annotate code_tutoriel/convolutional_mlp.py @ 584:81c6fde68a8a

corrections to techreport.tex
author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Sat, 18 Sep 2010 18:25:11 -0400
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children
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1 """
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2 This tutorial introduces the LeNet5 neural network architecture using Theano. LeNet5 is a
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3 convolutional neural network, good for classifying images. This tutorial shows how to build the
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4 architecture, and comes with all the hyper-parameters you need to reproduce the paper's MNIST
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5 results.
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6
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7
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8 This implementation simplifies the model in the following ways:
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9
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10 - LeNetConvPool doesn't implement location-specific gain and bias parameters
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11 - LeNetConvPool doesn't implement pooling by average, it implements pooling by max.
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12 - Digit classification is implemented with a logistic regression rather than an RBF network
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13 - LeNet5 was not fully-connected convolutions at second layer
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14
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15 References:
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16 - Y. LeCun, L. Bottou, Y. Bengio and P. Haffner: Gradient-Based Learning Applied to Document
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17 Recognition, Proceedings of the IEEE, 86(11):2278-2324, November 1998.
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18 http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf
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19 """
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20
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21 import numpy, time, cPickle, gzip
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22
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23 import theano
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24 import theano.tensor as T
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25 from theano.tensor.signal import downsample
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26 from theano.tensor.nnet import conv
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27
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28 from logistic_sgd import LogisticRegression, load_data
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29 from mlp import HiddenLayer
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30
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31
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32 class LeNetConvPoolLayer(object):
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33 """Pool Layer of a convolutional network """
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34
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35 def __init__(self, rng, input, filter_shape, image_shape, poolsize=(2,2)):
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36 """
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37 Allocate a LeNetConvPoolLayer with shared variable internal parameters.
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38
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39 :type rng: numpy.random.RandomState
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40 :param rng: a random number generator used to initialize weights
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41
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42 :type input: theano.tensor.dtensor4
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43 :param input: symbolic image tensor, of shape image_shape
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44
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45 :type filter_shape: tuple or list of length 4
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46 :param filter_shape: (number of filters, num input feature maps,
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47 filter height,filter width)
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48
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49 :type image_shape: tuple or list of length 4
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50 :param image_shape: (batch size, num input feature maps,
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51 image height, image width)
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52
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53 :type poolsize: tuple or list of length 2
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54 :param poolsize: the downsampling (pooling) factor (#rows,#cols)
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55 """
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56
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57 assert image_shape[1]==filter_shape[1]
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58 self.input = input
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59
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60 # initialize weights to temporary values until we know the shape of the output feature
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61 # maps
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62 W_values = numpy.zeros(filter_shape, dtype=theano.config.floatX)
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63 self.W = theano.shared(value = W_values)
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64
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65 # the bias is a 1D tensor -- one bias per output feature map
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66 b_values = numpy.zeros((filter_shape[0],), dtype= theano.config.floatX)
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67 self.b = theano.shared(value= b_values)
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68
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69 # convolve input feature maps with filters
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70 conv_out = conv.conv2d(input = input, filters = self.W,
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71 filter_shape=filter_shape, image_shape=image_shape)
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72
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73 # there are "num input feature maps * filter height * filter width" inputs
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74 # to each hidden unit
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75 fan_in = numpy.prod(filter_shape[1:])
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76 # each unit in the lower layer receives a gradient from:
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77 # "num output feature maps * filter height * filter width" / pooling size
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78 fan_out = filter_shape[0] * numpy.prod(filter_shape[2:]) / numpy.prod(poolsize)
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79 # replace weight values with random weights
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80 W_bound = numpy.sqrt(6./(fan_in + fan_out))
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81 self.W.value = numpy.asarray(
