annotate doc/v2_planning/layer_RP.txt @ 1526:5804e44d7a1b

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author Frederic Bastien <nouiz@nouiz.org>
date Fri, 09 Nov 2012 16:58:17 -0500
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1 ===============
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2 Layer committee
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3 ===============
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4
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5 Members : RP, XG, AB, DWF
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6
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7 Proposal (RP)
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8 =============
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9
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10 You construct your neural network by constructing a graph of connections
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11 between "layers" starting from data. While you construct the graph,
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12 different theano formulas are put together to construct your model.
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13
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14 The idea would be that you need to describe exactly what you would draw
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15 on the board if you are asked to draw the architecture. This would be of
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16 course optional ( you will get macros that will return this graph
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17 automatically for a well defined case). Things that are not neural networks,
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18 and you wouldn't have any structure to draw are just a box. For example a
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19 SVM, or PCA. This in case you want to connect their output to your network.
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20
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21 Hard details are not set yet, but all members of the committee agreed
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22 that this sound as a good idea.
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24
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25 Example Code (RP):
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26 ------------------
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28 # Assume you have the dataset as train_x, train_y, valid_x, valid_y, test_x, test_y
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30 h1 = sigmoid(dotW_b(train_x, n = 300))
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31 rbm1 = CDk( h1, train_x, k=5, sampler = binomial, cost = pseudolikelihood)
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34 h2 = sigmoid(dotW_b(h1, n = 300))
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35 rbm2 = CDk( h2, h1, k=5, sampler = binomial, cost= pseudolikelihood)
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36
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37 out = sigmoid( dotW_b(h2, n= 10))
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38
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39 train_err = cross_entropy( out, train_y)
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40
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41 grads = grad( train_err, err.parameters() )
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42 learner = SGD( err, err.parameters(), grads)
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44 valid_err = train_err.replace({ train_x : valid_x, train_y : valid_y})
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45 test_err = train_err.replace({ train_x : test_x , train_y : test_y})
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48
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49 Global observations :
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50 ---------------------
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51
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52 1) Your graph can have multiple terminal nodes; in this case rbm1,
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53 rbm2 and learner, valid_err, test_err are all end nodes of the graph;
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54
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55 2) Any node is an "iterator", when you would call out.next() you would get
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56 the next prediction; when you call err.next() you will get next error
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57 ( on the batch given by the data.next() ).
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58
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59 3) Replace can replace any subgraph or subgraphs with other
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60 subgraphs/subgraph as long as : there are the same number of input units
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61 and output units ( there is a 1 to 1 maping from those). I see replacing
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62 subgraphs as looping over the list of subgraphs to replace and call replace
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63 on which nothing fancier. Since nodes in my view produce the same interface
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64 (execpt parameter nodes and hyper-parameter nodes) this constraint is not
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65 hard to respect, so is up to the user to do a replace that makes sense.
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66
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67 4) You can have MACROS or SUBROUTINE that already give you the graph for
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68 known components ( in my view the CDk is such a macro, but simpler
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69 examples will be vanilla versions of MLP, DAA, DBN, LOGREG). After
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70 Guillaume pointed out a real shortcomming of the approach I've modified
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71 a bit what you get from a macro .. look below.
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72
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73 5) Any node has the entire graph ( though arguably you don't use that
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74 graph too much). Running such a node in general will be done by compiling
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75 the Theano expression up to that node( if you don't already have this
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76 function), and using the data object that you get initially. This theano
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77 function is compiled only if you need it. You use the graph only to :
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78 * update the Theano expression in case some part of the subgraph has
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79 changed (hyper-parameter or a replace call)
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80 * collect the list of parameters of the model
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81 * collect the list of hyper-parameters ( my personal view - this
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82 would mostly be useful for a hyper learner .. and not for day to
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83 day stuff, but I think is something easy to provide and we should )
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84 * collect constraints on parameters ( I believe they can be represented
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85 in the graph as dependency links to other graphs that compute the
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86 constraints..)
