sigmoid神经网络梯度下降更新连接权重重要公式推导

 

 

 

附：sigmoid神经网络核心代码

import numpy

class neuralNetwork :
    def __init__(self, inputnodes, hiddennodes, outputnodes,learningrate) :
        self.inodes = inputnodes
        self.hnodes = hiddennodes
        self.onodes = outputnodes
        self.wih = numpy.random.normal(0.0, pow(self.hnodes, 0.5),(self.hnodes, self.inodes))
        self.who = numpy.random.normal(0.0, pow(self.onodes, 0.5),(self.onodes, self.hnodes))
        self.lr = learningrate
        self.activation_function = lambda x:1/(1+numpy.exp(-x))
    
    def train(self, inputs_list, targets_list) :
        inputs = numpy.array(inputs_list, ndmin=2).T
        targets = numpy.array(targets_list, ndmin=2).T
        hidden_inputs = numpy.dot(self.wih, inputs)
        hidden_outputs = self.activation_function(hidden_inputs)
        final_inputs = numpy.dot(self.who, hidden_outputs)
        final_outputs = self.activation_function(final_inputs) 
        output_errors = targets-final_outputs
        hidden_errors = numpy.dot(self.who.T, output_errors)
        self.who += self.lr * numpy.dot((output_errors *  final_outputs * (1.0-final_outputs)),numpy.transpose(hidden_outputs))
        self.wih += self.lr * numpy.dot((hidden_errors *  hidden_outputs * (1.0-hidden_outputs)), numpy.transpose(inputs))

    def query(self, inputs_list) :
        inputs = numpy.array(inputs_list, ndmin=2).T
        hidden_inputs = numpy.dot(self.wih, inputs)
        hidden_outputs = self.activation_function(hidden_inputs)
        final_inputs = numpy.dot(self.who, hidden_outputs)
        final_outputs = self.activation_function(final_inputs)
        return final_outputs