|
| 1 | +"""network3.py |
| 2 | +~~~~~~~~~~~~~~ |
| 3 | +
|
| 4 | +A Theano-based program for training and running simple neural |
| 5 | +networks. |
| 6 | +
|
| 7 | +Supports several layer types (fully connected, convolutional, max |
| 8 | +pooling, softmax), and activation functions (sigmoid, tanh, and |
| 9 | +rectified linear units, with more easily added). |
| 10 | +
|
| 11 | +When run on a CPU, this program is much faster than network.py and |
| 12 | +network2.py. However, unlike network.py and network2.py it can also |
| 13 | +be run on a GPU, which makes it faster still. |
| 14 | +
|
| 15 | +Because the code is based on Theano, the code is different in many |
| 16 | +ways from network.py and network2.py. However, where possible I have |
| 17 | +tried to maintain consistency with the earlier programs. In |
| 18 | +particular, the API is similar to network2.py. Note that I have |
| 19 | +focused on making the code simple, easily readable, and easily |
| 20 | +modifiable. It is not optimized, and omits many desirable features. |
| 21 | +
|
| 22 | +""" |
| 23 | + |
| 24 | +#### Libraries |
| 25 | +# Standard library |
| 26 | +import cPickle |
| 27 | +import gzip |
| 28 | + |
| 29 | +# Third-party libraries |
| 30 | +import numpy as np |
| 31 | +import theano |
| 32 | +import theano.tensor as T |
| 33 | +from theano.tensor.nnet import conv |
| 34 | +from theano.tensor.nnet import softmax |
| 35 | +from theano.tensor.signal import downsample |
| 36 | + |
| 37 | +# Activation functions for neurons |
| 38 | +def linear(z): return z |
| 39 | +def ReLU(z): return T.maximum(0, z) |
| 40 | +from theano.tensor.nnet import sigmoid |
| 41 | +from theano.tensor import tanh |
| 42 | + |
| 43 | + |
| 44 | +#### Constants |
| 45 | +GPU = False |
| 46 | +if GPU: |
| 47 | + print "Trying to run under a GPU. If this is not desired, then modify "+\ |
| 48 | + "network3.py\nto set the GPU flag to False." |
| 49 | + try: theano.config.device = 'gpu' |
| 50 | + except: pass # it's already set |
| 51 | + theano.config.floatX = 'float32' |
| 52 | + |
| 53 | +def example(mini_batch_size=10): |
| 54 | + print("Loading the MNIST data") |
| 55 | + training_data, validation_data, test_data = load_data_shared("../data/mnist.pkl.gz") |
| 56 | + print("Building the network") |
| 57 | + net = create_net(10) |
| 58 | + print("Training the network") |
| 59 | + try: |
| 60 | + net.SGD(training_data, 200, mini_batch_size, 0.1, |
| 61 | + validation_data, test_data, lmbda=1.0) |
| 62 | + except KeyboardInterrupt: |
| 63 | + pass |
| 64 | + return net |
| 65 | + |
| 66 | +def create_net(mini_batch_size=10, activation_fn=tanh): |
| 67 | + return Network( |
| 68 | + [ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28), filter_shape=(20, 1, 5, 5), poolsize=(2, 2), activation_fn=activation_fn), |
| 69 | + #ConvPoolLayer(image_shape=(mini_batch_size, 20, 12, 12), filter_shape=(40, 20, 5, 5), poolsize=(2, 2), activation_fn=activation_fn), |
| 70 | + #FullyConnectedLayer(n_in=40*4*4, n_out=100, mini_batch_size=mini_batch_size, activation_fn=activation_fn), |
| 71 | + #FullyConnectedLayer(n_in=784, n_out=100, mini_batch_size=mini_batch_size, activation_fn=activation_fn), |
| 72 | + #FullyConnectedLayer(n_in=20*12*12, n_out=100, mini_batch_size=mini_batch_size), |
| 73 | + #FullyConnectedLayer(n_in=100, n_out=100, mini_batch_size=mini_batch_size, activation_fn=activation_fn), |
| 74 | + #SoftmaxLayer(n_in=100, n_out=10, mini_batch_size=mini_batch_size)], mini_batch_size) |
