1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
|
--[[
This file implements Batch Normalization as described in the paper:
"Batch Normalization: Accelerating Deep Network Training
by Reducing Internal Covariate Shift"
by Sergey Ioffe, Christian Szegedy
This implementation is useful for inputs NOT coming from convolution layers.
For Convolution layers, see SpatialBatchNormalization.lua
The operation implemented is:
y = ( x - mean(x) )
-------------------- * gamma + beta
standard-deviation(x)
where gamma and beta are learnable parameters.
The learning of gamma and beta is optional.
Usage:
with learnable parameters: nn.BatchNormalization(N [, eps] [,momentum])
where N = dimensionality of input
without learnable parameters: nn.BatchNormalization(0 [, eps] [,momentum])
eps is a small value added to the standard-deviation to avoid divide-by-zero.
Defaults to 1e-5
In training time, this layer keeps a running estimate of it's computed mean and std.
The running sum is kept with a default momentup of 0.1 (unless over-ridden)
In test time, this running mean/std is used to normalize.
]]--
local BN,parent = torch.class('nn.BatchNormalization', 'nn.Module')
function BN:__init(nOutput, eps, momentum, affine)
parent.__init(self)
assert(nOutput and type(nOutput) == 'number',
'Missing argument #1: dimensionality of input. ')
assert(nOutput ~= 0, 'To set affine=false call BatchNormalization'
.. '(nOutput, eps, momentum, false) ')
if affine ~= nil then
assert(type(affine) == 'boolean', 'affine has to be true/false')
self.affine = affine
else
self.affine = true
end
self.eps = eps or 1e-5
self.train = true
self.momentum = momentum or 0.1
self.running_mean = torch.zeros(nOutput)
self.running_std = torch.ones(nOutput)
if self.affine then
self.weight = torch.Tensor(nOutput)
self.bias = torch.Tensor(nOutput)
self.gradWeight = torch.Tensor(nOutput)
self.gradBias = torch.Tensor(nOutput)
self:reset()
end
end
function BN:reset()
self.weight:uniform()
self.bias:zero()
end
function BN:updateOutput(input)
assert(input:dim() == 2, 'only mini-batch supported (2D tensor), got '
.. input:dim() .. 'D tensor instead')
local nBatch = input:size(1)
-- buffers that are reused
self.buffer = self.buffer or input.new()
self.buffer2 = self.buffer2 or input.new()
self.centered = self.centered or input.new()
self.centered:resizeAs(input)
self.std = self.std or input.new()
self.normalized = self.normalized or input.new()
self.normalized:resizeAs(input)
self.output:resizeAs(input)
self.gradInput:resizeAs(input)
if self.train == false then
self.output:copy(input)
self.buffer:repeatTensor(self.running_mean, nBatch, 1)
self.output:add(-1, self.buffer)
self.buffer:repeatTensor(self.running_std, nBatch, 1)
self.output:cmul(self.buffer)
else -- training mode
-- calculate mean over mini-batch
self.buffer:mean(input, 1) -- E(x) = expectation of x.
self.running_mean:mul(1 - self.momentum):add(self.momentum, self.buffer) -- add to running mean
self.buffer:repeatTensor(self.buffer, nBatch, 1)
-- subtract mean
self.centered:add(input, -1, self.buffer) -- x - E(x)
-- calculate standard deviation over mini-batch
self.buffer:copy(self.centered):cmul(self.buffer) -- [x - E(x)]^2
-- 1 / E([x - E(x)]^2)
self.std:mean(self.buffer, 1):add(self.eps):sqrt():pow(-1)
self.running_std:mul(1 - self.momentum):add(self.momentum, self.std) -- add to running stdv
self.buffer:repeatTensor(self.std, nBatch, 1)
-- divide standard-deviation + eps
self.output:cmul(self.centered, self.buffer)
self.normalized:copy(self.output)
end
if self.affine then
-- multiply with gamma and add beta
self.buffer:repeatTensor(self.weight, nBatch, 1)
self.output:cmul(self.buffer)
self.buffer:repeatTensor(self.bias, nBatch, 1)
self.output:add(self.buffer)
end
return self.output
end
function BN:updateGradInput(input, gradOutput)
assert(input:dim() == 2, 'only mini-batch supported')
assert(gradOutput:dim() == 2, 'only mini-batch supported')
assert(self.train == true, 'should be in training mode when self.train is true')
local nBatch = input:size(1)
self.gradInput:cmul(self.centered, gradOutput)
self.buffer:mean(self.gradInput, 1)
self.gradInput:repeatTensor(self.buffer, nBatch, 1)
self.gradInput:cmul(self.centered):mul(-1)
self.buffer:repeatTensor(self.std, nBatch, 1)
self.gradInput:cmul(self.buffer):cmul(self.buffer)
self.buffer:mean(gradOutput, 1)
self.buffer:repeatTensor(self.buffer, nBatch, 1)
self.gradInput:add(gradOutput):add(-1, self.buffer)
self.buffer:repeatTensor(self.std, nBatch, 1)
self.gradInput:cmul(self.buffer)
if self.affine then
self.buffer:repeatTensor(self.weight, nBatch, 1)
self.gradInput:cmul(self.buffer)
end
return self.gradInput
end
function BN:accGradParameters(input, gradOutput, scale)
if self.affine then
scale = scale or 1.0
self.buffer2:resizeAs(self.normalized):copy(self.normalized)
self.buffer2:cmul(gradOutput)
self.buffer:sum(self.buffer2, 1) -- sum over mini-batch
self.gradWeight:add(scale, self.buffer)
self.buffer:sum(gradOutput, 1) -- sum over mini-batch
self.gradBias:add(scale, self.buffer)
end
end
|
