DL学习笔记【18】nn包中的各位Criterions

很多事情不是因为有多难才没完成,只是因为没有开始。come on,看好你哟!

参考自https://github.com/torch/nn/blob/master/doc/criterion.md

Criterions


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Classification criterions(分类准则)


[output]forward(input, target)

计算该准则下的损失函数的值。output需要是标量

The state variable self.output should be updated after a call to forward().


[gradInput] backward(input, target)

The state variable self.gradInput should be updated after a call to backward().


BCECriterion

基于sigmoid的二进制交叉熵(ClassNLLCriterion的二分类情况)

公式如下:

loss(o, t) = - 1/n sum_i (t[i] * log(o[i]) + (1 - t[i]) * log(1 - o[i]))


ClassNLLCriterion

criterion = nn.ClassNLLCriterion([weights])
如果要使用这个,就需要在网络最后一层添加logsoftmax层,如果不想额外添加layer,可以使用CrossEntropyCriterion
The loss can be described as:
loss(x, class) = -x[class]

网页上的这一句看不明白,class是y么?。。。(或许只要知道它和logsoftmax组合起来是交叉熵就ok了)


CrossEntropyCriterion

criterion = nn.CrossEntropyCriterion([weights])

用于多分类情况

The loss can be described as:
loss(x, class) = -log(exp(x[class]) / (\sum_j exp(x[j]))) = -x[class] + log(\sum_j exp(x[j]))

损失函数看不懂额(或许也不用看它这里的公式,只要知道理论,然后会用这个层就好了,可能它解释的并不是最好的)

通常将size average设置为false

crit = nn.CrossEntropyCriterion(weights)
crit.nll.sizeAverage = false

ClassSimplexCriterion

criterion = nn.ClassSimplexCriterion(nClasses)
该函数对于每一个类,学习一个embedding,embedding将极其稀疏的one-hot编码的词语进行降维。

在使用这个损失函数之前需要有这样两层(NormalizedLinearNoBias和Normalized),嗯。不太明白。。先记录一下,有时间再研究咯 -- 在教程中有论文,如果想了解,可以去看看论文,比多元逻辑回归更鲁棒

nInput = 10
nClasses = 30
nHidden = 100
mlp = nn.Sequential()
mlp:add(nn.Linear(nInput, nHidden)):add(nn.ReLU())
mlp:add(nn.NormalizedLinearNoBias(nHidden, nClasses))
mlp:add(nn.Normalize(2))

criterion = nn.ClassSimplexCriterion(nClasses)

function gradUpdate(mlp, x, y, learningRate)
   pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   mlp:zeroGradParameters()
   local t = criterion:backward(pred, y)
   mlp:backward(x, t)
   mlp:updateParameters(learningRate)
end

MarginCriterion

criterion = nn.MarginCriterion([margin])
二分类

例子代码:

function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

mlp = nn.Sequential()
mlp:add(nn.Linear(5, 1))

x1 = torch.rand(5)
x1_target = torch.Tensor{1}
x2 = torch.rand(5)
x2_target = torch.Tensor{-1}
criterion=nn.MarginCriterion(1)

for i = 1, 1000 do
   gradUpdate(mlp, x1, x1_target, criterion, 0.01)
   gradUpdate(mlp, x2, x2_target, criterion, 0.01)
end

print(mlp:forward(x1))
print(mlp:forward(x2))

print(criterion:forward(mlp:forward(x1), x1_target))
print(criterion:forward(mlp:forward(x2), x2_target))

输出:

 1.0043
[torch.Tensor of dimension 1]


-1.0061
[torch.Tensor of dimension 1]

0
0


By default, the losses are averaged over observations for each minibatch. However, if the field sizeAverage is set to false, the losses are instead summed.


