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metriclinear.lua
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metriclinear.lua
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require 'nn'
require 'mathx'
dofile 'metric.lua'
-- Priors. A prior is a function pr such that calling pr(theta) on a tensor theta
-- returns a pair ln pr(theta), d/dtheta (ln pr(theta))
function gaussianPrior(mean, variance)
local function theprior(theta)
local logPrior=(theta-mean):norm()
logPrior=-logPrior*logPrior/(2*variance)-.5*math.log(2.*math.pi*variance)*theta:nElement()
local gradlogPrior=-(theta-mean)/variance
return logPrior,gradlogPrior
end
return theprior
end
function conjugateGaussianPrior(alpha, beta, mean)
local mean=mean or 0
local beta=beta or .5
local alpha = alpha or .5
local function theprior(theta)
local S=(theta-mean):norm()
S=S*S
local n=theta:nElement()
logPrior=math.lgamma(.5*n+alpha)-math.lgamma(alpha)-(.5*n+alpha)*math.log(beta+.5*S)+alpha*math.log(beta)-.5*n*math.log(2.*math.pi)
gradlogPrior=((.5*n+alpha)/(beta+.5*S))*(mean-theta)
return logPrior,gradlogPrior
end
return theprior
end
local MetricLinear, parent = torch.class('nn.MetricLinear', 'nn.Linear')
function MetricLinear:__init(inputSize, outputSize, opt)
parent.__init(self,inputSize, outputSize)
if opt.metric == "dop" then
self.metric = DMetric(inputSize, outputSize, opt)
elseif opt.metric == "qdop" then
self.metric = QDMetric(inputSize, outputSize, opt)
elseif opt.metric == "rmsprop" then
self.metric = RMSMetric(inputSize, outputSize, opt)
elseif opt.metric == "eucl" then
self.metric = EuclMetric(inputSize, outputSize, opt)
else
print("Metric " .. opt.metric .. " not found!")
do return end
end
self.datasetSize = opt.datasetSize or 50000
self.langevin = opt.langevin or false
if self.langevin then
local prior = opt.prior or 'gaussian'
if prior == 'gaussian' then
print('gaussian')
local priorMu = opt.priorMu or 0.0
local priorSigma2 = opt.priorSigma2 or 0.0
if opt.priorSigma2 < 1e-12 then
self.priorSigma2 = 1./inputSize
end
self.prior = gaussianPrior(priorMu, priorSigma2)
self.priorBias = gaussianPrior(0,1)
elseif prior == 'conjGaussian' then
print('conjGaussian')
local priorMean = opt.priorMean or 0
local priotBeta = opt.priorBeta or .5
local priorAlpha = opt.priorAlpha or .5
self.prior = conjugateGaussianPrior(priorMean, priorBeta, priorAlpha)
self.priorBias = conjugateGaussianPrior(priorMean, priorBeta, priorAlpha)
end
end
self.lr = opt.lr or 1
self.n_update = 0
end
function MetricLinear:reset()
stdv = 1./math.sqrt(self.weight:size(2))
self.weight:normal(0, stdv)
self.bias:zero()
return self
end
function MetricLinear:accGradParameters(input, gradOutput)
-- Tensor dimension
-- gradOuput: n_ex x n_out
-- input: n_ex x n_in
local gradWeight = gradOutput:t()*input
local gradBias = torch.sum(gradOutput,1):t()
if self.langevin then
-- local weightPrior = torch.add(self.weight,-1.0*self.priorMu)/self.priorSigma2
-- local biasPrior = torch.add(self.bias,-1.0*self.priorMu)/self.priorSigma2
local _,weightGradPrior = self.prior(self.weight)
local _,biasGradPrior = self.priorBias(self.bias)
gradWeight:add(-1./self.datasetSize, weightGradPrior)
gradBias:add(-1./self.datasetSize, biasGradPrior)
end
self.metric:updateMetric(input, gradOutput)
--self.metric:updateMetric(gradWeight, gradBias)
local rieGradWeight, rieGradBias = self.metric:convertGradient(gradWeight, gradBias)
if self.langevin then
local weight_noise, bias_noise = self.metric:sampleNoise()
self.gradWeight:copy(rieGradWeight:mul(-1.*self.lr):add(math.sqrt(2.*self.lr/self.datasetSize),weight_noise))
