（原）torch的训练过程

转载请注明出处：

http://www.cnblogs.com/darkknightzh/p/6221622.html

参考网址：

http://ju.outofmemory.cn/entry/284587

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

1. 使用updateParameters

假设已经有了model=setupmodel（自己建立的模型），同时也有自己的训练数据input，实际输出outReal，以及损失函数criterion（参见第二个网址），则使用torch训练过程如下：

 -- given model, criterion, input, outReal
 model:training()
 model:zeroGradParameters()
 outPredict = model:forward(input)
 err= criterion:forward(outPredict, outReal)
 grad_criterion = criterion:backward(outPredict, outReal)
 model:backward(input, grad_criterion)
 model:updateParameters(learningRate)

上面第1行假定已知的参数

第2行设置为训练模式

第3行将model中每个模块保存的梯度清零（防止之前的干扰此次迭代）

第4行将输入input通过model，得到预测的输出outPredict

第5行通过损失函数计算在当前参数下模型的预测输出outPredict和实际输出outReal的误差err

第6行通过预测输出outPredict和实际输出outReal计算损失函数的梯度grad_criterion

第7行反向计算model中每个模块的梯度

第8行更新model每个模块的参数

每次迭代时，均需要执行第3行至第8行。

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2. 使用optim

170301更新：

http://x-wei.github.io/learn-torch-6-optim.html

中给出了更方便的方式（是否方便也说不清楚），可以使用torch中的optim来更新参数（直接使用model:updateParameters的话，只能使用最简单的梯度下降算法，optmi中封装了很多算法，梯度下降，adam之类的）。

params_new, fs, ... = optim._method_(feval, params[, config][, state])

其中，param：当前参数向量（1D的tensro），在优化时会被更新

feval：用户自定义的闭包，类似于f, df/dx = feval(x)

config：一个包含算法参数（如learning rate）的table

state：包含状态变量的table

params_new：最小化函数f的新的结果参数（1D的tensor）

fs：a table of f values evaluated during the optimization, fs[#fs] is the optimized function value

注意：由于optmi需要输入数据为1D的tensor，因而需要将模型中的参数变成拉平，通过下面的函数来实现：

params, gradParams = model:getParameters()

params和gradParams均为1D的tensor。

使用上面的方法后，开始得程序可以修改为：

-- given model, criterion, input, outReal, optimState
local params, gradParams = model:getParameters()

local function feval()
    return criterion.output, gradParams
end

for ...
    model:training()
    model:zeroGradParameters()
    outPredict = model:forward(input)
    err= criterion:forward(outPredict, outReal)
    grad_criterion = criterion:backward(outPredict, outReal)
    model:backward(input, grad_criterion)

    optim.sgd(feval, params, optimState)
end

170301更新结束

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3. 使用model:backward注意的问题

170405更新

需要注意的是，model:backward一定要和model:forward对应。

https://github.com/torch/nn/blob/master/doc/module.md中[gradInput] backward(input, gradOutput)写着：

In general this method makes the assumption forward(input) has been called before, with the same input. This is necessary for optimization reasons. If you do not respect this rule, backward() will compute incorrect gradients.

应该是由于backward时，可能会使用forward的某些中间变量，因而backward执行前，必须先执行forward，否则中间变量和backward不对应，导致结果错误。

我这边之前的程序由于最初forward后，保存的是最后一次forward时的中间变量，因而backward时的结果总是不正确（见method5注释的那句）。

只能使用比较坑的方式解决，之前先forward，最终在backward之前，在forward一次，这样能保证结果正确（缺点就是增加了一次计算。。。），代码如method5。

说明：method1为常规的batch的方法。但是该方法对显存要求较高。因而可以使用类似caffe中的iter_size的方式，如method2的方法（和caffe中的iter_size不完全一样）。如果需要使用更多的样本，同时criterion时使用尽可能多的样本，则前两种方法均会出现问题，此时可以使用method3的方法（但是实际上method3有问题，loss收敛的很慢）。method4对method3进行了进一步的改进及测试，如果method4注释那两行，则其收敛正常，但是不注释那两行，则收敛出现问题，和method3收敛类似。method5进行了最终的改进。该程序能正常收敛。同时为了验证forward和backward要对应，将method5中注释的取消注释，同时注释掉上面一行，可以看出，其收敛很慢（和method3,4类似）。下面是各种method前10次的的收敛情况。