SoftMarginCriterion

criterion = nn.SoftMarginCriterion()

二分类

例子代码:

function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

mlp = nn.Sequential()
mlp:add(nn.Linear(5, 1))

x1 = torch.rand(5)
x1_target = torch.Tensor{1}
x2 = torch.rand(5)
x2_target = torch.Tensor{-1}
criterion=nn.SoftMarginCriterion(1)

for i = 1, 1000 do
   gradUpdate(mlp, x1, x1_target, criterion, 0.01)
   gradUpdate(mlp, x2, x2_target, criterion, 0.01)
end

print(mlp:forward(x1))
print(mlp:forward(x2))

print(criterion:forward(mlp:forward(x1), x1_target))
print(criterion:forward(mlp:forward(x2), x2_target))

输出:

0.7471
[torch.DoubleTensor of size 1]

-0.9607
[torch.DoubleTensor of size 1]

0.38781049558836
0.32399356957564

MultiMarginCriterion

criterion = nn.MultiMarginCriterion(p, [weights], [margin])
多分类

使用时,前边需要加这两句:

mlp = nn.Sequential()
mlp:add(nn.Euclidean(n, m)) -- outputs a vector of distances
mlp:add(nn.MulConstant(-1)) -- distance to similarity
(公式还没有细看,先知道是多分类就好啦。。。)

MultiLabelMarginCriterion

criterion = nn.MultiLabelMarginCriterion()
一个物体属于多个类别

代码例子:

criterion = nn.MultiLabelMarginCriterion()
input = torch.randn(2, 4)
target = torch.Tensor{{1, 3, 0, 0}, {4, 0, 0, 0}} -- zero-values are ignored
criterion:forward(input, target)


MultiLabelSoftMarginCriterion

criterion = nn.MultiLabelSoftMarginCriterion()


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Regression criterions


AbsCriterion

criterion = nn.AbsCriterion()
公式如下:

loss(x, y)  = 1/n \sum |x_i - y_i|
如果x,y是d维的,也是除n,这样计算其实是不对的,所以我们可以通过以下方法来避免

criterion = nn.AbsCriterion()
criterion.sizeAverage = false
(问:如果不除,全都加起来岂不是很大?这样之后需要在后边加别的来归一化么?)


SmoothL1Criterion

criterion = nn.SmoothL1Criterion()
smooth version of  AbsCriterion
使用方法:

criterion = nn.SmoothL1Criterion()
criterion.sizeAverage = false

MSECriterion

criterion = nn.MSECriterion()
最小均方误差

使用方法:

criterion = nn.MSECriterion()
criterion.sizeAverage = false


SpatialAutoCropMSECriterion

criterion = nn.SpatialAutoCropMSECriterion()
如果目标和输出差得比较大,那么可以用这个。
使用方法,之前已经解释过很多次false,此处不解释了哦:

criterion = nn.SpatialAutoCropMSECriterion()
criterion.sizeAverage = false

SpatialAutoCropMSECriterion

criterion = nn.SpatialAutoCropMSECriterion()
如果目标和输出差得比较大,那么可以用这个。
使用方法,之前已经解释过很多次false,此处不解释了哦:

criterion = nn.SpatialAutoCropMSECriterion()
criterion.sizeAverage = false

DiskKLDivCriterion

criterion = nn.DistKLDivCriterion()
KL散度


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Embedding criterions (测量两个输入是否相似或者不相似)


HingeEmbeddingCriterion

criterion = nn.HingeEmbeddingCriterion([margin])

y=1改变weightbias使得输入的两个tensor越来越近,y=-1输入的两个tensor越来越远

(个人理解,可以使用l1距离,也可以自己设置距离,教程。。。写错了吧。。。只给一个tensor应该不能算距离吧)


L1HingeEmbeddingCriterion

criterion = nn.L1HingeEmbeddingCriterion([margin])

算输入两个向量的l1距离


CosineEmbeddingCriterion

criterion = nn.CosineEmbeddingCriterion([margin])

cosine距离


DistanceRatioCriterion

criterion = nn.DistanceRatioCriterion(sizeAverage)

共三个向量,第一个是anchor,第二个和第一个相似,第三个和第一个不相似,公式如下:

loss = -log( exp(-Ds) / ( exp(-Ds) + exp(-Dd) ) )