self.gradBias:copy(rieGradBias:mul(-1.*self.lr):add(math.sqrt(2.*self.lr/self.datasetSize),bias_noise))
self.n_update = self.n_update + 1
if self.n_update % 10000 == 0 then
self.lr = self.lr / 2
print("Changing learning rate to " .. self.lr)
end
else
self.gradWeight:copy(rieGradWeight)
self.gradBias:copy(rieGradBias)
end
end
-- function MetricLinear:accGradParameters(input, gradOutput)
-- -- Tensor dimension
-- -- gradOuput: n_ex x n_out
-- -- input: n_ex x n_in
-- --local miniSize = input:size(1)
-- local gradWeight = (gradOutput:t()*input)--/miniSize
-- local gradBias = torch.sum(gradOutput,1):t()--/miniSize
-- if self.langevin then
-- local weightPrior = torch.add(self.weight,-1.0*self.priorMu)/(self.datasetSize*self.priorSigma2)
-- local biasPrior = torch.add(self.bias,-1.0*self.priorMu)/(self.datasetSize*self.priorSigma2)
-- gradWeight = gradWeight + weightPrior
-- gradBias = gradBias + biasPrior
-- end
-- self.metric:updateMetric(input, gradOutput)
-- rieGradWeight, rieGradBias = self.metric:convertGradient(gradWeight, gradBias)
-- if self.langevin then
-- local weight_noise, bias_noise = self.metric:sampleNoise()
-- self.gradWeight:copy(self.dt*rieGradWeight - torch.sqrt(2*self.dt/self.datasetSize)*weight_noise)
-- self.gradBias:copy(self.dt*rieGradBias - torch.sqrt(2*self.dt/self.datasetSize)*bias_noise)
-- else
-- -- Update parameters
-- self.gradWeight:copy(self.dt*rieGradWeight)
-- self.gradBias:copy(self.dt*rieGradBias)
-- end
-- -- self.n_update = self.n_update + 1
-- -- if self.n_update % 500 == 0 then
-- -- self.dt = self.dt / 2
-- -- end
-- end
-- function MetricLinear:accGradParameters(input, gradOutput)
-- -- Tensor dimension
-- -- gradOuput: n_ex x n_out
-- -- input: n_ex x n_in
-- local miniSize = input:size(1)
-- -- Compute the gradient of loss and incorporate the gradient of prior
-- local gradWeight = (gradOutput:t()*input)/miniSize
-- local gradBias = torch.sum(gradOutput,1):t()/miniSize
-- if self.langevin then
-- gradWeight = gradWeight + torch.add(self.weight,-1.0*self.priorMu)/(self.datasetSize*self.priorSigma2)
-- gradBias = gradBias + torch.add(self.bias,-1.0*self.priorMu)/(self.datasetSize*self.priorSigma2)
-- end
-- self.metric:updateMetric(input, gradOutput)
-- rieGradWeight, rieGradBias = self.metric:convertGradient(gradWeight, gradBias)
-- if self.langevin then
-- -- Sample preconditioned noise
-- local weight_noise, bias_noise = self.metric:sampleNoise()
-- -- Update parameters
-- self.gradWeight:copy(self.dt*rieGradWeight - torch.sqrt(2*self.dt/self.datasetSize)*weight_noise)
-- self.gradBias:copy(self.dt*rieGradBias - torch.sqrt(2*self.dt/self.datasetSize)*bias_noise)
-- else
-- -- Update parameters
-- self.gradWeight:copy(self.dt*rieGradWeight)
-- self.gradBias:copy(self.dt*rieGradBias)
-- end
-- end
-- --th train.lua -gradient qdlangevin -numReg 1e-8 -dt 0.0001 -gamma 0.01 -n_hidden 10 -priorSigma2 1
-- --th train.lua -gradient qdlangevin -numReg 1e-8 -dt 0.0001 -gamma 0.01 -n_hidden 10 -priorSigma2 10 works better
-- function QDLangevinLayer:accGradParameters(input, gradOutput)
-- -- Tensor dimension
-- -- gradOuput: n_ex x n_out
-- -- input: n_ex x n_in
-- local miniSize = input:size(1)
-- -- Compute the gradient of loss and incorporate the gradient of prior
-- local gradWeight = (gradOutput:t()*input)
-- + miniSize*torch.add(self.weight,-1.0*self.priorMu)/(self.datasetSize*self.priorSigma2)
-- local gradBias = torch.sum(gradOutput,1):t()
-- + miniSize*torch.add(self.bias,-1.0*self.priorMu)/(self.datasetSize*self.priorSigma2)
-- -- Update preconditioner C
-- local gradOutputSqT = torch.pow(gradOutput,2):t() -- TODO: In-place ???
