请帮助我使用Python实现backprop

编辑2：

新的训练集

投入：

[
 [0.0, 0.0], 
 [0.0, 1.0], 
 [0.0, 2.0], 
 [0.0, 3.0], 
 [0.0, 4.0], 
 [1.0, 0.0], 
 [1.0, 1.0], 
 [1.0, 2.0], 
 [1.0, 3.0], 
 [1.0, 4.0], 
 [2.0, 0.0], 
 [2.0, 1.0], 
 [2.0, 2.0], 
 [2.0, 3.0], 
 [2.0, 4.0], 
 [3.0, 0.0], 
 [3.0, 1.0], 
 [3.0, 2.0], 
 [3.0, 3.0], 
 [3.0, 4.0],
 [4.0, 0.0], 
 [4.0, 1.0], 
 [4.0, 2.0], 
 [4.0, 3.0], 
 [4.0, 4.0]
]

产出：

[
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [1.0], 
 [1.0], 
 [0.0], 
 [0.0], 
 [0.0], 
 [1.0], 
 [1.0]
]

编辑1：

我已经用我的最新代码更新了这个问题。我修复了一些小问题，但在网络学习之后，我仍然得到了所有输入组合的相同输出

这里解释了backprop算法：

---

是的，这是一个家庭作业，从一开始就要弄清楚这一点

我应该在一个简单的神经网络上实现一个简单的反向传播算法

我选择Python作为这项任务的首选语言，并选择了如下神经网络：

3层：1个输入层，1个隐藏层，1个输出层：

O         O

                    O

O         O

输入神经元上都有一个整数，输出神经元上都有1或0

这是我的整个实现（有点长）。下面，我将选择较短的相关代码段，我认为错误可能位于：

import os
import math
import Image
import random
from random import sample

#------------------------------ class definitions

class Weight:
    def __init__(self, fromNeuron, toNeuron):
        self.value = random.uniform(-0.5, 0.5)
        self.fromNeuron = fromNeuron
        self.toNeuron = toNeuron
        fromNeuron.outputWeights.append(self)
        toNeuron.inputWeights.append(self)
        self.delta = 0.0 # delta value, this will accumulate and after each training cycle used to adjust the weight value

    def calculateDelta(self, network):
        self.delta += self.fromNeuron.value * self.toNeuron.error

class Neuron:
    def __init__(self):
        self.value = 0.0        # the output
        self.idealValue = 0.0   # the ideal output
        self.error = 0.0        # error between output and ideal output
        self.inputWeights = []
        self.outputWeights = []

    def activate(self, network):
        x = 0.0;
        for weight in self.inputWeights:
            x += weight.value * weight.fromNeuron.value
        # sigmoid function
        if x < -320:
            self.value = 0
        elif x > 320:
            self.value = 1
        else:
            self.value = 1 / (1 + math.exp(-x))

class Layer:
    def __init__(self, neurons):
        self.neurons = neurons

    def activate(self, network):
        for neuron in self.neurons:
            neuron.activate(network)

class Network:
    def __init__(self, layers, learningRate):
        self.layers = layers
        self.learningRate = learningRate # the rate at which the network learns
        self.weights = []
        for hiddenNeuron in self.layers[1].neurons:
            for inputNeuron in self.layers[0].neurons:
                self.weights.append(Weight(inputNeuron, hiddenNeuron))
            for outputNeuron in self.layers[2].neurons:
                self.weights.append(Weight(hiddenNeuron, outputNeuron))

    def setInputs(self, inputs):
        self.layers[0].neurons[0].value = float(inputs[0])
        self.layers[0].neurons[1].value = float(inputs[1])

    def setExpectedOutputs(self, expectedOutputs):
        self.layers[2].neurons[0].idealValue = expectedOutputs[0]

    def calculateOutputs(self, expectedOutputs):
        self.setExpectedOutputs(expectedOutputs)
        self.layers[1].activate(self) # activation function for hidden layer
        self.layers[2].activate(self) # activation function for output layer        