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87
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88 6) Registering parameters and hyper-parameters to the graph is the job of
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89 the transform and therefore of the user who implemented that
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90 transform; the same for initializing the parameters ( so if we have
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91 different ways to initialize the weight matrix that might be a
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92 hyperparameter with a default value or different transforms; to ease
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93 the number of such transforms you can define a transform on the fly for
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94 simple theano expressions )
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95
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97
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98 Detailed Proposal (RP)
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99 ======================
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100
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101 I would go through a list of scenarios and possible issues :
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102
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103 Delayed or feature values
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104 -------------------------
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105
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106
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107 This is can be dropped if people think is not useful.
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108
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109 Sometimes you might want future values of some nodes. For example you might
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110 be interested in :
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111
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112 y(t) = x(t) - x(t-1)
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113
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114 You can get that by having a "delayed" version of a node. A delayed version
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115 a node x is obtained by calling x.t(k) which will give you a node that has
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116 the value x(t+k). k can be positive or negative.
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117 In my view this can be done as follows :
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118 - a node is a class that points to :
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119 * a data object that feeds data
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120 * a theano expression up to that point
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121 * the entire graph that describes the model ( not Theano graph !!!)
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122 The only thing you need to do is to change the data object to reflect the
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123 delay ( we might need to be able to pad it with 0?). You need also to create
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124 a copy of the theano expression ( those are "new nodes" ) in the sense that
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125 the starting theano tensors are different since they point to different data.
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126
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127
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128
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129 Non-theano transformation ( or function or whatever)
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130 ----------------------------------------------------
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131
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132 Maybe you want to do something in the middle of your graph that is not Theano
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133 supported. Let say you have a function f which you can not write in Theano.
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134 You want to do something like
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135
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136
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137 W1*f( W2*data + b)
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138
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139 I think we can support that by doing the following :
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140 each node has a:
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141 * a data object that feeds data
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142 * a theano expression up to that point
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143 * the entire graph that describes the model
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144
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145 Let x1 = W2*data + b
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146 up to here everything is fine ( we have a theano expression )
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147 dot(W2, tensor) + b,
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148 where tensor is provided by the data object ( plus a dict of givens
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149 and whatever else you need to compile the function)
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150
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151 When you apply f, what you do you create a node that is exactly like the
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152 data object in the sense that it provides a new tensor and a new dict of
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153 givens
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154
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155 so x2 = W1*f( W2*data+b)
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156 will actually point to the expression
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157 dot(W1, tensor)
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158 and to the data node f(W2*data+b)
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159
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160 what this means is that you basically compile two theano functions t1 and t2
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161 and evaluate t2(f(t1(data))). So everytime you have a non theano operation you
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162 break the theano expression and start a new one.
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163
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164 What you loose :
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165 - there is no optimization or anything between t1,t2 and f ( we don't
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166 support that)
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167 - if you are running things on GPU, after t1, data will be copied on CPU and
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168 then probably again on GPU - so it doesn't make sense anymore
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169
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170
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171
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172 Recurrent Things
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173 ----------------
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174
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175 I think that you can write a recurrent operation by first defining a
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176 graph ( the recrrent relation ):
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177
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178 y_tm1 = recurrent_layer(init = zeros(50))
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179 x_t = slice(x, t=0)
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180 y = loop( dotW_b(y_tm1,50) + x_t, steps = 20)
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181
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182 This would basically give all the information you need to add a scan op
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183 to your theano expression of the result node y, it is just a different way
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184 of writing things .. which I think is more intuitive.
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185
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186 You create your primitives which are either a recurrent_layer that should
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187 have a initial value, or a slice of some other node ( a time slice that is).
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188 A tims slice is a special kind of node, which we should try to force people
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189 not to use outside of a loop. If you use it though you have some default
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190 behaviour like for example it behaves exactly like a delayed node.
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191 You call loop giving a expression that starts from those primitives and
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192 ta da, you have your recurrent expression in the graph.
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193
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194 Similarly you can have foldl or map or anything else.