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82 rng.uniform(low=-W_bound, high=W_bound, size=filter_shape),
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83 dtype = theano.config.floatX)
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84
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85 # downsample each feature map individually, using maxpooling
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86 pooled_out = downsample.max_pool2D( input = conv_out,
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87 ds = poolsize, ignore_border=True)
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88
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89 # add the bias term. Since the bias is a vector (1D array), we first
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90 # reshape it to a tensor of shape (1,n_filters,1,1). Each bias will thus
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91 # be broadcasted across mini-batches and feature map width & height
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92 self.output = T.tanh(pooled_out + self.b.dimshuffle('x', 0, 'x', 'x'))
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93
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94 # store parameters of this layer
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95 self.params = [self.W, self.b]
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96
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97
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98
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99 def evaluate_lenet5(learning_rate=0.1, n_epochs=200, dataset='mnist.pkl.gz', nkerns=[20,50]):
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100 """ Demonstrates lenet on MNIST dataset
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101
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102 :type learning_rate: float
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103 :param learning_rate: learning rate used (factor for the stochastic
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104 gradient)
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105
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106 :type n_epochs: int
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107 :param n_epochs: maximal number of epochs to run the optimizer
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108
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109 :type dataset: string
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110 :param dataset: path to the dataset used for training /testing (MNIST here)
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111
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112 :type nkerns: list of ints
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113 :param nkerns: number of kernels on each layer
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114 """
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115
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116 rng = numpy.random.RandomState(23455)
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117
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118 datasets = load_data(dataset)
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119
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120 train_set_x, train_set_y = datasets[0]
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121 valid_set_x, valid_set_y = datasets[1]
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122 test_set_x , test_set_y = datasets[2]
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123
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124
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125 batch_size = 500 # size of the minibatch
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126
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127 # compute number of minibatches for training, validation and testing
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128 n_train_batches = train_set_x.value.shape[0] / batch_size
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129 n_valid_batches = valid_set_x.value.shape[0] / batch_size
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130 n_test_batches = test_set_x.value.shape[0] / batch_size
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131
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132 # allocate symbolic variables for the data
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133 index = T.lscalar() # index to a [mini]batch
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134 x = T.matrix('x') # the data is presented as rasterized images
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135 y = T.ivector('y') # the labels are presented as 1D vector of
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136 # [int] labels
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137
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138
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139 ishape = (28,28) # this is the size of MNIST images
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140
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141 ######################
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142 # BUILD ACTUAL MODEL #
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143 ######################
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144 print '... building the model'
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145
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146 # Reshape matrix of rasterized images of shape (batch_size,28*28)
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147 # to a 4D tensor, compatible with our LeNetConvPoolLayer
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148 layer0_input = x.reshape((batch_size,1,28,28))
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149
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150 # Construct the first convolutional pooling layer:
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151 # filtering reduces the image size to (28-5+1,28-5+1)=(24,24)
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152 # maxpooling reduces this further to (24/2,24/2) = (12,12)
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153 # 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)
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154 layer0 = LeNetConvPoolLayer(rng, input=layer0_input,
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155 image_shape=(batch_size,1,28,28),
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156 filter_shape=(nkerns[0],1,5,5), poolsize=(2,2))
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157
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158 # Construct the second convolutional pooling layer
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159 # filtering reduces the image size to (12-5+1,12-5+1)=(8,8)
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160 # maxpooling reduces this further to (8/2,8/2) = (4,4)
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161 # 4D output tensor is thus of shape (nkerns[0],nkerns[1],4,4)
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162 layer1 = LeNetConvPoolLayer(rng, input=layer0.output,
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163 image_shape=(batch_size,nkerns[0],12,12),
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164 filter_shape=(nkerns[1],nkerns[0],5,5), poolsize=(2,2))
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165
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166 # the TanhLayer being fully-connected, it operates on 2D matrices of
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167 # shape (batch_size,num_pixels) (i.e matrix of rasterized images).