    def calculateOutputErrors(self):
        for neuron in self.layers[2].neurons:
            neuron.error = (neuron.idealValue - neuron.value) * neuron.value * (1 - neuron.value)

    def calculateHiddenErrors(self):
        for neuron in self.layers[1].neurons:
            error = 0.0
            for weight in neuron.outputWeights:
                error += weight.toNeuron.error * weight.value
            neuron.error = error * neuron.value * (1 - neuron.value)

    def calculateDeltas(self):
        for weight in self.weights:
            weight.calculateDelta(self)

    def train(self, inputs, expectedOutputs):
        self.setInputs(inputs)
        self.calculateOutputs(expectedOutputs)
        self.calculateOutputErrors()
        self.calculateHiddenErrors()
        self.calculateDeltas()

    def learn(self):
        for weight in self.weights:
            weight.value += self.learningRate * weight.delta

    def calculateSingleOutput(self, inputs):
        self.setInputs(inputs)
        self.layers[1].activate(self)
        self.layers[2].activate(self)
        #return round(self.layers[2].neurons[0].value, 0)
        return self.layers[2].neurons[0].value


#------------------------------ initialize objects etc


inputLayer = Layer([Neuron() for n in range(2)])
hiddenLayer = Layer([Neuron() for n in range(100)])
outputLayer = Layer([Neuron() for n in range(1)])

learningRate = 0.5

network = Network([inputLayer, hiddenLayer, outputLayer], learningRate)

# just for debugging, the real training set is much larger
trainingInputs = [
    [0.0, 0.0],
    [1.0, 0.0],
    [2.0, 0.0],
    [0.0, 1.0],
    [1.0, 1.0],
    [2.0, 1.0],
    [0.0, 2.0],
    [1.0, 2.0],
    [2.0, 2.0]
]
trainingOutputs = [
    [0.0],
    [1.0],
    [1.0],
    [0.0],
    [1.0],
    [0.0],
    [0.0],
    [0.0],
    [1.0]
]

#------------------------------ let's train

for i in range(500):
    for j in range(len(trainingOutputs)):
        network.train(trainingInputs[j], trainingOutputs[j])
        network.learn()

#------------------------------ let's check


for pattern in trainingInputs:
    print network.calculateSingleOutput(pattern)

这是我计算三角洲的方法：

def calculateDelta(self, network):
    self.delta += self.getFromNeuron(network).value * self.getToNeuron(network).error

这是我的算法的一般流程：

for i in range(numberOfIterations):
    for k,expectedOutput in trainingSet.iteritems():
        coordinates = k.split(",")
        network.setInputs((float(coordinates[0]), float(coordinates[1])))
        network.calculateOutputs([float(expectedOutput)])
        network.calculateOutputErrors()
        network.calculateHiddenErrors()
        network.calculateDeltas()
    oldWeights = network.weights
    network.adjustWeights()
    network.resetDeltas()
    print "Iteration ", i
    j = 0
    for weight in network.weights:
        print "Weight W", weight.i, weight.j, ": ", oldWeights[j].value, " ............ Adjusted value : ", weight.value
        j += j

输出的最后两行是：

0.552785449458 # this should be close to 1
0.552785449458 # this should be close to 0

它实际上返回所有输入组合的输出编号

---

我遗漏了什么吗？

看起来你得到的几乎是神经元的初始状态（几乎是

self.idealValue

）。也许你不应该在有实际数据提供之前初始化这个神经元

编辑：好的，我对代码进行了更深入的研究并对其进行了简化（将在下面发布简化版本）。基本上，您的代码有两个小错误（看起来像是您刚刚忽略的），但这会导致网络肯定无法工作