程序如下：

 require 'torch'
 require 'nn'
 require 'optim'
 require 'cunn'
 require 'cutorch'
 local mnist = require 'mnist'

 local fullset = mnist.traindataset()
 local testset = mnist.testdataset()

 local trainset = {
     size = ,
     data = fullset.data[{{,}}]:double(),
     label = fullset.label[{{,}}]
 }
 trainset.data = trainset.data - trainset.data:mean()
 trainset.data = trainset.data:cuda()
 trainset.label = trainset.label:cuda()

 local validationset = {
     size = ,
     data = fullset.data[{{,}}]:double(),
     label = fullset.label[{{,}}]
 }
 validationset.data = validationset.data - validationset.data:mean()
 validationset.data = validationset.data:cuda()
 validationset.label = validationset.label:cuda()

 local model = nn.Sequential()
 model:add(nn.Reshape(, , ))
 model:add(nn.MulConstant(/256.0*3.2))
 model:add(nn.SpatialConvolutionMM(, , , , , , , ))
 model:add(nn.SpatialMaxPooling(,  , , , , ))
 model:add(nn.SpatialConvolutionMM(, , , , , , , ))
 model:add(nn.SpatialMaxPooling(,  , , , , ))
 model:add(nn.Reshape(**))
 model:add(nn.Linear(**, ))
 model:add(nn.ReLU())
 model:add(nn.Linear(, ))
 model:add(nn.LogSoftMax())

 model = require('weight-init')(model, 'xavier')
 model = model:cuda()

 x, dl_dx = model:getParameters()

 local criterion = nn.ClassNLLCriterion():cuda()

 local sgd_params = {
    learningRate = 1e-2,
    learningRateDecay = 1e-4,
    weightDecay = 1e-3,
    momentum = 1e-4
 }

 local training = function(batchSize)
     local current_loss =
     local count =
     local shuffle = torch.randperm(trainset.size)
     batchSize = batchSize or
     for t = , trainset.size-, batchSize do
         -- setup inputs and targets for batch iteration
         local size = math.min(t + batchSize, trainset.size) - t
         local inputs = torch.Tensor(size, , ):cuda()
         local targets = torch.Tensor(size):cuda()
         for i = , size do
             inputs[i] = trainset.data[shuffle[i+t]]
             targets[i] = trainset.label[shuffle[i+t]] +
         end

         local feval = function(x_new)
             local miniBatchSize =
             if x ~= x_new then x:copy(x_new) end   -- reset data
             dl_dx:zero()

             --[[ ------------------ method 1 original batch
             local outputs = model:forward(inputs)
             local loss = criterion:forward(outputs, targets)
             local gradInput = criterion:backward(outputs, targets)
             model:backward(inputs, gradInput)
             --]]

             --[[ ------------------ method 2 iter-size with batch
             local loss = 0
             for idx = 1, batchSize, miniBatchSize do
                 local outputs = model:forward(inputs[{{idx, idx + miniBatchSize - 1}}])
                 loss = loss + criterion:forward(outputs, targets[{{idx, idx + miniBatchSize - 1}}])
                 local gradInput = criterion:backward(outputs, targets[{{idx, idx + miniBatchSize - 1}}])
                 model:backward(inputs[{{idx, idx + miniBatchSize - 1}}], gradInput)
             end
             dl_dx:mul(1.0 * miniBatchSize / batchSize)
             loss = loss * miniBatchSize / batchSize
             --]]

             --[[  ------------------ method 3 mini-batch in batch
             local outputs = torch.Tensor(batchSize, 10):zero():cuda()
             for idx = 1, batchSize, miniBatchSize do
                 outputs[{{idx, idx + miniBatchSize - 1}}]:copy(model:forward(inputs[{{idx, idx + miniBatchSize - 1}}]))
             end
             local loss = 0
             for idx = 1, batchSize, miniBatchSize do
                 loss = loss + criterion:forward(outputs[{{idx, idx + miniBatchSize - 1}}],
                     targets[{{idx, idx + miniBatchSize - 1}}])
             end
             local gradInput = torch.Tensor(batchSize, 10):zero():cuda()
             for idx = 1, batchSize, miniBatchSize do
                 gradInput[{{idx, idx + miniBatchSize - 1}}]:copy(criterion:backward(
                     outputs[{{idx, idx + miniBatchSize - 1}}], targets[{{idx, idx + miniBatchSize - 1}}]))
             end
             for idx = 1, batchSize, miniBatchSize do
                 model:backward(inputs[{{idx, idx + miniBatchSize - 1}}], gradInput[{{idx, idx + miniBatchSize - 1}}])
             end
             dl_dx:mul( 1.0 * miniBatchSize / batchSize)
             loss = loss * miniBatchSize / batchSize
             --]]

