initial commit

Author: doomie

code/convolutional_mlp.py

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+
+"""
+This tutorial introduces the LeNet5 neural network architecture using Theano.  LeNet5 is a
+convolutional neural network, good for classifying images. This tutorial shows how to build the
+architecture, and comes with all the hyper-parameters you need to reproduce the paper's MNIST
+results.
+
+The best results are obtained after X iterations of the main program loop, which takes ***
+minutes on my workstation (an Intel Core i7, circa July 2009), and *** minutes on my GPU (an
+NVIDIA GTX 285 graphics processor).
+
+This implementation simplifies the model in the following ways:
+
+ - LeNetConvPool doesn't implement location-specific gain and bias parameters
+
+ - LeNetConvPool doesn't implement pooling by average, it implements pooling by max.
+
+ - Digit classification is implemented with a logistic regression rather than an RBF network
+
+ - LeNet5 was not fully-connected convolutions at second layer
+
+References:
+
+ - Y. LeCun, L. Bottou, Y. Bengio and P. Haffner: Gradient-Based Learning Applied to Document
+   Recognition, Proceedings of the IEEE, 86(11):2278-2324, November 1998.
+   http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf
+
+
+"""
+import numpy
+from theano.compile.sandbox import shared, pfunc
+from theano import tensor
+from pylearn.shared.layers import LogisticRegression, SigmoidalLayer
+import theano.sandbox.softsign
+import pylearn.datasets.MNIST
+
+
+try:
+    # this tells theano to use the GPU if possible
+    from theano.sandbox.cuda import use
+    use()
+except Exception, e:
+    print('Warning: Attempt to use GPU resulted in error "%s"' % str(e))
+
+class LeNetConvPool(object):
+    """WRITEME 
+
+    Math of what the layer does, and what symbolic variables are created by the class (w, b,
+    output).
+
+    """
+
+    #TODO: implement biases & scales properly. There are supposed to be more parameters.
+    #    - one bias & scale per filter
+    #    - one bias & scale per downsample feature location (a 2d bias)
+    #    - more?
+
+    def __init__(self, rng, input, n_examples, n_imgs, img_shape, n_filters, filter_shape=(5,5),
+            poolsize=(2,2)):
+        """
+        Allocate a LeNetConvPool layer with shared variable internal parameters.
+
+        :param rng: a random number generator used to initialize weights
+        
+        :param input: symbolic images.  Shape: (n_examples, n_imgs, img_shape[0], img_shape[1])
+
+        :param n_examples: input's shape[0] at runtime
+
+        :param n_imgs: input's shape[1] at runtime
+
+        :param img_shape: input's shape[2:4] at runtime
+
+        :param n_filters: the number of filters to apply to the image.
+
+        :param filter_shape: the size of the filters to apply
+        :type filter_shape: pair (rows, cols)
+
+        :param poolsize: the downsampling (pooling) factor
+        :type poolsize: pair (rows, cols)
+        """
+
+        #TODO: make a simpler convolution constructor!!
+        #    - make dx and dy optional
+        #    - why do we have to pass shapes? (Can we make them optional at least?)
+        conv_op = ConvOp((n_imgs,)+img_shape, filter_shape, n_filters, n_examples,
+                dx=1, dy=1, output_mode='valid')
+
+        # - why is poolsize an op parameter here?
+        # - can we just have a maxpool function that creates this Op internally?
+        ds_op = DownsampleFactorMax(poolsize, ignore_border=True)
+
+        # the filter tensor that we will apply is a 4D tensor
+        w_shp = (n_filters, n_imgs) + filter_shape
+
+        # the bias we add is a 1D tensor
+        b_shp = (n_filters,)
+
+        self.w = shared(
+                numpy.asarray(
+                    rng.uniform(
+                        low=-1.0 / numpy.sqrt(filter_shape[0] * filter_shape[1] * n_imgs), 
+                        high=1.0 / numpy.sqrt(filter_shape[0] * filter_shape[1] * n_imgs),
+                        size=w_shp), 
+                    dtype=input.dtype))
+        self.b = shared(
+                numpy.asarray(
+                    rng.uniform(low=-.0, high=0., size=(n_filters,)),
+                    dtype=input.dtype))
+
+        self.input = input
+        conv_out = conv_op(input, self.w)
+        self.output = tensor.tanh(ds_op(conv_out) + b.dimshuffle('x', 0, 'x', 'x'))
+        self.params = [self.w, self.b]
+
+class SigmoidalLayer(object):
+    def __init__(self, input, n_in, n_out):
+        """
+        :param input: a symbolic tensor of shape (n_examples, n_in)
+        :param w: a symbolic weight matrix of shape (n_in, n_out)
+        :param b: symbolic bias terms of shape (n_out,)
+        :param squash: an squashing function
+        """
+        self.input = input
+        self.w = shared(