代码如下(没有看懂):

torch.setdefaulttensortype("torch.FloatTensor")

   require 'nn'

   -- triplet : with batchSize of 32 and dimensionality 512
   sample = {torch.rand(32, 512), torch.rand(32, 512), torch.rand(32, 512)}

   embeddingModel = nn.Sequential()
   embeddingModel:add(nn.Linear(512, 96)):add(nn.ReLU())

   tripleModel = nn.ParallelTable()
   tripleModel:add(embeddingModel)
   tripleModel:add(embeddingModel:clone('weight', 'bias', 
                                        'gradWeight', 'gradBias'))
   tripleModel:add(embeddingModel:clone('weight', 'bias',
                                        'gradWeight', 'gradBias'))

   -- Similar sample distance w.r.t anchor sample
   posDistModel = nn.Sequential()
   posDistModel:add(nn.NarrowTable(1,2)):add(nn.PairwiseDistance())

   -- Different sample distance w.r.t anchor sample
   negDistModel = nn.Sequential()
   negDistModel:add(nn.NarrowTable(2,2)):add(nn.PairwiseDistance())

   distanceModel = nn.ConcatTable():add(posDistModel):add(negDistModel)

   -- Complete Model
   model = nn.Sequential():add(tripleModel):add(distanceModel)

   -- DistanceRatioCriterion
   criterion = nn.DistanceRatioCriterion(true)

   -- Forward & Backward
   output = model:forward(sample)
   loss   = criterion:forward(output)
   dLoss  = criterion:backward(output)
   model:backward(sample, dLoss)

怎么合在一起的。。怎么连接的。。

9632的关系是什么情况

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Miscelaneus criterions(混合准则)


MultiCriterion

criterion = nn.MultiCriterion()

将多个准则放在一起。并赋予权重。代码如下:

input = torch.rand(2,10)
target = torch.IntTensor{1,8}
nll = nn.ClassNLLCriterion()
nll2 = nn.CrossEntropyCriterion()
mc = nn.MultiCriterion():add(nll, 0.5):add(nll2)
output = mc:forward(input, target)


ParallelCriterion

criterion = nn.ParallelCriterion([repeatTarget])

两个输入?两个输出?计算tensor中对应的损失然后按权重相加?

为什么要这样?可以用在哪里呢?


MarginRankingCriterion

criterion = nn.MarginRankingCriterion(margin)

输入3tensor

例子代码看不懂啊啊啊

p1_mlp = nn.Linear(5, 2)
p2_mlp = p1_mlp:clone('weight', 'bias')

prl = nn.ParallelTable()
prl:add(p1_mlp)
prl:add(p2_mlp)

mlp1 = nn.Sequential()
mlp1:add(prl)
mlp1:add(nn.DotProduct())

mlp2 = mlp1:clone('weight', 'bias')

mlpa = nn.Sequential()
prla = nn.ParallelTable()
prla:add(mlp1)
prla:add(mlp2)
mlpa:add(prla)

crit = nn.MarginRankingCriterion(0.1)

x=torch.randn(5)
y=torch.randn(5)
z=torch.randn(5)

-- Use a typical generic gradient update function
function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

for i = 1, 100 do
   gradUpdate(mlpa, {{x, y}, {x, z}}, 1, crit, 0.01)
   if true then
      o1 = mlp1:forward{x, y}[1]
      o2 = mlp2:forward{x, z}[1]
      o = crit:forward(mlpa:forward{{x, y}, {x, z}}, 1)
      print(o1, o2, o)
   end
end

print "--"

for i = 1, 100 do
   gradUpdate(mlpa, {{x, y}, {x, z}}, -1, crit, 0.01)
   if true then
      o1 = mlp1:forward{x, y}[1]
      o2 = mlp2:forward{x, z}[1]
      o = crit:forward(mlpa:forward{{x, y}, {x, z}}, -1)
      print(o1, o2, o)
   end
end

第一个比第二个value更高?



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