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
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
|
local LBFGS,parent = torch.class('nn.LBFGSOptimization', 'nn.Optimization')
function LBFGS:__init(...)
require 'liblbfgs'
parent.__init(self)
xlua.unpack_class(self, {...},
'LBFGSOptimization', nil,
{arg='module', type='nn.Module', help='a module to train', req=true},
{arg='criterion', type='nn.Criterion', help='a criterion to estimate the error', req=true},
{arg='maxIterations', type='number', help='maximum nb of iterations per pass (0 = no max)', default=0},
{arg='maxLineSearch', type='number', help='maximum nb of steps in line search', default=20},
{arg='sparsity', type='number', help='sparsity coef (Orthantwise C)', default=0},
{arg='parallelize', type='number', help='parallelize onto N cores (experimental!)', default=1},
{arg='verbose', type='number', help='verbose level during training [0-2]', default=0}
)
self.parametersT = nnx.getParameters(self.module)
self.gradParametersT = nnx.getGradParameters(self.module)
lbfgs.verbose = self.verbose
if self.parallelize > 1 then
if not xrequire 'parallel' then
xerror('install parallel for Lua to enable parallel computing (luarocks install parallel)',
'nn.LBFGSOptimization')
end
parallel.setSharedSize(4*1024*1024)
end
end
function LBFGS:forward(inputs, targets, options)
options = options or {}
if self.parallelize > 1 then
return self:forward_mapreduce(inputs, targets, options)
else
return self:forward_sequential(inputs, targets, options)
end
end
function LBFGS:forward_sequential(inputs, targets, options)
-- (1) construct a closure that compute f(inputs) + df/dW
-- after each call to that function:
-- + self.parameters contains the current X vector
-- + self.gradParameters contains the estimated dF/dX vector
-- + self.output contains the estimated (average) F(X)
lbfgs.evaluate
= function()
-- set parameters from current state
self:unflatten(self.parametersT, self.gradParametersT)
-- reset gradients
self.module:zeroGradParameters()
-- f is the average of all criterions
self.output = 0
-- given all inputs, evaluate gradients
for i = 1,#inputs do
-- user hook
if self.prehook then
self.prehook(self, {inputs[i], targets[i], options[i]})
end
-- estimate f
local output = self.module:forward(inputs[i])
local err = self.criterion:forward(output, targets[i])
self.output = self.output + err
-- estimate df/dW
local df_do = self.criterion:backward(output, targets[i])
self.module:backward(inputs[i], df_do)
-- user hook
if self.posthook then
self.posthook(self, {inputs[i], targets[i], options[i]})
end
end
-- update state from computed parameters
self:flatten(self.parametersT, self.gradParametersT)
-- normalize gradients
self.gradParameters:div(#inputs)
-- return average f(X)
return self.output/#inputs
end
-- (2) store current parameters/gradParameters
self:flatten(self.parametersT, self.gradParametersT)
-- (3) the magic function: will update the parameter vector
-- according to the l-BFGS method
self.output = lbfgs.run(self.parameters, self.gradParameters,
self.maxIterations, self.maxLineSearch,
self.sparsity)
-- (4) last: read parameters back into the model
self:unflatten(self.parametersT, self.gradParametersT)
-- (5) return current output after optimization
return self.output
end
function LBFGS:forward_mapreduce(inputs, targets, options)
-- parameters
local P = self.parallelize
-- (0a) replicate output and gradParameters
local outputs = {}
local gradParameters = {}
-- (0b) divide input/target batch into N batches
local inputss = {}
local targetss = {}
for t = 1,P do
inputss[t] = {}
targetss[t] = {}
for i = t,#inputs,P do
table.insert(inputss[t], inputs[i])
table.insert(targetss[t], targets[i])
end
end
-- (1) construct a closure that compute f(inputs) + df/dW
-- after each call to that function:
-- + self.parameters contains the current X vector
-- + self.gradParameters contains the estimated dF/dX vector
-- + self.output contains the estimated (average) F(X)
lbfgs.evaluate
= function()
-- reset parallel state
parallel.reset()
-- dispatch N parallel jobs
for t = 1,P do
parallel.run(lbfgs.evaluate_map)
end
-- load parameters into current model
self:unflatten(self.parametersT, self.gradParametersT)
-- transmit data to all jobs
for t = 1,P do
-- transmit all necessary data
parallel.children[t]:send(self.module)
parallel.children[t]:send(self.criterion)
parallel.children[t]:send(inputss[t])
parallel.children[t]:send(targetss[t])
end
-- then wait for all workers to return their trained modules
for t = 1,P do
gradParameters = parallel.children[t]:receive()
outputs[t] = parallel.children[t]:receive()
end
-- and join
parallel.children:join()
-- reduce
return lbfgs.evaluate_reduce()
end
-- (1a) the map part of the evaluation: compute partial gradients
-- in separate threads
lbfgs.evaluate_map = [[
-- require packages
require 'nnx'
-- retrieve module + criterion + mini-batch
module = parallel.parent:receive()
criterion = parallel.parent:receive()
inputs = parallel.parent:receive()
targets = parallel.parent:receive()
-- reset gradients
module:zeroGradParameters()
-- f is the average of all criterions
local output = 0
-- evaluate gradients on inputs for this thread
for i = 1,#inputs do
-- estimate f
local output = module:forward(inputs[i])
local err = criterion:forward(output, targets[i])
output = output + err
-- estimate df/dW
local df_do = criterion:backward(output, targets[i])
module:backward(inputs[i], df_do)
end
-- return partial gradParameters + output
parallel.parent:send( nnx.getGradParameters(module) )
parallel.parent:send(output)
]]
-- (1b) the reduce part of the evaluation: accumulate all
-- partial estimates of the gradients
lbfgs.evaluate_reduce
= function()
-- temp vectors for accumulation
self.gradParametersAcc = self.gradParametersAcc or torch.Tensor()
self.gradParametersAcc:resizeAs(self.gradParameters):zero()
-- update state from computed parameters
for t = 1,P do
self:flatten(self.parametersT, gradParameters)
self.gradParametersAcc:add(self.gradParameters)
end
self.gradParameters:copy(self.gradParametersAcc)
-- normalize gradients
self.gradParameters:div(#inputs)
-- return average f(X)
self.output = 0
for t = 1,P do
self.output = self.output + outputs[t]
end
-- export parameters, again
return self.output/#inputs
end
-- (2) store current parameters/gradParameters
self:flatten(self.parametersT, self.gradParametersT)
-- (3) the magic function: will update the parameter vector
-- according to the l-BFGS method
self.output = lbfgs.run(self.parameters, self.gradParameters,
self.maxIterations, self.maxLineSearch,
self.sparsity)
-- (4) last: read parameters back into the main (not parrallel) model
self:unflatten(self.parametersT, self.gradParametersT)
-- (5) return current output after optimization
return self.output
end
|