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195
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196 You would use this instead of writing scan especially if the formulas are
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197 more complicated and you want to automatically collect parameters,
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198 hyper-parameters and so on. You could also just use the scan op and
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199 using a general apply command if you like that more.
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200
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201 Optimizer
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202 ---------
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203
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204 Personally I would respect the findings of the optimization committee,
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205 and have the SGD to require a Node that produces some error ( which can
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206 be omitted) and the parameter nodes and nodes that compute gradients for
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207 those paramters. For this I would also have the grad function which would
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208 actually only call T.grad.
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209
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210 If you have non-theano thing in the middle? I don't have any smart
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211 solution besides ignoring any parameter that it is below the first
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212 non-theano node and throw a warning.
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213
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214 Learner
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215 -------
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216
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217 In my case I would not have a predict() and eval() method of the learner,
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218 but just a eval(). If you want the predictions you should use the
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219 corresponding node ( before applying the error measure ). This was
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220 for example **out** in my first example. Note eval() in this case is
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221 the same as next(). ( you might just have next for simplicity). The
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222 only semantically important difference is that a call to next has now
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223 side-effects in the sense that the parameters are updated.
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224
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225 Of course we could require learners to be special nodes that also have
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226 a predict output. In that case I'm not sure what the iterating behaiour
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227 of the node should produce.
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228
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229 Granularity
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230 -----------
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231
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232 Guillaume nicely pointed out that this library might be an overkill.
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233 In the sense that you have a dotW_b transform, and then you will need
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234 a dotW_b_sparse transform and so on. Plus way of initializing each param
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235 would result in many more transforms.
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236
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237 I don't have a perfect answer yet, but my argument will go as this :
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238
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239 you would have transforms for the most popular option ( dotW_b) for example.
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240 If you need something else you can always decorate a function that takes
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241 theano arguments and produces theano arguments. The formulas produced by
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242 the formula committee might be a rich source of such function to decorate.
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243 More then decoratting, you can have a general apply transform that does
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244 something like :
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245
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246 apply( lambda x,y,z: x*y+z, inputs = x,
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247 hyperparams = [(name,2)],
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248 params = [(name,theano.shared(..)])
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249 The order of the arguments in lambda is nodes, params, hyper-params or so.
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250 This would apply the theano expression but it will also register the
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251 the parameters. It is like creating a transform on the fly.
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252 You should, or could provide names for parameters, you might need them
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253 later.
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254
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255 I think you can do such that the result of the apply is
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256 pickable, but not the general apply transform. What I mean is that
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257 the output node does not store the lambda expression but some theano
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258 graph (?) and it know which are the input ( and when you can replace
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259 them so that you link this little graph to the rest of the
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260 theano expression. Is just an ugly hack given that you can not save
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261 lambda expressions, but I'm open to other alternatives ..
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262
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263
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264 What this way of doing things would buy you hopefully is that you do not
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265 need to worry about most of your model ( would be just a few macros) that
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266 will get you to the point you want to change and then you do surgery on
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267 that point. Compare this with hacking a class, it feels cleaner, because
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268 you what is up to that point you want to change is sort of separated from
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269 what you change. Plus you could do this in your script, and you don't need
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270 to create your local branch of the library where you hack the class, or
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271 duplicate the class file under a different name ..
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272 Once what you are doing becomes stable it can be converted in either a
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273 different macro or a parameter to the initial macro.
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274
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275 ** New part **
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276
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277 If this is not convincing enough, there is another point that I want to
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278 make. While creating the graph you can optionally create a model object.
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279 I will encourage most people to do that ! This idea I had a long time ago,
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280 but then I used a singleton class as the world which could potentially create
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281 a lot of issues. This is a nicer version of that.
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282
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283 This model class is optional but it can be extremely useful. What you do in
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284 this model class is to store the graph, together with different annotations
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285 on that graph. What I would do is identify different subgraphs in the model
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286 and register them under different names. For example if err is the node that
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287 points to the graph that represents a DBN, that graph will be registerd to
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288 a model in which I have annotated which subgraphs represent the different
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289 rbms, which represents the logistic regression and so on. The model will also
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290 have a list of all the input nodes and all the output nodes of the graph.
