1つのニューラルネットワークモデル
例えば、以下のニューラルネットワークモデルは、順方向伝搬及び逆伝播ニューラルネットワークとコードのためのプロセスを例示するために
1.1前方伝播
（1）入力層ニューロン\（I_1、I_2を\使用されている）、中間層処理への入力層
\ [HiddenNeth_1 = w_1i_1 + w_2i_2 + B_1 \]
\ [HiddenNeth_2 = w_3i_1 + w_4i_2 + B_1 \]
\ [H_1 =シグモイド（HiddenNeth_1）\]
\ [H_2 =シグモイド（HiddenNeth_2）\]
（2）中間層：ニューロン\（H_1、H_2 \） 、出力層プロセスに隠れ層
\ [OutputNeto_1 = w_5h_1 + w_6h_2 \]
\ [OutputNeto_2 = w_7h_1 + w_8h_2 \]
\ [O_1 =シグモイド（OutputNeto_1）\]
\ [O_2 =シグモイド（OutputNeto_2）\]
1.2バックプロパゲーション
各エラー伝搬の影響は、その各ニューラルネットワーク層重量を取得し、右下の更新の重量がために、連鎖ルールに従って重みを更新する処理と勾配に低下する前に、バックプロパゲーションを評価する\します（w_5とW_1の\）の例として
- 0.01 totalo1基準値を表します
- 150 totalo2を参照
1.2.1アップデートの重みw_5
\ [\ FRAC {\部分totalo1} {\部分w_5} = \ FRAC {\部分totalo1} {\部分O_1} * \ FRAC {\部分O_1} {\部分outputneto_1} * \ FRAC {\部分outputneto_1} {\部分w_5} \]
其中：\ [\ FRAC {\部分totalo1} {\部分O_1} = \ FRAC {\部分の\ FRAC {1} {2} {（totalo_1 - O_1）} ^ 2} {\部分O_1} = - （totalo_1 -o_1）\]
\ [\ FRAC {\部分O_1} {\部分outputneto_1} = O_1（1-O_1）\]
\ [\ FRAC {\部分outputneto_1} {\部分w_5} = H_1 \]
则：\ [\ FRAC {\部分totalo1} {\部分w_5} = - （totalo_1 -o_1）O_1（1-O_1）H_1 \]
更新w_5的值：[w_5new = w_5 \ - learningrate * \ FRAC {\部分totalo1} {\部分w_5} \]
1.2.2アップデートウェイトW_1
\（W_1偏向器を探しているとの唯一の違いは、W_1の値がO_1とO_2 \に影響を与えていることであるw_5デフレクタを要求する）ので、
[\ FRAC {\部分合計\ } {\部分W_1} = \ FRAC {\部分totalol } {\部分W_1} + \ FRAC {\部分totalo2} {\部分W_1} \]
上記のアイデアとして、以下の導出
部分の\ FRAC {部分の\ H1} {\部分} hiddenneth1の\ [\ FRAC {\部分totalol} {\部分W_1} = \ FRAC {\部分totalol {} \} * H1 * \ FRAC {\部分hiddenneth1} {\部分W_1} \]
\ [\ FRAC {\部分合計} {\部分W_1} = - （totalo1 - O1）O1（1-O1）w_5 * H1（1-H1）I1 + - （totalo2 - O 2）O 2（1-O 2）w_7 * H1（1-H1）I1 \]
更新W_1的值：\ [w_1new = W_1 - learningrate * \ FRAC {\部分合計} {\部分W_1} \]
順方向伝搬アルゴリズムを逆2.コード
import random
import math
class NeuralNetwork:
learning_rate = 0.5
def __init__(self,input_num,hidden_num,output_num,input_hidden_weights=None,
input_hidden_bias=None,hidden_output_weights=None,hidden_output_bias=None):
self.input_num = input_num
# 构建掩藏层
self.hidden_layer = NeuralLayer(hidden_num,input_hidden_bias)
# 构建输出层
self.output_layer = NeuralLayer(output_num,hidden_output_bias)
# 初始化输入层到隐藏层权重
self.init_input_to_hidden_weights(input_hidden_weights)
# 初始化隐藏层到输出层权重
self.init_hidden_to_output_weights(hidden_output_weights)
def init_input_to_hidden_weights(self,weights):
weight_num = 0
for i_num in range(len(self.hidden_layer.neurons)):
for o_num in range(self.input_num):
if weights is None:
self.hidden_layer.neurons[i_num].weights.append(random.random())
else:
self.hidden_layer.neurons[i_num].weights.append(weights[weight_num])
weight_num += 1
def init_hidden_to_output_weights(self,weights):
weight_num = 0
for i_num in range(len(self.output_layer.neurons)):
for o_num in range(len(self.hidden_layer.neurons)):
if weights is None:
self.output_layer.neurons[i_num].weights.append(random.random())
else:
self.output_layer.neurons[i_num].weights.append(weights[weight_num])
weight_num += 1
def inspect(self):
print('..................')