             --[[ ------------------ method 4 mini-batch in batch
             local outputs = torch.Tensor(batchSize, 10):zero():cuda()
             local loss = 0
             local gradInput = torch.Tensor(batchSize, 10):zero():cuda()
             for idx = 1, batchSize, miniBatchSize do
                 outputs[{{idx, idx + miniBatchSize - 1}}]:copy(model:forward(inputs[{{idx, idx + miniBatchSize - 1}}]))
                 loss = loss + criterion:forward(outputs[{{idx, idx + miniBatchSize - 1}}],
                     targets[{{idx, idx + miniBatchSize - 1}}])
                 gradInput[{{idx, idx + miniBatchSize - 1}}]:copy(criterion:backward(
                     outputs[{{idx, idx + miniBatchSize - 1}}], targets[{{idx, idx + miniBatchSize - 1}}]))
             --  end
             --  for idx = 1, batchSize, miniBatchSize do
                 model:backward(inputs[{{idx, idx + miniBatchSize - 1}}], gradInput[{{idx, idx + miniBatchSize - 1}}])
             end

             dl_dx:mul( 1.0 * miniBatchSize / batchSize)
             loss = loss * miniBatchSize / batchSize
             --]]

             ---[[ ------------------ method 5 mini-batch in batch
             local loss =
             local gradInput = torch.Tensor(batchSize, ):zero():cuda()

             for idx = , batchSize, miniBatchSize do
                 local outputs = model:forward(inputs[{{idx, idx + miniBatchSize - }}])
                 loss = loss + criterion:forward(outputs, targets[{{idx, idx + miniBatchSize - }}])
                 gradInput[{{idx, idx + miniBatchSize - }}]:copy(criterion:backward(outputs, targets[{{idx, idx + miniBatchSize - }}]))
             end

             for idx = , batchSize, miniBatchSize do
                 model:forward(inputs[{{idx, idx + miniBatchSize - }}])
                 --model:forward(inputs[{{batchSize - miniBatchSize + 1, batchSize}}])
                 model:backward(inputs[{{idx, idx + miniBatchSize - }}], gradInput[{{idx, idx + miniBatchSize - }}])
             end

             dl_dx:mul( 1.0 * miniBatchSize / batchSize)
             loss = loss * miniBatchSize / batchSize
             --]]

             return loss, dl_dx
         end

         _, fs = optim.sgd(feval, x, sgd_params)

         count = count +
         current_loss = current_loss + fs[]
     end

     return current_loss / count   -- normalize loss
 end

 local eval = function(dataset, batchSize)
     local count =
     batchSize = batchSize or 

     for i = , dataset.size, batchSize do
         local size = math.min(i + batchSize - , dataset.size) - i
         local inputs = dataset.data[{{i,i+size-}}]:cuda()
         local targets = dataset.label[{{i,i+size-}}]
         local outputs = model:forward(inputs)
         local _, indices = torch.max(outputs, )
         indices:add(-)
         indices = indices:cuda()
         local guessed_right = indices:eq(targets):sum()
         count = count + guessed_right
     end

     return count / dataset.size
 end

 local max_iters =
 local last_accuracy =
 local decreasing =
 local threshold =  -- how many deacreasing epochs we allow
 for i = ,max_iters do
    -- timer = torch.Timer()

     model:training()
     local loss = training()

     model:evaluate()
     local accuracy = eval(validationset)
     print(string.format('Epoch: %d Current loss: %4f; validation set accu: %4f', i, loss, accuracy))
     if accuracy < last_accuracy then
         if decreasing > threshold then break end
         decreasing = decreasing +
     else
         decreasing =
     end
     last_accuracy = accuracy