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168 # This will generate a matrix of shape (20,32*4*4) = (20,512)
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169 layer2_input = layer1.output.flatten(2)
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170
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171 # construct a fully-connected sigmoidal layer
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172 layer2 = HiddenLayer(rng, input=layer2_input, n_in=nkerns[1]*4*4,
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173 n_out=500, activation = T.tanh)
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174
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175 # classify the values of the fully-connected sigmoidal layer
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176 layer3 = LogisticRegression(input=layer2.output, n_in=500, n_out=10)
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177
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178 # the cost we minimize during training is the NLL of the model
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179 cost = layer3.negative_log_likelihood(y)
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180
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181 # create a function to compute the mistakes that are made by the model
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182 test_model = theano.function([index], layer3.errors(y),
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183 givens = {
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184 x: test_set_x[index*batch_size:(index+1)*batch_size],
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185 y: test_set_y[index*batch_size:(index+1)*batch_size]})
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186
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187 validate_model = theano.function([index], layer3.errors(y),
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188 givens = {
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189 x: valid_set_x[index*batch_size:(index+1)*batch_size],
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190 y: valid_set_y[index*batch_size:(index+1)*batch_size]})
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191
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192 # create a list of all model parameters to be fit by gradient descent
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193 params = layer3.params+ layer2.params+ layer1.params + layer0.params
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194
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195 # create a list of gradients for all model parameters
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196 grads = T.grad(cost, params)
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197
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198 # train_model is a function that updates the model parameters by SGD
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199 # Since this model has many parameters, it would be tedious to manually
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200 # create an update rule for each model parameter. We thus create the updates
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201 # dictionary by automatically looping over all (params[i],grads[i]) pairs.
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202 updates = {}
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203 for param_i, grad_i in zip(params, grads):
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204 updates[param_i] = param_i - learning_rate * grad_i
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205
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206 train_model = theano.function([index], cost, updates=updates,
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207 givens = {
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208 x: train_set_x[index*batch_size:(index+1)*batch_size],
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209 y: train_set_y[index*batch_size:(index+1)*batch_size]})
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210
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211
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212 ###############
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213 # TRAIN MODEL #
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214 ###############
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215 print '... training'
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216 # early-stopping parameters
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217 patience = 10000 # look as this many examples regardless
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218 patience_increase = 2 # wait this much longer when a new best is
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219 # found
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220 improvement_threshold = 0.995 # a relative improvement of this much is
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221 # considered significant
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222 validation_frequency = min(n_train_batches, patience/2)
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223 # go through this many
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224 # minibatche before checking the network
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225 # on the validation set; in this case we
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226 # check every epoch
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227
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228 best_params = None
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229 best_validation_loss = float('inf')
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230 best_iter = 0
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231 test_score = 0.
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232 start_time = time.clock()
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233
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234 epoch = 0
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235 done_looping = False
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236
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237 while (epoch < n_epochs) and (not done_looping):
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238 epoch = epoch + 1
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239 for minibatch_index in xrange(n_train_batches):
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240
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241 iter = epoch * n_train_batches + minibatch_index
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242
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243 if iter %100 == 0:
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244 print 'training @ iter = ', iter
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245 cost_ij = train_model(minibatch_index)
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246
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247 if (iter+1) % validation_frequency == 0:
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248
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249 # compute zero-one loss on validation set
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250 validation_losses = [validate_model(i) for i in xrange(n_valid_batches)]
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251 this_validation_loss = numpy.mean(validation_losses)
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252 print('epoch %i, minibatch %i/%i, validation error %f %%' % \
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253 (epoch, minibatch_index+1, n_train_batches, \
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254 this_validation_loss*100.))
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255
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256
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257 # if we got the best validation score until now
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258 if this_validation_loss < best_validation_loss:
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259
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260 #improve patience if loss improvement is good enough
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261 if this_validation_loss < best_validation_loss * \
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262 improvement_threshold :
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263 patience = max(patience, iter * patience_increase)
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264
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265 # save best validation score and iteration number
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266 best_validation_loss = this_validation_loss
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267 best_iter = iter
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268
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269 # test it on the test set
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270 test_losses = [test_model(i) for i in xrange(n_test_batches)]
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271 test_score = numpy.mean(test_losses)
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272 print((' epoch %i, minibatch %i/%i, test error of best '
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273 'model %f %%') %
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274 (epoch, minibatch_index+1, n_train_batches,
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275 test_score*100.))
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276
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277 if patience <= iter :
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278 done_looping = False
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279 break
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280
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281 end_time = time.clock()
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282 print('Optimization complete.')
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283 print('Best validation score of %f %% obtained at iteration %i,'\
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284 'with test performance %f %%' %
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285 (best_validation_loss * 100., best_iter, test_score*100.))
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286 print('The code ran for %f minutes' % ((end_time-start_time)/60.))
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287
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288 if __name__ == '__main__':
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289 evaluate_lenet5()
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290
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291 def experiment(state, channel):
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292 evaluate_lenet5(state.learning_rate, dataset=state.dataset)