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291 We could potentially use this model class to control some global default
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292 parameters initialization or hyper-parameters. This all might sound like
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293 magic but is actually easy to implement.
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294
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295 If you have such a model, which is just some annotations on the graph, this
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296 approach makes it easy to change components of the graph based on their names.
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297 For example I can replace rbm1 with a daa, because based on these annotations
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298 I know which part is rbm1.
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299
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300 Why do I feel you need such a thing? It is just because you get the DBN by
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301 calling a macro, and you don't have variables that point to different nodes
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302 of your network so that you can define where a subgraph starts or not. But
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303 if a graph returns such a model, you can introspect what annotations you have.
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304 There should also be standard conventions, but you could also in the
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305 interactive shell look at :
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306
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307 model.annotations(depth = 2)
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308
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309 This would print something like :
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310
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311 'DBN'
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312 'rbm1'
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313 'hidden_layer1'
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314 'CDk_layer1'
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315 'rbm2'
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316 'hidden_layer2'
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317 'CDk_layer2'
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318 'logreg'
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319 'cross_entropy'
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320
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321 And then you can say
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322
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323 daa1 = daa(..)
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324 daa2 = daa(..)
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325 new_model = model.replace('rbm1', daa1, new_name = 'daa1')
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326 new_model = new_model.replace('rbm2', daa2, new_name = 'daa2')
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327
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328 and you get a SDAA.
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329 What is the hierarhical structure ? Well, in my view if some subgrah
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330 (annotated as S1) is part of another subgraph (annotated as S2) then
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331 S1 is a child of S2 in this hierarchy of annotations. If they share
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332 just a few nodes, but have nodes that are not shared, then they are on
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333 the same level. We might one a flat space for the annotations, but I think
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334 this simple convention can get as a lot.
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335
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336
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337 So macros should in general return such models. It is up to you if you want to
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338 ground the graph that you create in your script into a model or not. You do
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339 so by manually adding nodes to the model. The annotations are also manually
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340 done .. So this might be a bit annoying for a developer of a macro, but I
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341 don't think is cognitively complicated, and it would help a lot when using
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342 the macros.
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343
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344 You can see how this annotation system becomes easily interesting. You can
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345 also annotate parameters ( and it is not too overwhelming to do so when
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346 you create the graph as well) and you can use this to sort of collect all
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347 parameters that you annotated in some way and then do something to them.
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348
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349 The way I see it is just that a transform could have an optional annotations
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350 argument and it will add that string to all parameters and hyper-parameters.
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351 How much sense this makes is debatable, but I strongly believe that is not
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352 complicated to implement ( I actually have something like this already
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353 implemented, just that I use that single ton class, and I sort of made the
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354 framework work mostly for DAA by making a few poor choices).
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355
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356
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357 Params and hyperparams
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358 ----------------------
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359
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360 I think it is obvious from what I wrote above that there is a node wrapper
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361 around the theano expression. I haven't wrote down all the details of that
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362 class. I think there should be such a wrapper around parameters and
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363 hyper-parameters as well. By default those wrappers might not provide
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364 any informtion. But you can potentially add interesting information for
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365 "graph" aware transforms. For example you can add annotations for a find
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366 or replace function that will collect you all parameters or hyper-parameter
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367 so you do some common thing to all of them (when it makes sense).
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368
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369 You could have a freeze property for parameters. If you change that property
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370 the theano function (where needed) for all nodes that follow this one is
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371 recomputed. This argument would be used by the collecting paramters function
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372 used to compute the gradient. If parameters are frozen they are ignored,
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373 if not they are updated.
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374
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375 For hyper-parameters you would also have a different wrapper that would
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376 contain, possibly, the distribution of that hyper-parameters for a
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377 hyper-learner.