-- if self.initMetric then
-- self.Mii = gradOutputSqT * torch.pow(input,2)
-- self.M0i = gradOutputSqT * input
-- self.M00:mv(gradOutputSqT,self.addBuffer)
-- self.initMetric = false
-- else
-- self.Mii:addmm(1.-self.gamma,self.gamma,gradOutputSqT,torch.pow(input,2))
-- self.M0i:addmm(1.-self.gamma,self.gamma,gradOutputSqT,input)
-- self.M00:addmv(1.-self.gamma,self.gamma,gradOutputSqT,self.addBuffer)
-- end
-- local numerator = torch.add(torch.cmul(gradWeight,self.M00:view(-1,1):expandAs(gradWeight)),
-- -1.0, torch.cmul(self.M0i,gradBias:view(-1,1):expandAs(self.M0i)))
-- local denominator = torch.add(torch.cmul(self.Mii,self.M00:view(-1,1):expandAs(self.Mii)),
-- -1.0,torch.pow(self.M0i,2)):clamp(self.numReg,1e25)
-- -- Apply preconditioner
-- local preGradWeight = numerator:cdiv(denominator)
-- local temp = torch.cmul(self.M0i,self.gradWeight):sum(2)
-- local preGradBias = gradBias:add(-1.,temp):cdiv(self.M00:clamp(self.numReg,1e25))
-- -- Sample preconditioned noise
-- local weight_noise, bias_noise = self:sampleNoise3()
-- -- Update parameters
-- self.gradWeight:copy(self.dt*preGradWeight - torch.sqrt(2*self.dt/self.datasetSize)*weight_noise)
-- self.gradBias:copy(self.dt*preGradBias - torch.sqrt(2*self.dt/self.datasetSize)*bias_noise)
-- end
-- th train.lua -gradient qdlangevin -numReg 1e-8 -dt 0.0001 -gamma 0.01 -n_hidden 10 -priorSigma2 1
-- function QDLangevinLayer:accGradParameters(input, gradOutput)
-- -- print(self.numReg)
-- -- print(self.dt)
-- -- print(self.gamma)
-- -- Tensor dimension
-- -- gradOuput: n_ex x n_out
-- -- input: n_ex x n_in
-- local miniSize = input:size(1)
-- -- Compute the gradient of loss and incorporate the gradient of prior
-- local gradWeight = (gradOutput:t()*input)
-- local gradBias = torch.sum(gradOutput,1):t()
-- -- Update preconditioner C
-- local gradOutputSqT = torch.pow(gradOutput,2):t() -- TODO: In-place ???
-- if self.initMetric then
-- self.Mii = gradOutputSqT * torch.pow(input,2)
-- self.M0i = gradOutputSqT * input
-- self.M00:mv(gradOutputSqT,self.addBuffer)
-- self.initMetric = false
-- else
-- self.Mii:addmm(1.-self.gamma,self.gamma,gradOutputSqT,torch.pow(input,2))
-- self.M0i:addmm(1.-self.gamma,self.gamma,gradOutputSqT,input)
-- self.M00:addmv(1.-self.gamma,self.gamma,gradOutputSqT,self.addBuffer)
-- end
-- local numerator = torch.add(torch.cmul(gradWeight,self.M00:view(-1,1):expandAs(gradWeight)),
-- -1.0, torch.cmul(self.M0i,gradBias:view(-1,1):expandAs(self.M0i)))
-- local denominator = torch.add(torch.cmul(self.Mii,self.M00:view(-1,1):expandAs(self.Mii)),
-- -1.0,torch.pow(self.M0i,2)):clamp(self.numReg,1e25)
-- -- Apply preconditioner
-- -- Why do I sum: probably to keep the semantic of Linear...???
