（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 = 50000,
    data = fullset.data[{{1,50000}}]:double(),
    label = fullset.label[{{1,50000}}]
}
trainset.data = trainset.data - trainset.data:mean()
trainset.data = trainset.data:cuda()
trainset.label = trainset.label:cuda()

local validationset = {
    size = 10000,
    data = fullset.data[{{50001,60000}}]:double(),
    label = fullset.label[{{50001,60000}}]
}
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(1, 28, 28))
model:add(nn.MulConstant(1/256.0*3.2))
model:add(nn.SpatialConvolutionMM(1, 20, 5, 5, 1, 1, 0, 0))
model:add(nn.SpatialMaxPooling(2, 2 , 2, 2, 0, 0))
model:add(nn.SpatialConvolutionMM(20, 50, 5, 5, 1, 1, 0, 0))
model:add(nn.SpatialMaxPooling(2, 2 , 2, 2, 0, 0))
model:add(nn.Reshape(4*4*50))
model:add(nn.Linear(4*4*50, 500))
model:add(nn.ReLU())
model:add(nn.Linear(500, 10))
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 = 0
    local count = 0
    local shuffle = torch.randperm(trainset.size)
    batchSize = batchSize or 200
    for t = 0, trainset.size-1, batchSize do
        -- setup inputs and targets for batch iteration
        local size = math.min(t + batchSize, trainset.size) - t
        local inputs = torch.Tensor(size, 28, 28):cuda()
        local targets = torch.Tensor(size):cuda()
        for i = 1, size do
            inputs[i] = trainset.data[shuffle[i+t]]
            targets[i] = trainset.label[shuffle[i+t]] + 1
        end

        local feval = function(x_new)
            local miniBatchSize = 20
            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 = 0
            local gradInput = torch.Tensor(batchSize, 10):zero():cuda()

            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}}])
                gradInput[{{idx, idx + miniBatchSize - 1}}]:copy(criterion:backward(outputs, targets[{{idx, idx + miniBatchSize - 1}}]))
            end

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

    return current_loss / count   -- normalize loss
end

local eval = function(dataset, batchSize)
    local count = 0
    batchSize = batchSize or 200

    for i = 1, dataset.size, batchSize do
        local size = math.min(i + batchSize - 1, dataset.size) - i
        local inputs = dataset.data[{{i,i+size-1}}]:cuda()
        local targets = dataset.label[{{i,i+size-1}}]
        local outputs = model:forward(inputs)
        local _, indices = torch.max(outputs, 2)
        indices:add(-1)
        indices = indices:cuda()
        local guessed_right = indices:eq(targets):sum()
        count = count + guessed_right
    end

    return count / dataset.size
end


local max_iters = 50
local last_accuracy = 0
local decreasing = 0
local threshold = 1 -- how many deacreasing epochs we allow
for i = 1,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 + 1
    else
        decreasing = 0
    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(1/(3*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(2/(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(1/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(4/(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 = 1, #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*1*1, m.nOutputPlane*1*1))
      elseif m.__typename == 'nn.VerticalConvolution' then
         m:reset(method(1*m.kH*m.kW, 1*m.kH*m.kW))
      elseif m.__typename == 'nn.HorizontalConvolution' then
         m:reset(method(1*m.kH*m.kW, 1*m.kH*m.kW))
      elseif m.__typename == 'nn.Linear' then
         m:reset(method(m.weight:size(2), m.weight:size(1)))
      elseif m.__typename == 'nn.TemporalConvolution' then
         m:reset(method(m.weight:size(2), m.weight:size(1)))            
      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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