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378
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379 I would also have the learning rate or noise_amounts as some strange
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380 hyper-paramter. I would say by default, if any hyper-paramter changes its
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381 value, then the theano expressions need to be recompiled. If you are dealing
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382 with this strange types of hyper-parameters you don't need to do that.
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383 This can be automatically for you and I guess it will all boil down to,
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384 is you hyper-paramter a theano shared variable or theano tensor ? If so we
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385 are dealing with the second type. So this kind of stuff can be detected
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386 automatically.
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387
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388 How does this work?
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389 -------------------
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390
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391 You always have a pointer to the entire graph. Whenever a hyper-param
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392 changes ( or a param freezes) all region of the graph affected get recompiled.
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393 This is by traversing the graph from the bottom node and re-constructing the
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394 theano expression. Where needed this theano expression get compiled.
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395
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396 This function that updates / re-constructs the graph is sligthly more complex
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397 if you have non-theano functions in the middle of the graph .. but not too
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398 much in my view.
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399
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400 replace & find
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401 --------------
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402
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403 Replace, replaces a part of the graph. The way it works in my view is that
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404 if I write :
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405
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406 x = x1+x2+x3
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407 y = x.replace({x2:x5})
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408
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409 You would first copy the graph that is represented by x ( the params or
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410 hyper-params are not copied) and then replace the subgraphs. I.e., x will
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411 still point to x1+x2+x3, y will point to x1+x5+x3. Replace is not done
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412 inplace !
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413
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414 I think these Node classes as something light-weighted, like theano variables
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415 and creating copy is not harmful. Also params & shared variables are shared
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416 between these graphs. If you want new params / shared variables we can offer
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417 a copy / deepcopy command.
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418
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419 Replace (given that it starts from a model) can take string(s) that indicate
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420 specific annotations.
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421
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422 Find does the same ( without the copying).
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423
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424
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425
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426 If you have two things named the same in the graph you would return the first
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427 one in a breadth search starting from the top node. The idea is that if you
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428 have all the weight matrices annotated as 'W' and you look for 'W' starting
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429 from node hiddens2, you want the W of the second layer, and not of the first.
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430
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431 I wold support :
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432 model.replace( look_at , search_for , replace_with, annotate_as)
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433 replace(model , look_at , search_for , replace_with, annotate_as)
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434 node.replace(model , look_at, replace_with, annotate_as)
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435
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436 look_at if it is a node it reffers to the subgraph that has as a final
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437 node that node. I.e. all up to that point. If it is a string, you would look
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438 at the subgraph annotated by that string.
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439
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440 Of course we can optionally choose not to allow things to be annotate with
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441 the same name, though I sort of liked it. It makes a lot of things easy. For
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442 a DBN I would have the annotations :
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443
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444 DBN
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445 rbm1
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446 hidden
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447 CDk
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448 rbm2
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449 hidden
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450 CDk
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451 logreg
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452
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453 If I want to change the first CDk with PCD I would do
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454
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455 pcd1 = PCD (..)
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456 model.replace(look_at='rbm1', search_for='CDk', replace_with=pcd1,
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457 annotate_as='PCD1')
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458
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459
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460 Bottom line is :
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461
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462 I think having a graph and having a way to search in that graph and replace
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463 parts is a very flexible and powerful way of doing things.
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464
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465
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466 reconstruct
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467 -----------
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468
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469 This is something nice for DAA. It is definetely not useful for the rest.
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470 I think though that is a shame having that transformation graph and not
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471 being able to use it to do this. It will make life so much easier when you
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472 do deep auto-encoders. I wouldn't put it in the core library, but I would
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473 have in the DAA module. For reconstruct to work you need to have inverse
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474 transforms for the ones you use.