-- local preGradWeight = numerator:cdiv(denominator)
-- local temp = torch.cmul(self.M0i,self.gradWeight):sum(2)
-- local preGradBias = gradBias:add(-1.,temp):cdiv(self.M00:clamp(self.numReg,1e25))
-- self.gradWeight:copy(self.dt*preGradWeight)
-- self.gradBias:copy(self.dt*preGradBias)
-- end
-- local function sampleNoise(self)
-- A00 = torch.Tensor(self.bias:size())
-- A0i = torch.Tensor(self.weight:size())
-- Aii = torch.Tensor(self.weight:size())
-- -- Invert metric (verify the iteration order)
-- print(self.weight:size(2))
-- for j=1,self.weight:size(2) do
-- A00[j] = 1./torch.sqrt(self.M00[j])
-- for i= 1,self.weight:size(1) do
-- A0i_inv = A00[j] * self.M0i[i][j]
-- Aii[i][j] = 1./torch.sqrt(self.Mii[i][j] - A0i_inv*A0i_inv)
-- A0i[i][j] = -A00[j] * Aii[i][j] * A0i_inv
-- end
-- end
-- -- void VIQDOPLayer::updateInvMetric(){
-- -- for(unsigned j = 0; j < A0i_.cols(); j++){
-- -- A00_(j) = 1./sqrt(VIM00_(j));
-- -- for(unsigned i = 0; i < A0i_.rows(); i++){
-- -- double A0i_inv = A00_(j) * VIM0i_(i,j);
-- -- Aii_(i,j) = 1./sqrt(VIMii_(i,j) - A0i_inv*A0i_inv);
-- -- A0i_(i,j) = -A00_(j) * Aii_(i,j) * A0i_inv;
-- -- }
-- -- }
-- -- }
-- -- Sample noise
-- weight_noise = torch.Tensor(self.weight:size())
-- bias_noise = torch.Tensor(self.bias:size())
-- for j =1,self.weight:size(2) do
-- v = torch.randn(self.weight:size(1)+1,1)
-- bias_noise[j] = A00[j]/torch.sqrt(self.datasetSize) * v[1]
-- for i=1,self.weight:size(1) do
-- weight_noise[i][j] = Aii[i][j]/torch.sqrt(self.datasetSize) * v[i+1]
-- bias_noise[j] = bias_noise[j] + A0i[i][j]/sqrt(self.datasetSize) * v[i+1]
-- end
-- end
-- weight_noise = torch.mul(weight_noise,torch.sqrt(2.0*self.dt))
-- bias_noise = torch.mul(bias_noise,torch.sqrt(2.0*self.dt))
-- -- for(unsigned j = 0; j < W_.cols(); j++){
-- -- MyVector v(W_.rows()+1);
-- -- param_sampler_->sampleStdNormal(v);
-- -- B_(j) = Bmu_(j) + (A00_(j)/sqrt(n_training_))*v(0);
-- -- for(unsigned i = 0; i < W_.rows(); i++){
-- -- W_(i,j) = Wmu_(i,j) + (Aii_(i,j)/sqrt(n_training_)) * v(i+1);
-- -- B_(j) += (A0i_(i,j)/sqrt(n_training_)) * v(i+1);
-- -- }
-- -- }
-- return weight_noise, bias_noise
-- end
-- function QDLangevinLayer:sampleNoise2()
-- A00 = torch.Tensor(self.bias:size())
-- A0i = torch.Tensor(self.weight:size())
-- Aii = torch.Tensor(self.weight:size())
-- -- Invert metric (verify the iteration order)
-- for j=1,self.weight:size(1) do
-- A00[j] = 1./torch.sqrt(self.M00[j])
-- for i= 1,self.weight:size(2) do
-- A0i_inv = A00[j] * self.M0i[j][i]
-- Aii[j][i] = 1./torch.sqrt(self.Mii[j][i] - A0i_inv*A0i_inv)
-- A0i[j][i] = -A00[j] * Aii[j][i] * A0i_inv
-- end
-- end
-- -- Sample noise