+                numpy.asarray(
+                    rng.uniform(low=-2/numpy.sqrt(n_in), high=2/numpy.sqrt(n_in),
+                    size=(n_in, n_out)), dtype=input.dtype))
+        self.b = shared(numpy.asarray(numpy.zeros(n_out), dtype=input.dtype))
+        self.output = tensor.tanh(tensor.dot(input, self.w) + self.b)
+        self.params = [self.w, self.b]
+
+class LogisticRegression(object):
+    """WRITEME"""
+
+    def __init__(self, input, n_in, n_out):
+        self.w = shared(numpy.zeros((n_in, n_out), dtype=input.dtype))
+        self.b = shared(numpy.zeros((n_out,), dtype=input.dtype))
+        self.l1=abs(self.w).sum()
+        self.l2_sqr = (self.w**2).sum()
+        self.output=nnet.softmax(theano.dot(input, self.w)+self.b)
+        self.argmax=theano.tensor.argmax(self.output, axis=1)
+        self.params = [self.w, self.b]
+
+    def nll(self, target):
+        """Return the negative log-likelihood of the prediction of this model under a given
+        target distribution.  Passing symbolic integers here means 1-hot.
+        WRITEME
+        """
+        return nnet.categorical_crossentropy(self.output, target)
+
+    def errors(self, target):
+        """Return a vector of 0s and 1s, with 1s on every line that was mis-classified.
+        """
+        if target.ndim != self.argmax.ndim:
+            raise TypeError('target should have the same shape as self.argmax', ('target', target.type,
+                'argmax', self.argmax.type))
+        if target.dtype.startswith('int'):
+            return theano.tensor.neq(self.argmax, target)
+        else:
+            raise NotImplementedError()
+
+def evaluate_lenet5(batch_size=30, n_iter=1000):
+    rng = numpy.random.RandomState(23455)
+
+    mnist = pylearn.datasets.MNIST.train_valid_test()
+
+    ishape=(28,28) #this is the size of MNIST images
+
+    # allocate symbolic variables for the data
+    x = tensor.fmatrix()  # the data is presented as rasterized images
+    y = tensor.lvector()  # the labels are presented as 1D vector of [long int] labels
+
+    # construct the first convolutional pooling layer
+    layer0 = LeNetConvPool.new(rng, input=x.reshape((batch_size,1,28,28)), n_examples=batch_size, 
+            n_imgs=1, img_shape=ishape, 
+            n_filters=6, filter_shape=(5,5), 
+            poolsize=(2,2))
+
+    # construct the second convolutional pooling layer
+    layer1 = LeNetConvPool.new(rng, input=layer0.output, n_examples=batch_size, 
+            n_imgs=6, img_shape=(12,12),
+            n_filters=16, filter_shape=(5,5),
+            poolsize=(2,2))
+
+    # construct a fully-connected sigmoidal layer
+    layer2 = SigmoidalLayer.new(rng, input=layer1.output.flatten(2), n_in=16*16, n_out=128) # 128 ?
+
+    # classify the values of the fully-connected sigmoidal layer
+    layer3 = LogisticRegression.new(input=layer2.output, n_in=128, n_out=10)
+
+    # the cost we minimize during training is the NLL of the model
+    cost = layer3.nll(y).mean()
+
+    # create a function to compute the mistakes that are made by the model
+    test_model = pfunc([x,y], layer3.errors(y))
+
+    # create a list of all model parameters to be fit by gradient descent
+    params = layer3.params+ layer2.params+ layer1.params + layer0.params
+    learning_rate = numpy.asarray(0.01, dtype='float32')
+
+    # train_model is a function that updates the model parameters by SGD
+    train_model = pfunc([x, y], cost, 
+            updates=[(p, p - learning_rate*gp) for p,gp in zip(params, tensor.grad(cost, params))])
+
+    # IS IT MORE SIMPLE TO USE A MINIMIZER OR THE DIRECT CODE?
+
+    best_valid_score = float('inf')
+    for i in xrange(n_iter):
+        for j in xrange(len(mnist.train.x)/batch_size):
+            cost_ij = train_model(
+                    mnist.train.x[j*batch_size:(j+1)*batch_size],
+                    mnist.train.y[j*batch_size:(j+1)*batch_size])
+            #if 0 == j % 100:
+                #print('epoch %i:%i, training error %f' % (i, j*batch_size, cost_ij))
+        valid_score = numpy.mean([test_model(
+                    mnist.valid.x[j*batch_size:(j+1)*batch_size],
+                    mnist.valid.y[j*batch_size:(j+1)*batch_size])
+                for j in xrange(len(mnist.valid.x)/batch_size)])
+        print('epoch %i, validation error %f' % (i, valid_score))
+        if valid_score < best_valid_score:
+            best_valid_score = valid_score
+            test_score = numpy.mean([test_model(
+                        mnist.test.x[j*batch_size:(j+1)*batch_size],
+                        mnist.test.y[j*batch_size:(j+1)*batch_size])
+                    for j in xrange(len(mnist.test.x)/batch_size)])
+            print('epoch %i, test error of best model %f' % (i, test_score))
+
+if __name__ == '__main__':
+    evaluate_lenet5()
+