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475
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476 The way I see it you can either have something like
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477
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478 # generate your inversable transforms on the fly
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479 fn = create_transform(lambda : , params, hyper-params )
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480 inv = create_transform(lambda : , params, hyper-params )
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481 my_transform = couple_transforms( forward = fn, inv = inv)
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482
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483 and generate special transforms on the fly that have some pseudo-inverses
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484 when you construct the graph. Maybe you can also have spcific pre-defined
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485 transforms for the most used cases, whith specific names. Even more I don't
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486 see the harm of something as simple as dotW_b to have a inverse defined ( as
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487 using tied weights) in all cases, but you would only use it for the DAA.
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488 It just to reduce the number of names of transforms you have, is like a
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489 feature that doesn't hurt or help in 95% of times but it helps in 5% of times.
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490
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491
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492 But this is up to debate. The only reason I bring it up is to say that the
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493 class that represents a transform should have a inverse method that by
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494 default throws an exception.
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495
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496
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497 transforms
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498 ----------
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499
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500 In my view there will be quite a few of such standard transforms.
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501 This can be annoying, but I think that if we group them by
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502 architectures (MLP, DAA, RBM), sampler, optimizers it will be less of a mess.
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503 This would be crucial for their documentation as well. This categories should
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504 also come with macros. There will be though some basic transforms that
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505 are available at the core ( like replace, find, things related to annotating
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506 and creating a model, collecting parameters and hyper-paramters)
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507
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508 I also think that we can start small by having just very few such transforms
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509 and add them as the library grows. We don't need many of this, most are
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510 nice to have ..
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511
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512
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513 Constraints
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514 -----------
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515
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516 You can always add constraints. I think the easier to make this explicit is to
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517 get a hand on the parameter or ndoe on which you want to add constraint and
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518 do something like
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519
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520 add_constraint(on_what, what)
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521
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522 on_what can be a node, a parameter node, a list of nodes, a list of parameter
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523 nodes, an annotation string, given that you provided a model, and what is a
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524 graph. In terms of the graph that you are creating what this does is to
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525 create a dependency link from your main graph to that constraint graph.
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526 This means that the grad function that computes the grad function that
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527 computes the gradients with respect to parameters will also (if there are
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528 such dependency links) add the gradient of those parameters with respect
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529 to the output of that dependency graph. There are some constraints on
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530 what a dependency graph can be, in the sense that it should start from only
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531 one input ( the parameters / node) and it should end in only one node that
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532 is a scalar.
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533
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534 From an implementation point of view, this can be done by just collecting a
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535 list of constraints cost, that will be added to the cost before calling
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536 T.grad. But I like to think about it in terms of graph linked through
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537 dependency links.
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538
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539
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540
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541
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542 Some general comments
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543 ---------------------
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544
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545 I think that what you get in the end is a very flexible framework, where
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546 adding new things is just a matter of putting together a few transforms and
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547 annotating the entire thing. Worst case scenario you would need to invent a
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548 transform, which I do believe could be quite painless.
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549
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550 The harder part to implement is the back-bone. It is not difficult in my
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551 view, mostly sligthly tideous. I had something like this implemented in a
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552 matter of a week, though it was a bit less restrictive. I do believe though
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553 that we should not oversimplify the backbone of the library just to make it
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554 easy to implement, but we should rather carefully consider what you get in
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555 the end
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556
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557
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558 Connection to the architecture committee
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559 -----------------------------------------
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560
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561 I think that if you get such iterator objects that can produce either
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562 the error, or do an update step it is easy to wrap them in a plug-in,
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563 or use it with the imperative language James proposed.
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564
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565 I actually have ideas ( using non theano nodes) how to break the algo at
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566 points such that you can have different parts run on remote machines ..
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567 though we might not want to support that ( using the plug-in system ..
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568 though it might work with other systems that support the same idea)
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569
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570 I think it goes more natural with the imperative language that James
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571 proposed, because that would create a graph as well. His graph is
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572 in general simpler ( it always has only one termination node) where
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573 the nodes have a different interpretation (?) so I would use a different
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574 node class on those. But from writing the code, using some syntactic sugar
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575 the difference can be blurred ( do we want this ?). I think that one
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576 can come up with ways of making the approaches look alike and sligtly
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577 homogeneous.