| 75 | + SoftmaxLayer(n_in=20*12*12, n_out=10)], mini_batch_size) |
| 76 | + |
| 77 | +#### Load the MNIST data |
| 78 | +def load_data_shared(filename="../data/mnist.pkl.gz"): |
| 79 | + f = gzip.open(filename, 'rb') |
| 80 | + training_data, validation_data, test_data = cPickle.load(f) |
| 81 | + f.close() |
| 82 | + def shared(data): |
| 83 | + """Place the data into shared variables. This allows Theano to copy |
| 84 | + the data to the GPU, if one is available. |
| 85 | +
|
| 86 | + """ |
| 87 | + shared_x = theano.shared( |
| 88 | + np.asarray(data[0], dtype=theano.config.floatX), borrow=True) |
| 89 | + shared_y = theano.shared( |
| 90 | + np.asarray(data[1], dtype=theano.config.floatX), borrow=True) |
| 91 | + return shared_x, T.cast(shared_y, "int32") |
| 92 | + return [shared(training_data), shared(validation_data), shared(test_data)] |
| 93 | + |
| 94 | +#### Main class used to construct and train networks |
| 95 | +class Network(): |
| 96 | + |
| 97 | + def __init__(self, layers, mini_batch_size): |
| 98 | + """Takes a list of `layers`, describing the network architecture, and |
| 99 | + a value for the `mini_batch_size` to be used during training |
| 100 | + by stochastic gradient descent. |
| 101 | +
|
| 102 | + """ |
| 103 | + self.layers = layers |
| 104 | + self.mini_batch_size = mini_batch_size |
| 105 | + self.params = [param for layer in self.layers for param in layer.params] |
| 106 | + self.x = T.matrix("x") |
| 107 | + self.y = T.ivector("y") |
| 108 | + init_layer = self.layers[0] |
| 109 | + init_layer.set_inpt(self.x, mini_batch_size) |
| 110 | + for j in xrange(1, len(self.layers)): |
| 111 | + prev_layer, layer = self.layers[j-1], self.layers[j] |
| 112 | + layer.set_inpt(prev_layer.output, mini_batch_size) |
| 113 | + self.output = self.layers[-1].output |
| 114 | + |
| 115 | + def SGD(self, training_data, epochs, mini_batch_size, eta, |
| 116 | + validation_data, test_data, lmbda=0.0): |
| 117 | + """Train the network using mini-batch stochastic gradient descent.""" |
| 118 | + training_x, training_y = training_data |
| 119 | + validation_x, validation_y = validation_data |
| 120 | + test_x, test_y = test_data |
| 121 | + |
| 122 | + # compute number of minibatches for training, validation and testing |
| 123 | + num_training_batches = size(training_data)/mini_batch_size |
| 124 | + num_validation_batches = size(validation_data)/mini_batch_size |
| 125 | + num_test_batches = size(test_data)/mini_batch_size |
| 126 | + |
| 127 | + # define the (regularized) cost function, symbolic gradients, and updates |
| 128 | + l2_norm_squared = sum([(layer.w**2).sum() for layer in self.layers]) |
| 129 | + cost = self.log_likelihood()+0.5*lmbda*l2_norm_squared/num_training_batches |
| 130 | + grads = T.grad(cost, self.params) |
| 131 | + updates = [(param, param-eta*grad) |
| 132 | + for param, grad in zip(self.params, grads)] |
| 133 | + |
| 134 | + # define functions to train a mini-batch, and to compute the |
| 135 | + # accuracy in validation and test mini-batches. |
| 136 | + i = T.lscalar() # mini-batch index |
| 137 | + train_mb = theano.function( |
| 138 | + [i], cost, updates=updates, |
| 139 | + givens={ |
| 140 | + self.x: |
| 141 | + training_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size], |
| 142 | + self.y: |
| 143 | + training_y[i*self.mini_batch_size: (i+1)*self.mini_batch_size] |
| 144 | + }) |
| 145 | + validate_mb_accuracy = theano.function( |
