我正在使用一个具有1个隐藏层（2个神经元）和1个输出神经元的神经网络来解决XOR问题。

这是我使用的代码。代码中包含主运行文件xor.py，它创建了在model.py中定义的模型。每个神经元由neuron.py中的Neuron类定义。

xor.py

from model import Modelimport numpy as npinputs = [[0,0], [0,1], [1,0], [1,1]]outputs = [0, 1, 1, 0]m = Model()m.train(inputs, outputs)for i in inputs:    p = m.predict(i)    print str(i) + ' => ' + str(p)

model.py

from neuron import HiddenNeuron, OutputNeuronimport numpy as np    class Model(object):    def __init__(self):        self.hidden = [HiddenNeuron(2) for i in range(2)]        self.output = OutputNeuron(2)    def predict(self, input):        temp = []        for x in range(2):            self.hidden[x].forward(input)            temp.append(self.hidden[x].out)        self.output.forward(temp)        return self.output.out    def train(self, inputs, targets):        it = 0        i = 0        size = len(inputs)        while it < 4:            if i == size:                i = 0            feature = inputs[i]            print '\n\nFeature : ' + str(feature) + '\n'            print 'Output weights : ' + str(self.output.weights)            print 'Hidden 1 weights : ' + str(self.hidden[0].weights)            print 'Hidden 2 weights : ' + str(self.hidden[1].weights)            temp = []            for x in range(2):                self.hidden[x].forward(feature)                temp.append(self.hidden[x].out)            self.output.forward(temp)            self.output.backward(targets[i])            deltas = []            deltas.append(self.output.error)            weights = []            weights.append([self.output.weights[0]])            weights.append([self.output.weights[1]])            for x in range(2):                self.hidden[x].backward(deltas, weights[x])            for x in range(2):                self.hidden[x].update(feature)            self.output.update(temp)            it += 1            i += 1

neuron.py

import numpy as npfrom random import uniformclass Neuron(object):    def activation(self, fx):        return 1/(1 + np.exp(-fx))    def __init__(self, dim, lrate):        self.dim = dim        self.weights = np.empty([dim])        self.weights = [uniform(0,1) for x in range(dim)]        self.bias = uniform(0, 1)        self.lrate = lrate        self.out = None        self.error = None    def update(self, input):        j = 0        for i in input:            delta = self.lrate * self.error            self.weights[j] -= (delta*i)            self.bias += delta            j+=1    def forward(self, input):        j = 0        sum = self.bias        for f in input:            sum += f * self.weights[j]            j+=1        self.out = self.activation(sum)    def backward(self):        passclass OutputNeuron(Neuron):    def __init__(self, dim, lrate=0.2):        super(OutputNeuron, self).__init__(dim, lrate)    def backward(self, target):        self.error = self.out * (1 - self.out) * (self.out - target)class HiddenNeuron(Neuron):    def __init__(self, dim, lrate=0.2):        super(HiddenNeuron, self).__init__(dim, lrate)    def backward(self, deltas, weights):        sum = 0        size = len(deltas)        for x in range(size):            sum += deltas[x] * weights[x]        self.error = self.out * (1 - self.out) * sum

最终输出结果是

[0, 0] => 0.999999991272[0, 1] => 0.999999970788[1, 0] => 0.999999952345[1, 1] => 0.999715564446

回答：

我认为错误出在neuron.py中的update()函数。如果你将self.bias += delta改为self.bias -= delta，应该会正常工作，至少对我来说是这样的。否则，你会修改偏置以在错误曲面上升向最大值。

下面是你可以在100000次训练周期后的输出结果。

[0, 0] => 0.0174550173543[0, 1] => 0.983899954593[1, 0] => 0.983895388655[1, 1] => 0.0164172288168