-- weight_noise = torch.Tensor(self.weight:size())
-- bias_noise = torch.Tensor(self.bias:size())
-- for j =1,self.weight:size(1) do
-- v = torch.randn(self.weight:size(2)+1,1)
-- bias_noise[j] = A00[j]/torch.sqrt(self.datasetSize) * v[1]
-- for i=1,self.weight:size(2) do
-- weight_noise[j][i] = Aii[j][i]/torch.sqrt(self.datasetSize) * v[i+1]
-- bias_noise[j] = bias_noise[j] + A0i[j][i]/torch.sqrt(self.datasetSize) * v[i+1]
-- end
-- end
-- return weight_noise, bias_noise
-- end
-- function QDLangevinLayer:sampleNoise2()
-- A00 = torch.Tensor(self.bias:size())
-- A0i = torch.Tensor(self.weight:size())
-- Aii = torch.Tensor(self.weight:size())
-- -- Invert metric (verify the iteration order)
-- for j=1,self.weight:size(1) do
-- A00[j] = 1./torch.sqrt(self.M00[j])
-- for i= 1,self.weight:size(2) do
-- A0i_inv = A00[j] * self.M0i[j][i]
-- Aii[j][i] = 1./torch.sqrt(self.Mii[j][i] - A0i_inv*A0i_inv)
-- A0i[j][i] = -A00[j] * Aii[j][i] * A0i_inv
-- end
-- end
-- -- Sample noise
-- weight_noise = torch.Tensor(self.weight:size())
-- bias_noise = torch.Tensor(self.bias:size())
-- for j =1,self.weight:size(1) do
-- v = torch.randn(self.weight:size(2)+1,1)
-- bias_noise[j] = A00[j]/torch.sqrt(self.datasetSize) * v[1]
-- for i=1,self.weight:size(2) do
-- weight_noise[j][i] = Aii[j][i]/torch.sqrt(self.datasetSize) * v[i+1]
-- bias_noise[j] = bias_noise[j] + A0i[j][i]/torch.sqrt(self.datasetSize) * v[i+1]
-- end
-- end
-- return weight_noise, bias_noise
-- end
-- function QDLangevinLayer:sampleNoise3()
-- -- Invert metric
-- local A00 = torch.rsqrt(self.M00)
-- local A0i_inv = torch.cmul(A00:view(-1,1):expandAs(self.M0i),self.M0i)
-- local Aii = torch.rsqrt(self.Mii-torch.pow(A0i_inv,2))
-- local A0i = torch.cmul(torch.cmul(torch.mul(A00,-1):view(-1,1):expandAs(Aii),Aii),A0i_inv)
-- -- for j=1,self.weight:size(1) do
-- -- A00[j] = 1./torch.sqrt(self.M00[j])
-- -- for i= 1,self.weight:size(2) do
-- -- A0i_inv = A00[j] * self.M0i[j][i]
-- -- Aii[j][i] = 1./torch.sqrt(self.Mii[j][i] - A0i_inv*A0i_inv)
-- -- A0i[j][i] = -A00[j] * Aii[j][i] * A0i_inv
-- -- end
-- -- end
-- -- Sample noise
-- v_bias = torch.randn(self.bias:size())
-- v_weight = torch.randn(self.weight:size())
-- weight_noise = Aii:mul(1./torch.sqrt(self.datasetSize)):cmul(v_weight)
-- bias_noise = torch.sum(A0i:mul(1./torch.sqrt(self.datasetSize)):cmul(v_weight),2)
-- + torch.mul(A00, 1./torch.sqrt(self.datasetSize)):cmul(v_bias)
-- -- weight_noise = torch.cmul(torch.mul(Aii, 1./torch.sqrt(self.datasetSize)),v_weight)
-- -- bias_noise = torch.sum(torch.cmul(torch.mul(A0i, 1./torch.sqrt(self.datasetSize)),v_weight),2)
-- -- + torch.cmul(torch.mul(A00, 1./torch.sqrt(self.datasetSize)),v_bias)
