto1 * pdOuto1Neto1 * pdNeto1W6
    pdEOuto2 = - (target2 - outo2)
    pdOuto2Neto2 = sigmoidDerivationx(outo2)
    pdNeto1W7 = outh1
    pdEW7 = pdEOuto2 * pdOuto2Neto2 * pdNeto1W7
    pdNeto1W8 = outh2
    pdEW8 = pdEOuto2 * pdOuto2Neto2 * pdNeto1W8

    # 計(jì)算w1-w4(輸出層權(quán)重)的誤差
    pdEOuto1 = - (target1 - outo1) #之前算過
    pdEOuto2 = - (target2 - outo2) #之前算過
    pdOuto1Neto1 = sigmoidDerivationx(outo1)  #之前算過
    pdOuto2Neto2 = sigmoidDerivationx(outo2)  #之前算過
    pdNeto1Outh1 = weight[5-1]
    pdNeto2Outh2 = weight[7-1]

    pdEOuth1 = pdEOuto1 * pdOuto1Neto1 * pdNeto1Outh1 + pdEOuto2 * pdOuto2Neto2 * pdNeto1Outh1
    pdOuth1Neth1 = sigmoidDerivationx(outh1)
    pdNeth1W1 = i1
    pdNeth1W2 = i2
    pdEW1 = pdEOuth1 * pdOuth1Neth1 * pdNeth1W1
    pdEW2 = pdEOuth1 * pdOuth1Neth1 * pdNeth1W2
    pdNeto1Outh2 = weight[6-1]
    pdNeto2Outh2 = weight[8-1]
    pdOuth2Neth2 = sigmoidDerivationx(outh2)
    pdNeth2W3 = i1
    pdNeth2W4 = i2
    pdEOuth2 = pdEOuto1 * pdOuto1Neto1 * pdNeto1Outh2 + pdEOuto2 * pdOuto2Neto2 * pdNeto2Outh2
    pdEW3 = pdEOuth2 * pdOuth2Neth2 * pdNeth2W3
    pdEW4 = pdEOuth2 * pdOuth2Neth2 * pdNeth2W4
    #權(quán)重更新
    weight[1-1] = weight[1-1] - alpha * pdEW1
    weight[2-1] = weight[2-1] - alpha * pdEW2
    weight[3-1] = weight[3-1] - alpha * pdEW3
    weight[4-1] = weight[4-1] - alpha * pdEW4
    weight[5-1] = weight[5-1] - alpha * pdEW5
    weight[6-1] = weight[6-1] - alpha * pdEW6
    weight[7-1] = weight[7-1] - alpha * pdEW7
    weight[8-1] = weight[8-1] - alpha * pdEW8
    # print(weight[1-1])
    # print(weight[2-1])
    # print(weight[3-1])
    # print(weight[4-1])
    # print(weight[5-1])
    # print(weight[6-1])
    # print(weight[7-1])
    # print(weight[8-1])

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