     --print('    Time elapsed: ' .. i .. 'iter: ' .. timer:time().real .. ' seconds')
 end

 testset.data = testset.data:double()
 eval(testset)

weight-init.lua

 --
 -- Different weight initialization methods
 --
 -- > model = require('weight-init')(model, 'heuristic')
 --
 require("nn")

 -- "Efficient backprop"
 -- Yann Lecun, 1998
 local function w_init_heuristic(fan_in, fan_out)
    return math.sqrt(/(*fan_in))
 end

 -- "Understanding the difficulty of training deep feedforward neural networks"
 -- Xavier Glorot, 2010
 local function w_init_xavier(fan_in, fan_out)
    return math.sqrt(/(fan_in + fan_out))
 end

 -- "Understanding the difficulty of training deep feedforward neural networks"
 -- Xavier Glorot, 2010
 local function w_init_xavier_caffe(fan_in, fan_out)
    return math.sqrt(/fan_in)
 end

 -- "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification"
 -- Kaiming He, 2015
 local function w_init_kaiming(fan_in, fan_out)
    return math.sqrt(/(fan_in + fan_out))
 end

 local function w_init(net, arg)
    -- choose initialization method
    local method = nil
    if     arg == 'heuristic'    then method = w_init_heuristic
    elseif arg == 'xavier'       then method = w_init_xavier
    elseif arg == 'xavier_caffe' then method = w_init_xavier_caffe
    elseif arg == 'kaiming'      then method = w_init_kaiming
    else
       assert(false)
    end

    -- loop over all convolutional modules
    for i = , #net.modules do
       local m = net.modules[i]
       if m.__typename == 'nn.SpatialConvolution' then
          m:reset(method(m.nInputPlane*m.kH*m.kW, m.nOutputPlane*m.kH*m.kW))
       elseif m.__typename == 'nn.SpatialConvolutionMM' then
          m:reset(method(m.nInputPlane*m.kH*m.kW, m.nOutputPlane*m.kH*m.kW))
       elseif m.__typename == 'cudnn.SpatialConvolution' then
          m:reset(method(m.nInputPlane*m.kH*m.kW, m.nOutputPlane*m.kH*m.kW))
       elseif m.__typename == 'nn.LateralConvolution' then
          m:reset(method(m.nInputPlane**, m.nOutputPlane**))
       elseif m.__typename == 'nn.VerticalConvolution' then
          m:reset(method(*m.kH*m.kW, *m.kH*m.kW))
       elseif m.__typename == 'nn.HorizontalConvolution' then
          m:reset(method(*m.kH*m.kW, *m.kH*m.kW))
       elseif m.__typename == 'nn.Linear' then
          m:reset(method(m.weight:size(), m.weight:size()))
       elseif m.__typename == 'nn.TemporalConvolution' then
          m:reset(method(m.weight:size(), m.weight:size()))
       end

       if m.bias then
          m.bias:zero()
       end
    end
    return net
 end

 return w_init

Method 1

Epoch: 1 Current loss: 0.616950; validation set accu: 0.920900
Epoch: 2 Current loss: 0.228665; validation set accu: 0.942400
Epoch: 3 Current loss: 0.168047; validation set accu: 0.957900
Epoch: 4 Current loss: 0.134796; validation set accu: 0.961800
Epoch: 5 Current loss: 0.113071; validation set accu: 0.966200
Epoch: 6 Current loss: 0.098782; validation set accu: 0.968800
Epoch: 7 Current loss: 0.088252; validation set accu: 0.970000
Epoch: 8 Current loss: 0.080225; validation set accu: 0.971200
Epoch: 9 Current loss: 0.073702; validation set accu: 0.972200
Epoch: 10 Current loss: 0.068171; validation set accu: 0.972400	

method 2
Epoch: 1 Current loss: 0.624633; validation set accu: 0.922200
Epoch: 2 Current loss: 0.238459; validation set accu: 0.945200
Epoch: 3 Current loss: 0.174089; validation set accu: 0.959000
Epoch: 4 Current loss: 0.140234; validation set accu: 0.963800
Epoch: 5 Current loss: 0.116498; validation set accu: 0.968000
Epoch: 6 Current loss: 0.101376; validation set accu: 0.968800
Epoch: 7 Current loss: 0.089484; validation set accu: 0.972600
Epoch: 8 Current loss: 0.080812; validation set accu: 0.973000
Epoch: 9 Current loss: 0.073929; validation set accu: 0.975100
Epoch: 10 Current loss: 0.068330; validation set accu: 0.975400	