| 146 | + [i], self.layers[-1].accuracy(self.y), |
| 147 | + givens={ |
| 148 | + self.x: |
| 149 | + validation_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size], |
| 150 | + self.y: |
| 151 | + validation_y[i*self.mini_batch_size: (i+1)*self.mini_batch_size] |
| 152 | + }) |
| 153 | + test_mb_accuracy = theano.function( |
| 154 | + [i], self.layers[-1].accuracy(self.y), |
| 155 | + givens={ |
| 156 | + self.x: |
| 157 | + test_x[i*self.mini_batch_size: (i+1)*self.mini_batch_size], |
| 158 | + self.y: |
| 159 | + test_y[i*self.mini_batch_size: (i+1)*self.mini_batch_size] |
| 160 | + }) |
| 161 | + |
| 162 | + # Do the actual training |
| 163 | + best_validation_accuracy = 0.0 |
| 164 | + for epoch in xrange(epochs): |
| 165 | + for minibatch_index in xrange(num_training_batches): |
| 166 | + iteration = num_training_batches*epoch+minibatch_index |
| 167 | + if iteration % 1000 == 0: |
| 168 | + print("Training mini-batch number {0}".format(iteration)) |
| 169 | + cost_ij = train_mini_batch(minibatch_index) |
| 170 | + if (iteration+1) % num_training_batches == 0: |
| 171 | + validation_accuracy = np.mean( |
| 172 | + [validate_mb_accuracy(j) for j in xrange(num_validation_batches)]) |
| 173 | + print("Epoch {0}: validation accuracy {1:.2%}".format( |
| 174 | + epoch, validation_accuracy)) |
| 175 | + if validation_accuracy >= best_validation_accuracy: |
| 176 | + print("This is the best validation accuracy to date.") |
| 177 | + best_validation_accuracy = validation_accuracy |
| 178 | + best_iteration = iteration |
| 179 | + test_accuracy = np.mean( |
| 180 | + [test_mb_accuracy(j) for j in xrange(num_test_batches)]) |
| 181 | + print('The corresponding test accuracy is {0:.2%}'.format( |
| 182 | + test_accuracy)) |
| 183 | + print("Finished training network.") |
| 184 | + print("Best validation accuracy of {0:.2%} obtained at iteration {1}".format( |
| 185 | + best_validation_accuracy, best_iteration)) |
| 186 | + print("Corresponding test accuracy of {0:.2%}".format(test_accuracy)) |
| 187 | + |
| 188 | + def log_likelihood(self): |
| 189 | + "Return the log-likelihood cost." |
| 190 | + return -T.mean(T.log(self.output)[T.arange(self.y.shape[0]), self.y]) |
| 191 | + |
| 192 | + |
| 193 | +#### Define layer types |
| 194 | + |
| 195 | +class ConvPoolLayer(): |
| 196 | + """Used to create a combination of a convolutional and a max-pooling |
| 197 | + layer. A more sophisticated implementation would separate the |
| 198 | + two, but for our purposes we'll always use them together, and it |
| 199 | + simplifies the code, so it makes sense to combine them. |
| 200 | +
|
| 201 | + """ |
| 202 | + |
| 203 | + def __init__(self, filter_shape, image_shape, poolsize=(2, 2), |
| 204 | + activation_fn=sigmoid): |
| 205 | + """`filter_shape` is a tuple of length 4, whose entries are the number |
| 206 | + of filters, the number of input feature maps, the filter height, and the |
| 207 | + filter width. |
| 208 | +
|
| 209 | + `image_shape` is a tuple of length 4, whose entries are the |
| 210 | + mini-batch size, the number of input feature maps, the image |
| 211 | + height, and the image width. |
| 212 | +
|
| 213 | + `poolsize` is a tuple of length 2, whose entries are the y and |
| 214 | + x pooling sizes. |
| 215 | +
|
| 216 | + """ |
| 217 | + self.inpt = None |
| 218 | + self.output = None |
| 219 | + self.filter_shape = filter_shape |
| 220 | + self.image_shape = image_shape |
| 221 | + self.poolsize = poolsize |