-- -- weight_noise = torch.Tensor(self.weight:size())
-- -- bias_noise = torch.Tensor(self.bias:size())
-- -- for j =1,self.weight:size(1) do
-- -- v = torch.randn(self.weight:size(2)+1,1)
-- -- bias_noise[j] = A00[j]/torch.sqrt(self.datasetSize) * v[1]
-- -- for i=1,self.weight:size(2) do
-- -- weight_noise[j][i] = Aii[j][i]/torch.sqrt(self.datasetSize) * v[i+1]
-- -- bias_noise[j] = bias_noise[j] + A0i[j][i]/torch.sqrt(self.datasetSize) * v[i+1]
-- -- end
-- -- end
-- return weight_noise, bias_noise
-- end
-- function QDLangevinLayer:accGradParameters(input, gradOutput)
-- local gradOutputSqT = torch.pow(gradOutput,2):t()
-- if self.initMetric then
-- self.Mii:mm(gradOutputSqT,torch.pow(input,2))
-- self.M0i:mm(gradOutputSqT,input)
-- self.M00:mv(gradOutputSqT,self.addBuffer)
-- self.initMetric = false
-- else
-- self.Mii:addmm(1.-self.gamma,self.gamma,gradOutputSqT,torch.pow(input,2))
-- self.M0i:addmm(1.-self.gamma,self.gamma,gradOutputSqT,input)
-- self.M00:addmv(1.-self.gamma,self.gamma,gradOutputSqT,self.addBuffer)
-- end
-- local gradWeight = (self.datasetSize / input:size(1)) * gradOutput:t()*input
-- + torch.add(self.weight,-1.0*self.priorMu)/self.priorSigma2
-- local gradBias = (self.datasetSize / input:size(1))
-- * gradOutput:t()*self.addBuffer
-- + torch.add(self.bias,-1.0*self.priorMu)/self.priorSigma2
-- -- quasi-diagonal metric
-- local numerator = torch.add(torch.cmul(gradWeight,self.M00:view(-1,1):expandAs(gradWeight)),
-- -1.0, torch.cmul(self.M0i,gradBias:view(-1,1):expandAs(self.M0i)))
-- local denominator = torch.add(torch.cmul(self.Mii,self.M00:view(-1,1):expandAs(self.Mii)),
-- -1.0,torch.pow(self.M0i,2)):clamp(self.numReg,1e25)
-- self.gradWeight:add(numerator:cdiv(denominator):div(inputs:size(1)))
-- local temp = torch.cmul(self.M0i,self.gradWeight):sum(2)
-- self.gradBias:add(gradBias:add(-1.,temp):cdiv(self.M00:clamp(self.numReg,1e25)):div(inputs:size(1)))
-- -- QD inverse
-- local secondTermWeight, secondTermBias = self:sampleNoise3()
-- -- local secondTermWeight = torch.mul(torch.Tensor(self.gradWeight:size()):normal(),torch.sqrt(2.0*self.dt))
-- -- secondTermWeight:cdiv(torch.sqrt(self.datasetSize*self.Mii/input:size(1)+self.numReg))
-- self.gradWeight:copy(torch.add(self.dt*gradWeight,secondTermWeight))
-- --self.gradWeight:copy(self.dt*gradWeight)
-- -- local secondTermBias = torch.mul(torch.Tensor(self.gradBias:size()):normal(),torch.sqrt(2.0*self.dt))
-- -- secondTermBias:cdiv(torch.sqrt(self.datasetSize*self.M00/input:size(1)+self.numReg))
-- self.gradBias:copy(torch.add(self.dt*gradBias,secondTermBias))
-- --self.gradBias:copy(self.dt*gradBias)
-- end