• 在学习阶段，您忘记在输出层设置expectedOutput的值。没有这一点，网络肯定学不到任何东西，而且总是停留在最初的理想价值上。（这就是我在第一次阅读时看到的巴哈维奥）。这一点甚至可以在您对培训步骤的描述中发现（如果您没有发布代码，可能会发现，这是我所知道的少数情况之一，实际上发布代码是隐藏错误，而不是让错误变得明显）。你在编辑后修复了这个
• 在calculateSingleOutputs中激活网络时，忘记激活隐藏层

显然，这两个问题中的任何一个都会导致一个不稳定的网络

一旦更正，它就可以工作了（在我简化的代码版本中就是这样）

这些错误不容易发现，因为初始代码太复杂了。在引入新类或新方法之前，您应该三思而后行。没有创建足够的方法或类会使代码难以阅读和维护，但是创建太多的方法或类可能会使代码更难阅读和维护。你必须找到正确的平衡。我个人找到这种平衡的方法是，无论它们引导我到哪里，都要遵循和重构技术。有时添加方法或创建类，有时删除它们。这当然不是完美的，但这对我来说是有效的

下面是我在应用一些重构后的代码版本。我花了大约一个小时修改你的代码，但总是保持它的功能相同。我认为这是一个很好的重构练习，因为最初的代码读起来非常糟糕。重构后，只需5分钟就能发现问题

import os
import math

"""
A simple backprop neural network. It has 3 layers:
    Input layer: 2 neurons
    Hidden layer: 2 neurons
    Output layer: 1 neuron
"""

class Weight:
    """
    Class representing a weight between two neurons
    """
    def __init__(self, value, from_neuron, to_neuron):
        self.value = value
        self.from_neuron = from_neuron
        from_neuron.outputWeights.append(self)
        self.to_neuron = to_neuron
        to_neuron.inputWeights.append(self)

        # delta value, this will accumulate and after each training cycle
        # will be used to adjust the weight value
        self.delta = 0.0

class Neuron:
    """
    Class representing a neuron.
    """
    def __init__(self):
        self.value = 0.0        # the output
        self.idealValue = 0.0   # the ideal output
        self.error = 0.0        # error between output and ideal output
        self.inputWeights = []    # weights that end in the neuron
        self.outputWeights = []  # weights that starts in the neuron

    def activate(self):
        """
        Calculate an activation function of a neuron which is 
        a sum of all input weights * neurons where those weights start
        """
        x = 0.0;
        for weight in self.inputWeights:
            x += weight.value * weight.from_neuron.value
        # sigmoid function
        self.value = 1 / (1 + math.exp(-x))

class Network:
    """
    Class representing a whole neural network. Contains layers.
    """
    def __init__(self, layers, learningRate, weights):
        self.layers = layers
        self.learningRate = learningRate    # the rate at which the network learns
        self.weights = weights

    def training(self, entries, expectedOutput):
        for i in range(len(entries)):
            self.layers[0][i].value = entries[i]
        for i in range(len(expectedOutput)):
            self.layers[2][i].idealValue = expectedOutput[i]
        for layer in self.layers[1:]:
            for n in layer:
                n.activate()
        for n in self.layers[2]:
            error = (n.idealValue - n.value) * n.value * (1 - n.value)
            n.error = error
        for n in self.layers[1]:
            error = 0.0
            for w in n.outputWeights:
                error += w.to_neuron.error * w.value
            n.error = error
        for w in self.weights:
            w.delta += w.from_neuron.value * w.to_neuron.error

    def updateWeights(self):
        for w in self.weights:
            w.value += self.learningRate * w.delta

    def calculateSingleOutput(self, entries):
        """
        Calculate a single output for input values.
        This will be used to debug the already learned network after training.
        """
        for i in range(len(entries)):
            self.layers[0][i].value = entries[i]
        # activation function for output layer
        for layer in self.layers[1:]:
            for n in layer:
                n.activate()
        print self.layers[2][0].value