print('input inspect:',[i for i in self.inputs])
print('..................')
print('hidden inspect:')
self.hidden_layer.inspect()
print('..................')
print('output inspect:')
self.output_layer.inspect()
print('..................')
def forward(self,inputs):
hidden_layer_outout = self.hidden_layer.forward(inputs)
print('hidden_layer_outout',hidden_layer_outout)
ouput_layer_ouput = self.output_layer.forward(hidden_layer_outout)
print('ouput_layer_ouput',ouput_layer_ouput)
return ouput_layer_ouput
def train(self,x,y):
ouput_layer_ouput = self.forward(x)
# 求total / neto的偏导
total_o_pd = [0] * len(self.output_layer.neurons)
for o in range(len(self.output_layer.neurons)):
total_o_pd[o] = self.output_layer.neurons[o].calculate_total_net_pd(y[o])
# 求total / h的偏导 = total.1 / h的偏导 + total.2 / h的偏导
total_neth_pd = [0] * len(self.hidden_layer.neurons)
for h in range(len(self.hidden_layer.neurons)):
total_h_pd = 0
for o in range(len(self.output_layer.neurons)):
total_h_pd += total_o_pd[o] * self.hidden_layer.neurons[h].weights[o]
total_neth_pd[h] = total_h_pd * self.output_layer.neurons[h].calculate_output_net_pd()
# 更新输出层神经元权重
for o in range(len(self.output_layer.neurons)):
for ho_w in range(len(self.output_layer.neurons[o].weights)):
ho_w_gradient = total_o_pd[o] * self.output_layer.neurons[o].calculate_net_linear_pd(ho_w)
self.output_layer.neurons[o].weights[ho_w] -= self.learning_rate * ho_w_gradient
# 更新隐藏层神经元权重
for h in range(len(self.hidden_layer.neurons)):
for ih_w in range(len(self.hidden_layer.neurons[h].weights)):
ih_w_gradient = total_neth_pd[h] * self.hidden_layer.neurons[h].calculate_net_linear_pd(ih_w)
self.hidden_layer.neurons[h].weights[ih_w] -= self.learning_rate * ih_w_gradient
def calculate_total_error(self, training_sets):
total_error = 0
for t in range(len(training_sets)):
training_inputs, training_outputs = training_sets[t]
self.forward(training_inputs)
for o in range(len(training_outputs)):
total_error += self.output_layer.neurons[o].calculate_error(training_outputs[o])
return total_error
class NeuralLayer:
def __init__(self,neural_num,bias):
self.bias = bias if bias else random.random()
self.neurons = []
for i in range(neural_num):
self.neurons.append(Neuron(self.bias))
def inspect(self):
print('weights:',[neuron.weights for neuron in self.neurons])
print('bias:',[neuron.bias for neuron in self.neurons])
def get_output(self,inputs):
outputs = []
for neuron in self.neurons:
outputs.append(neuron.output)
return outputs
def forward(self,inputs):
outputs = []
for neuron in self.neurons:
outputs.append(neuron.calculate_output(inputs))
return outputs
class Neuron:
def __init__(self,bias):
self.bias = bias
self.weights = []
def calculate_output(self,inputs):
self.inputs = inputs
