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--[[
Probabilistic Criterion for Triplet Siamese Model for learning embedding.
Ref: https://arxiv.org/pdf/1610.00243.pdf
loss = -log( exp(-X) / ( exp(-X) + exp(-Y) ) )
where
X : Distance between similar samples
Y : Distance between dissimilar samples
The loss could be break down to following log expansion
loss = -log( exp(-X) ) - (-log( exp(-X) + exp(-Y) ))
= -log( exp(-X) ) + log( exp(-X) + exp(-Y) )
= -(-X) + log( exp(-X) + exp(-Y) )
= X + log( exp(-X) + exp(-Y) )
Gradients:
dLoss/dX = 1 + 1 / (exp(-X) + exp(-Y)) * -1 * exp(-X)
= 1 - exp(-X) / (exp(-X) + exp(-Y))
dLoss/dY = 0 + 1 / (exp(-X) + exp(-Y)) * -1 * exp(-Y)
= -exp(-Y) / (exp(-X) + exp(-Y))
--]]
local DistanceRatioCriterion, parent = torch.class('nn.DistanceRatioCriterion',
'nn.Criterion')
function DistanceRatioCriterion:__init(sizeAverage)
parent.__init(self)
if sizeAverage ~= nil then
self.sizeAverage = sizeAverage
else
self.sizeAverage = true
end
end
-- Forward
--[[
-- X : Distance between similar samples
-- Y : Distance between dissimilar samples
loss = -log( exp(-X) ) - (-log( exp(-X) + exp(-Y) ))
= -log( exp(-X) ) + log( exp(-X) + exp(-Y) )
= -(-X) + log( exp(-X) + exp(-Y) )
= X + log( exp(-X) + exp(-Y) )
--]]
function DistanceRatioCriterion:updateOutput(input)
assert(#input == 2, "Invalid number of inputs")
local X = input[1]
local Y = input[2]
assert(X:nElement() == Y:nElement(), "Number of distances don't match.")
assert(X:size(1) == Y:size(1), "Invalid distances' size.")
-- Compute exp(-X) and exp(-Y)
self._expMinusX = self._expMinusX or X.new()
self._expMinusY = self._expMinusY or Y.new()
-- Compute ( exp(-X) + exp(-Y) )
self._expMinusX:resizeAs(X):copy(X):mul(-1):exp()
self._expMinusY:resizeAs(Y):copy(Y):mul(-1):exp()
self._sumExpMinusXY = self.sumExpMinusExp or X.new()
self._sumExpMinusXY:resizeAs(self._expMinusX):copy(self._expMinusX)
:add(self._expMinusY)
-- Compute log( exp(-X) + exp(-Y) )
self._logSumExpMinusXY = self._logSumExpMinusXY or self._sumExpMinusXY.new()
self._logSumExpMinusXY:resizeAs(self._sumExpMinusXY)
:copy(self._sumExpMinusXY):log()
-- Compute log( exp(-X) + exp(-Y) )
self.loss = self.loss or self._logSumExpMinusXY.new()
self.loss:resizeAs(X):copy(X):add(self._logSumExpMinusXY)
if self.sizeAverage then
return self.loss:sum()/X:size(1)
else
return self.loss:sum()
end
end
-- Backward
--[[
-- X : Distance between similar samples
-- Y : Distance between dissimilar samples
Gradients:
dLoss/dX = 1 + 1 / (exp(-X) + exp(-Y)) * -1 * exp(-X)
= 1 - exp(-X) / (exp(-X) + exp(-Y))
dLoss/dY = 0 + 1 / (exp(-X) + exp(-Y)) * -1 * exp(-Y)
= -exp(-Y) / (exp(-X) + exp(-Y))
--]]
function DistanceRatioCriterion:updateGradInput(input)
assert(#input == 2, "Invalid number of inputs")
local X = input[1]
local Y = input[2]
assert(X:nElement() == Y:nElement(), "Number of distances don't match.")
assert(X:size(1) == Y:size(1), "Invalid distances' size.")
-- dLoss/dX
-- -exp(-X)
self.dX = self.dX or X.new()
self.dX:resizeAs(self._expMinusX):copy(self._expMinusX):mul(-1)
-- -exp(-X) / (exp(-X) + exp(-Y))
self.dX:cdiv(self._sumExpMinusXY)
-- 1 - exp(-X) / (exp(-X) + exp(-Y))
self.dX:add(1)
-- dLoss/dY
-- -exp(-Y)
self.dY = self.dY or Y.new()
self.dY:resizeAs(self._expMinusY):copy(self._expMinusY):mul(-1)
-- -exp(-Y) / (exp(-X) + exp(-Y))
self.dY:cdiv(self._sumExpMinusXY)
if self.sizeAverage then
self.dX:div(X:size(1))
self.dY:div(X:size(1))
end
return {self.dX, self.dY}
end
function DistanceRatioCriterion:type(type, tensorCache)
if type then
self._expMinusX = nil
self._expMinusY = nil
self._sumExpMinusXY = nil
self._logSumExpMinusXY = nil
self.loss = nil
self.dX = nil
self.dY = nil
end
return parent.type(self, type, tensorCache)
end
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