#------------------------------ initialize objects etc

neurons = [Neuron() for n in range(5)]

w1 = Weight(-0.79, neurons[0], neurons[2])
w2 = Weight( 0.51, neurons[0], neurons[3])
w3 = Weight( 0.27, neurons[1], neurons[2])
w4 = Weight(-0.48, neurons[1], neurons[3])
w5 = Weight(-0.33, neurons[2], neurons[4])
w6 = Weight( 0.09, neurons[3], neurons[4])

weights = [w1, w2, w3, w4, w5, w6]
inputLayer  = [neurons[0], neurons[1]]
hiddenLayer = [neurons[2], neurons[3]]
outputLayer = [neurons[4]]
learningRate = 0.3
network = Network([inputLayer, hiddenLayer, outputLayer], learningRate, weights)

# just for debugging, the real training set is much larger
trainingSet = [([0.0,0.0],[0.0]),
               ([1.0,0.0],[1.0]),
               ([2.0,0.0],[1.0]),
               ([0.0,1.0],[0.0]),
               ([1.0,1.0],[1.0]),
               ([2.0,1.0],[0.0]),
               ([0.0,2.0],[0.0]),
               ([1.0,2.0],[0.0]),
               ([2.0,2.0],[1.0])]

#------------------------------ let's train
for i in range(100): # training iterations
    for entries, expectedOutput in trainingSet:
        network.training(entries, expectedOutput)
    network.updateWeights()

#network has learned, let's check
network.calculateSingleOutput((1, 0)) # this should be close to 1
network.calculateSingleOutput((0, 0)) # this should be close to 0

---

顺便说一下，还有第三个问题我没有纠正（但很容易纠正）。如果x太大或太小（>320或<-320）

math.exp（）

将引发异常。如果您申请培训迭代（比如几千次），就会出现这种情况。我所看到的最简单的纠正方法是检查x的值，如果x太大或太小，根据情况将神经元的值设置为0或1，这是极限值。

我认为您需要自己做更多的工作——这比您合理期望人们为您调试的代码还要多。在所有重要位置添加

logging.log

语句，以跟踪边的权重，并使用计算器对数字进行几步运算，以查看它们不一致的地方。请阅读以下内容：。对于Bayseian过滤器，这是一个标准问题，具有标准解决方案。对于非常非常小的浮点数，你似乎也有同样的标准问题。@Katrielex是的，我当然也会继续研究这个问题。@S.Lott：问题不可能从这里开始，因为OP已经使用对数作为权重，这就是为什么

math.exp

是必要的。这导致了另一个问题：当x变得太小或太大时，python会引发一个异常，但这与观察到的虚假行为无关（只是一个普通的老错误）。只需添加：

self.layers[2]。在
calculateSingleOutput
中运行所有神经元（self）的激活函数即可。但除了错误修复，收敛性不如编辑后的第一个版本，这令人惊讶。我看不出哪种变化有这种效果。好吧，我明天会试试。非常感谢。是的，我想我把它复杂化了。我只是想避免程序化编程，在OOP中做所有的事情，所以我被冲昏头脑了。顺便说一句，试试print network.calculateSingleOutput（2.0，1.0）。它将打印不正确的输出：）@Richard Knop:你是说
网络。calculateSingleOutput（[2.0，1.0]）
？（entries参数只需要一个由两个数字组成的输入，您的版本将给出语法错误）。经过100次学习迭代，它的结果是：0.04，并不像预期的那样完全为零，但我不会说这两件事不正确，它仍然接近于零。@Richard Knop:好的，我知道了。它适用于我的版本，而不是你的版本。我想这是EDIT1改变了的，因为我从最初的版本进行了重构。问题的原因（再次）对我来说并不明显，你必须自己检查差异。
import os
import math

"""
A simple backprop neural network. It has 3 layers:
    Input layer: 2 neurons
    Hidden layer: 2 neurons
    Output layer: 1 neuron
"""

class Weight:
    """
    Class representing a weight between two neurons
    """
    def __init__(self, value, from_neuron, to_neuron):
        self.value = value
        self.from_neuron = from_neuron
        from_neuron.outputWeights.append(self)
        self.to_neuron = to_neuron
        to_neuron.inputWeights.append(self)