total_net_outputs = self.calculate_total_net_output()
self.output = self.sigmoid(total_net_outputs)
return self.output
def calculate_total_net_output(self):
total = 0
for i in range(len(self.inputs)):
total += self.inputs[i] * self.weights[i]
return total + self.bias
def sigmoid(self,total_net_input):
return 1 / (1 + math.exp(-total_net_input))
def calculate_total_output_pd(self,total_output):
return -(total_output - self.output)
def calculate_output_net_pd(self):
return self.output * (1 - self.output)
def calculate_total_net_pd(self,total_output):
return self.calculate_total_output_pd(total_output) * self.calculate_output_net_pd()
def calculate_net_linear_pd(self,index):
return self.inputs[index]
def calculate_error(self, target_output):
return 0.5 * (target_output - self.output) ** 2nn = NeuralNetwork(2, 2, 2, input_hidden_weights=[0.15, 0.2, 0.25, 0.3], input_hidden_bias=0.35,
hidden_output_weights=[0.4, 0.45, 0.5, 0.55], hidden_output_bias=0.6)
for i in range(10000):
nn.train([0.05, 0.1], [0.01, 0.99])
print(i, round(nn.calculate_total_error([[[0.05, 0.1], [0.01, 0.99]]]), 9))hidden_layer_outout [0.5932699921071872, 0.596884378259767]
ouput_layer_ouput [0.7513650695523157, 0.7729284653214625]
hidden_layer_outout [0.5932662857458805, 0.5968782561589732]
ouput_layer_ouput [0.7420894573166411, 0.775286681791022]
迭代1次 误差0.291028391
hidden_layer_outout [0.5932662857458805, 0.5968782561589732]
ouput_layer_ouput [0.7420894573166411, 0.775286681791022]
hidden_layer_outout [0.5932623797502049, 0.5968720205376407]
ouput_layer_ouput [0.7324789213021788, 0.7775850216973027]
迭代2次 误差 0.283547957
hidden_layer_outout [0.5932623797502049, 0.5968720205376407]
ouput_layer_ouput [0.7324789213021788, 0.7775850216973027]
hidden_layer_outout [0.5932582778661456, 0.5968656853189723]
ouput_layer_ouput [0.7225410209751278, 0.7798256906644981]
迭代3次 误差 0.275943973
hidden_layer_outout [0.5932582778661456, 0.5968656853189723]
ouput_layer_ouput [0.7225410209751278, 0.7798256906644981]
hidden_layer_outout [0.5932539857457403, 0.5968592652405116]
ouput_layer_ouput [0.7122866732919141, 0.7820107943242337]
迭代4次 误差0.268233041
...
...
...
hidden_layer_outout [0.5930355856011269, 0.5965960242813179]
ouput_layer_ouput [0.016365976874939202, 0.9836751989707726]
hidden_layer_outout [0.5930355857116121, 0.5965960243868048]
ouput_layer_ouput [0.016365393177895763, 0.9836757760229975]
迭代10000次 误差 4.0257e-05イテレーション万結果：
hidden_layer_outout [0.5930355856011269、0.5965960242813179]
[0.016365976874939202、0.9836751989707726] ouput_layer_ouput
hidden_layer_outout [0.5930355857116121、0.5965960243868048]
[0.016365393177895763、0.9836757760229975] ouput_layer_ouput
10000反復エラー4.0257e-05
参考：https://www.cnblogs.com/charlotte77/p/5629865.html、感謝分析ブロガー