简单神经网络无法学习异或
gro*_*ace 6 ruby machine-learning neural-network
我正在尝试学习神经网络并编写一个简单的反向传播神经网络,该网络使用S形激活函数,随机权重初始化和学习/梯度动量.
当配置2个输入,2个隐藏节点和1时,它无法学习XOR和AND.但是,它会正确学习OR.
我没有看到我做错了什么,所以任何帮助都将不胜感激.
谢谢
编辑:如上所述,我测试了2个隐藏节点,但下面的代码显示了3的配置.我只是忘了在使用3个隐藏节点运行测试后将其更改回2.
network.rb:
module Neural
class Network
attr_accessor :num_inputs, :num_hidden_nodes, :num_output_nodes, :input_weights, :hidden_weights, :hidden_nodes,
:output_nodes, :inputs, :output_error_gradients, :hidden_error_gradients,
:previous_input_weight_deltas, :previous_hidden_weight_deltas
def initialize(config)
initialize_input(config)
initialize_nodes(config)
initialize_weights
end
def initialize_input(config)
self.num_inputs = config[:inputs]
self.inputs = Array.new(num_inputs+1)
self.inputs[-1] = -1
end
def initialize_nodes(config)
self.num_hidden_nodes = config[:hidden_nodes]
self.num_output_nodes = config[:output_nodes]
# treat threshold as an additional input/hidden node with no incoming inputs and a value of -1
self.output_nodes = Array.new(num_output_nodes)
self.hidden_nodes = Array.new(num_hidden_nodes+1)
self.hidden_nodes[-1] = -1
end
def initialize_weights
# treat threshold as an additional input/hidden node with no incoming inputs and a value of -1
self.input_weights = Array.new(hidden_nodes.size){Array.new(num_inputs+1)}
self.hidden_weights = Array.new(output_nodes.size){Array.new(num_hidden_nodes+1)}
set_random_weights(input_weights)
set_random_weights(hidden_weights)
self.previous_input_weight_deltas = Array.new(hidden_nodes.size){Array.new(num_inputs+1){0}}
self.previous_hidden_weight_deltas = Array.new(output_nodes.size){Array.new(num_hidden_nodes+1){0}}
end
def set_random_weights(weights)
(0...weights.size).each do |i|
(0...weights[i].size).each do |j|
weights[i][j] = (rand(100) - 49).to_f / 100
end
end
end
def calculate_node_values(inputs)
inputs.each_index do |i|
self.inputs[i] = inputs[i]
end
set_node_values(self.inputs, input_weights, hidden_nodes)
set_node_values(hidden_nodes, hidden_weights, output_nodes)
end
def set_node_values(values, weights, nodes)
(0...weights.size).each do |i|
nodes[i] = Network::sigmoid(values.zip(weights[i]).map{|v,w| v*w}.inject(:+))
end
end
def predict(inputs)
calculate_node_values(inputs)
output_nodes.size == 1 ? output_nodes[0] : output_nodes
end
def train(inputs, desired_results, learning_rate, momentum_rate)
calculate_node_values(inputs)
backpropogate_weights(desired_results, learning_rate, momentum_rate)
end
def backpropogate_weights(desired_results, learning_rate, momentum_rate)
output_error_gradients = calculate_output_error_gradients(desired_results)
hidden_error_gradients = calculate_hidden_error_gradients(output_error_gradients)
update_all_weights(inputs, desired_results, hidden_error_gradients, output_error_gradients, learning_rate, momentum_rate)
end
def self.sigmoid(x)
1.0 / (1 + Math::E**-x)
end
def self.dsigmoid(x)
sigmoid(x) * (1 - sigmoid(x))
end
def calculate_output_error_gradients(desired_results)
desired_results.zip(output_nodes).map{|desired, result| (desired - result) * Network::dsigmoid(result)}