        # delta value, this will accumulate and after each training cycle
        # will be used to adjust the weight value
        self.delta = 0.0

class Neuron:
    """
    Class representing a neuron.
    """
    def __init__(self):
        self.value = 0.0        # the output
        self.idealValue = 0.0   # the ideal output
        self.error = 0.0        # error between output and ideal output
        self.inputWeights = []    # weights that end in the neuron
        self.outputWeights = []  # weights that starts in the neuron

    def activate(self):
        """
        Calculate an activation function of a neuron which is 
        a sum of all input weights * neurons where those weights start
        """
        x = 0.0;
        for weight in self.inputWeights:
            x += weight.value * weight.from_neuron.value
        # sigmoid function
        self.value = 1 / (1 + math.exp(-x))

class Network:
    """
    Class representing a whole neural network. Contains layers.
    """
    def __init__(self, layers, learningRate, weights):
        self.layers = layers
        self.learningRate = learningRate    # the rate at which the network learns
        self.weights = weights

    def training(self, entries, expectedOutput):
        for i in range(len(entries)):
            self.layers[0][i].value = entries[i]
        for i in range(len(expectedOutput)):
            self.layers[2][i].idealValue = expectedOutput[i]
        for layer in self.layers[1:]:
            for n in layer:
                n.activate()
        for n in self.layers[2]:
            error = (n.idealValue - n.value) * n.value * (1 - n.value)
            n.error = error
        for n in self.layers[1]:
            error = 0.0
            for w in n.outputWeights:
                error += w.to_neuron.error * w.value
            n.error = error
        for w in self.weights:
            w.delta += w.from_neuron.value * w.to_neuron.error

    def updateWeights(self):
        for w in self.weights:
            w.value += self.learningRate * w.delta

    def calculateSingleOutput(self, entries):
        """
        Calculate a single output for input values.
        This will be used to debug the already learned network after training.
        """
        for i in range(len(entries)):
            self.layers[0][i].value = entries[i]
        # activation function for output layer
        for layer in self.layers[1:]:
            for n in layer:
                n.activate()
        print self.layers[2][0].value


#------------------------------ initialize objects etc

neurons = [Neuron() for n in range(5)]

w1 = Weight(-0.79, neurons[0], neurons[2])
w2 = Weight( 0.51, neurons[0], neurons[3])
w3 = Weight( 0.27, neurons[1], neurons[2])
w4 = Weight(-0.48, neurons[1], neurons[3])
w5 = Weight(-0.33, neurons[2], neurons[4])
w6 = Weight( 0.09, neurons[3], neurons[4])

weights = [w1, w2, w3, w4, w5, w6]
inputLayer  = [neurons[0], neurons[1]]
hiddenLayer = [neurons[2], neurons[3]]
outputLayer = [neurons[4]]
learningRate = 0.3
network = Network([inputLayer, hiddenLayer, outputLayer], learningRate, weights)

# just for debugging, the real training set is much larger
trainingSet = [([0.0,0.0],[0.0]),
               ([1.0,0.0],[1.0]),
               ([2.0,0.0],[1.0]),
               ([0.0,1.0],[0.0]),
               ([1.0,1.0],[1.0]),
               ([2.0,1.0],[0.0]),
               ([0.0,2.0],[0.0]),
               ([1.0,2.0],[0.0]),
               ([2.0,2.0],[1.0])]

#------------------------------ let's train
for i in range(100): # training iterations
    for entries, expectedOutput in trainingSet:
        network.training(entries, expectedOutput)
    network.updateWeights()

#network has learned, let's check
network.calculateSingleOutput((1, 0)) # this should be close to 1
network.calculateSingleOutput((0, 0)) # this should be close to 0