| 222 | + self.activation_fn=activation_fn |
| 223 | + # initialize weights and biases |
| 224 | + n_out = (filter_shape[0]*np.prod(filter_shape[2:])/np.prod(poolsize)) |
| 225 | + self.w = theano.shared( |
| 226 | + np.asarray( |
| 227 | + np.random.normal(loc=0, scale=np.sqrt(1.0/n_out), size=filter_shape), |
| 228 | + dtype=theano.config.floatX), |
| 229 | + borrow=True) |
| 230 | + self.b = theano.shared( |
| 231 | + np.asarray( |
| 232 | + np.random.normal(loc=0, scale=1.0, size=(filter_shape[0],)), |
| 233 | + dtype=theano.config.floatX), |
| 234 | + borrow=True) |
| 235 | + self.params = [self.w, self.b] |
| 236 | + |
| 237 | + def set_inpt(self, inpt, mini_batch_size): |
| 238 | + self.inpt = inpt.reshape(self.image_shape) |
| 239 | + conv_out = conv.conv2d( |
| 240 | + input=self.inpt, filters=self.w, filter_shape=self.filter_shape, |
| 241 | + image_shape=self.image_shape) |
| 242 | + pooled_out = downsample.max_pool_2d( |
| 243 | + input=conv_out, ds=self.poolsize, ignore_border=True) |
| 244 | + self.output = self.activation_fn( |
| 245 | + pooled_out + self.b.dimshuffle('x', 0, 'x', 'x')) |
| 246 | + |
| 247 | + |
| 248 | +class FullyConnectedLayer(): |
| 249 | + |
| 250 | + def __init__(self, n_in, n_out, mini_batch_size=10, activation_fn=sigmoid): |
| 251 | + self.n_in = n_in |
| 252 | + self.n_out = n_out |
| 253 | + self.activation_fn = activation_fn |
| 254 | + self.inpt = None |
| 255 | + self.output = None |
| 256 | + # Initialize weights and biases |
| 257 | + self.w = theano.shared( |
| 258 | + np.asarray( |
| 259 | + np.random.normal( |
| 260 | + loc=0.0, scale=np.sqrt(1.0/n_out), size=(n_in, n_out)), |
| 261 | + dtype=theano.config.floatX), |
| 262 | + name='w', borrow=True) |
| 263 | + self.b = theano.shared( |
| 264 | + np.asarray(np.random.normal(loc=0.0, scale=1.0, size=(n_out,)), |
| 265 | + dtype=theano.config.floatX), |
| 266 | + name='b', borrow=True) |
| 267 | + self.params = [self.w, self.b] |
| 268 | + |
| 269 | + def set_inpt(self, inpt, mini_batch_size): |
| 270 | + self.mini_batch_size = mini_batch_size |
| 271 | + self.inpt = inpt.reshape((self.mini_batch_size, self.n_in)) |
| 272 | + self.output = self.activation_fn(T.dot(inpt, self.w)+self.b) |
| 273 | + |
| 274 | +class SoftmaxLayer(): |
| 275 | + |
| 276 | + def __init__(self, n_in, n_out): |
| 277 | + self.inpt = None |
| 278 | + self.output = None |
| 279 | + self.n_in = n_in |
| 280 | + self.n_out = n_out |
| 281 | + # Initialize weights and biases |
| 282 | + self.w = theano.shared( |
| 283 | + np.zeros((n_in, n_out), dtype=theano.config.floatX), |
| 284 | + name='w', borrow=True) |
| 285 | + self.b = theano.shared( |
| 286 | + np.zeros((n_out,), dtype=theano.config.floatX), |
| 287 | + name='b', borrow=True) |
| 288 | + self.params = [self.w, self.b] |
| 289 | + |
| 290 | + def set_inpt(self, inpt, mini_batch_size): |
| 291 | + self.mini_batch_size = mini_batch_size |
| 292 | + self.inpt = inpt.reshape((self.mini_batch_size, self.n_in)) |
| 293 | + self.output = softmax(T.dot(self.inpt, self.w)+self.b) |
| 294 | + self.y_out = T.argmax(self.output, axis=1) |
| 295 | + |
| 296 | + def accuracy(self, y): |
| 297 | + "Return the accuracy for the mini-batch." |
| 298 | + return T.mean(T.eq(y, self.y_out)) |
| 299 | + |
| 300 | + |
| 301 | +#### Miscellanea |
| 302 | +def size(data): |
| 303 | + "Return the size of the dataset `data`." |
| 304 | + return data[0].get_value(borrow=True).shape[0] |
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