end
def reversed_hidden_weights
# array[hidden node][weights to output nodes]
reversed = Array.new(hidden_nodes.size){Array.new(output_nodes.size)}
hidden_weights.each_index do |i|
hidden_weights[i].each_index do |j|
reversed[j][i] = hidden_weights[i][j];
end
end
reversed
end
def calculate_hidden_error_gradients(output_error_gradients)
reversed = reversed_hidden_weights
hidden_nodes.each_with_index.map do |node, i|
Network::dsigmoid(hidden_nodes[i]) * output_error_gradients.zip(reversed[i]).map{|error, weight| error*weight}.inject(:+)
end
end
def update_all_weights(inputs, desired_results, hidden_error_gradients, output_error_gradients, learning_rate, momentum_rate)
update_weights(hidden_nodes, inputs, input_weights, hidden_error_gradients, learning_rate, previous_input_weight_deltas, momentum_rate)
update_weights(output_nodes, hidden_nodes, hidden_weights, output_error_gradients, learning_rate, previous_hidden_weight_deltas, momentum_rate)
end
def update_weights(nodes, values, weights, gradients, learning_rate, previous_deltas, momentum_rate)
weights.each_index do |i|
weights[i].each_index do |j|
delta = learning_rate * gradients[i] * values[j]
weights[i][j] += delta + momentum_rate * previous_deltas[i][j]
previous_deltas[i][j] = delta
end
end
end
end
end
test.rb:
#!/usr/bin/ruby
load "network.rb"
learning_rate = 0.3
momentum_rate = 0.2
nn = Neural::Network.new(:inputs => 2, :hidden_nodes => 3, :output_nodes => 1)
10000.times do |i|
# XOR - doesn't work
nn.train([0, 0], [0], learning_rate, momentum_rate)
nn.train([1, 0], [1], learning_rate, momentum_rate)
nn.train([0, 1], [1], learning_rate, momentum_rate)
nn.train([1, 1], [0], learning_rate, momentum_rate)
# AND - very rarely works
# nn.train([0, 0], [0], learning_rate, momentum_rate)
# nn.train([1, 0], [0], learning_rate, momentum_rate)
# nn.train([0, 1], [0], learning_rate, momentum_rate)
# nn.train([1, 1], [1], learning_rate, momentum_rate)
# OR - works
# nn.train([0, 0], [0], learning_rate, momentum_rate)
# nn.train([1, 0], [1], learning_rate, momentum_rate)
# nn.train([0, 1], [1], learning_rate, momentum_rate)
# nn.train([1, 1], [1], learning_rate, momentum_rate)
end
puts "--- TESTING ---"
puts "[0, 0]"
puts "result "+nn.predict([0, 0]).to_s
puts
puts "[1, 0]"
puts "result "+nn.predict([1, 0]).to_s
puts
puts "[0, 1]"
puts "result "+nn.predict([0, 1]).to_s
puts
puts "[1, 1]"
puts "result "+nn.predict([1, 1]).to_s
puts
Ale*_*eut 13
我的答案不是关于红宝石,而是关于神经网络.首先,您必须了解如何在纸上编写输入和网络.如果您实现二元operatos,您的空间将由XY平面上的四个点组成.在X和Y轴上标记真假,并绘制您的四个点.如果你正确,你会得到这样的东西
现在(也许你不知道神经元的这种解释)试图将神经元绘制成一个平面线,根据需要将你的点分开.例如,这是AND的行:
该行将正确答案与错误分开.如果您了解,可以为OR编写行.XOR将是一个麻烦.
作为此调试的最后一步,将神经元视为一条线.查找有关它的文献,我不记得如何通过现有的线构建神经元.这很简单,真的.然后为AND构建一个神经元向量来实现它.实现AND作为单个神经元网络,其中神经元被定义为您的AND,在纸上计算.如果一切正确,您的网络将执行AND功能.我写了这么多信件只是因为你在理解任务之前写了一个程序.我不想粗暴,但你提到XOR就表明了这一点.如果你试图在一个神经元上建立XOR,你将什么都得不到 - 将正确答案与错误分开是不可能的.在书中它被称为"XOR不是线性可分离的".因此,对于XOR,您需要构建一个双层网络.例如,您将AND和NOT-OR作为第一层,AND作为第二层.
如果您仍然阅读本文并了解我所写的内容,那么您将不会遇到调试网络的麻烦.如果您的网络无法学习某些功能,请将其构建在纸上,然后对网络进行硬编码并对其进行测试.如果它仍然失败,你在纸上构建不正确 - 重新阅读我的讲座;)