method 3
Epoch: 1 Current loss: 2.202240; validation set accu: 0.548500
Epoch: 2 Current loss: 2.049710; validation set accu: 0.669300
Epoch: 3 Current loss: 1.993560; validation set accu: 0.728900
Epoch: 4 Current loss: 1.959818; validation set accu: 0.774500
Epoch: 5 Current loss: 1.945992; validation set accu: 0.757600
Epoch: 6 Current loss: 1.930599; validation set accu: 0.809600
Epoch: 7 Current loss: 1.911803; validation set accu: 0.837200
Epoch: 8 Current loss: 1.904754; validation set accu: 0.842100
Epoch: 9 Current loss: 1.903705; validation set accu: 0.846400
Epoch: 10 Current loss: 1.903911; validation set accu: 0.848100	

method 4
Epoch: 1 Current loss: 0.624240; validation set accu: 0.924900
Epoch: 2 Current loss: 0.213469; validation set accu: 0.948500
Epoch: 3 Current loss: 0.156797; validation set accu: 0.959800
Epoch: 4 Current loss: 0.126438; validation set accu: 0.963900
Epoch: 5 Current loss: 0.106664; validation set accu: 0.965900
Epoch: 6 Current loss: 0.094166; validation set accu: 0.967200
Epoch: 7 Current loss: 0.084848; validation set accu: 0.971200
Epoch: 8 Current loss: 0.077244; validation set accu: 0.971800
Epoch: 9 Current loss: 0.071417; validation set accu: 0.973300
Epoch: 10 Current loss: 0.065737; validation set accu: 0.971600	

取消注释
Epoch: 1 Current loss: 2.178319; validation set accu: 0.542200
Epoch: 2 Current loss: 2.031493; validation set accu: 0.648700
Epoch: 3 Current loss: 1.982282; validation set accu: 0.703700
Epoch: 4 Current loss: 1.956709; validation set accu: 0.762700
Epoch: 5 Current loss: 1.927590; validation set accu: 0.808100
Epoch: 6 Current loss: 1.924535; validation set accu: 0.817200
Epoch: 7 Current loss: 1.911364; validation set accu: 0.820100
Epoch: 8 Current loss: 1.898206; validation set accu: 0.855400
Epoch: 9 Current loss: 1.885394; validation set accu: 0.836500
Epoch: 10 Current loss: 1.880787; validation set accu: 0.870200	

method 5

Epoch: 1 Current loss: 0.619814; validation set accu: 0.924300
Epoch: 2 Current loss: 0.232870; validation set accu: 0.948800
Epoch: 3 Current loss: 0.172606; validation set accu: 0.954900
Epoch: 4 Current loss: 0.137763; validation set accu: 0.961800
Epoch: 5 Current loss: 0.116268; validation set accu: 0.967700
Epoch: 6 Current loss: 0.101985; validation set accu: 0.968800
Epoch: 7 Current loss: 0.091154; validation set accu: 0.970900
Epoch: 8 Current loss: 0.083219; validation set accu: 0.972700
Epoch: 9 Current loss: 0.074921; validation set accu: 0.972800
Epoch: 10 Current loss: 0.070208; validation set accu: 0.972800	

取消注释，同时注释上面一行

Epoch: 1 Current loss: 2.161032; validation set accu: 0.497500
Epoch: 2 Current loss: 2.027255; validation set accu: 0.690900
Epoch: 3 Current loss: 1.972939; validation set accu: 0.767600
Epoch: 4 Current loss: 1.940982; validation set accu: 0.766000
Epoch: 5 Current loss: 1.933135; validation set accu: 0.812800
Epoch: 6 Current loss: 1.913039; validation set accu: 0.799300
Epoch: 7 Current loss: 1.896871; validation set accu: 0.848800
Epoch: 8 Current loss: 1.899655; validation set accu: 0.854400
Epoch: 9 Current loss: 1.889465; validation set accu: 0.845700
Epoch: 10 Current loss: 1.878703; validation set accu: 0.846400	

170301更新结束

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