"""Pool Layer of a convolutional network """

def __init__(self, rng, input, filter_shape, image_shape, poolsize=(2, 2)):

"""

assert image_shape[1] == filter_shape[1]

self.input = input

# there are "num input feature maps * filter height * filter width"

# inputs to each hidden unit

fan_in = numpy.prod(filter_shape[1:])

# each unit in the lower layer receives a gradient from:

# "num output feature maps * filter height * filter width" /

# pooling size

fan_out = (filter_shape[0] * numpy.prod(filter_shape[2:]) /

numpy.prod(poolsize))

# initialize weights with random weights

W_bound = numpy.sqrt(6. / (fan_in + fan_out))

self.W = theano.shared(numpy.asarray(

rng.uniform(low=-W_bound, high=W_bound, size=filter_shape),

dtype=theano.config.floatX),

borrow=True)

# the bias is a 1D tensor -- one bias per output feature map

b_values = numpy.zeros((filter_shape[0],), dtype=theano.config.floatX)

self.b = theano.shared(value=b_values, borrow=True)

# convolve input feature maps with filters

conv_out = conv.conv2d(input=input, filters=self.W,

filter_shape=filter_shape, image_shape=image_shape)

# downsample each feature map individually, using maxpooling

pooled_out = downsample.max_pool_2d(input=conv_out,

ds=poolsize, ignore_border=True)

# add the bias term. Since the bias is a vector (1D array), we first

# reshape it to a tensor of shape (1,n_filters,1,1). Each bias will

# thus be broadcasted across mini-batches and feature map

# width & height

self.output = T.tanh(pooled_out + self.b.dimshuffle('x', 0, 'x', 'x'))

# store parameters of this layer

dataset='mnist.pkl.gz',

nkerns=[20, 50], batch_size=500):

""" Demonstrates lenet on MNIST dataset

rng = numpy.random.RandomState(23455)

datasets = load_data(dataset)

train_set_x, train_set_y = datasets[0]

valid_set_x, valid_set_y = datasets[1]

test_set_x, test_set_y = datasets[2]

# compute number of minibatches for training, validation and testing

n_train_batches = train_set_x.get_value(borrow=True).shape[0]

n_valid_batches = valid_set_x.get_value(borrow=True).shape[0]

n_test_batches = test_set_x.get_value(borrow=True).shape[0]

n_train_batches /= batch_size

n_valid_batches /= batch_size

n_test_batches /= batch_size

# allocate symbolic variables for the data

index = T.lscalar() # index to a [mini]batch

x = T.matrix('x') # the data is presented as rasterized images

y = T.ivector('y') # the labels are presented as 1D vector of

# [int] labels

ishape = (28, 28) # this is the size of MNIST images

######################

# BUILD ACTUAL MODEL #

######################

print '... building the model'

# Reshape matrix of rasterized images of shape (batch_size,28*28)

# to a 4D tensor, compatible with our LeNetConvPoolLayer

layer0_input = x.reshape((batch_size, 1, 28, 28))

# Construct the first convolutional pooling layer:

# filtering reduces the image size to (28-5+1,28-5+1)=(24,24)

# maxpooling reduces this further to (24/2,24/2) = (12,12)

# 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)

layer0 = LeNetConvPoolLayer(rng, input=layer0_input,

image_shape=(batch_size, 1, 28, 28),

filter_shape=(nkerns[0], 1, 5, 5), poolsize=(2, 2))

# Construct the second convolutional pooling layer

# filtering reduces the image size to (12-5+1,12-5+1)=(8,8)

# maxpooling reduces this further to (8/2,8/2) = (4,4)

# 4D output tensor is thus of shape (nkerns[0],nkerns[1],4,4)

layer1 = LeNetConvPoolLayer(rng, input=layer0.output,

image_shape=(batch_size, nkerns[0], 12, 12),

filter_shape=(nkerns[1], nkerns[0], 5, 5), poolsize=(2, 2))

# the HiddenLayer being fully-connected, it operates on 2D matrices of

# shape (batch_size,num_pixels) (i.e matrix of rasterized images).

# This will generate a matrix of shape (20,32*4*4) = (20,512)

layer2_input = layer1.output.flatten(2)

# construct a fully-connected sigmoidal layer

layer2 = HiddenLayer(rng, input=layer2_input, n_in=nkerns[1] * 4 * 4,

n_out=500, activation=T.tanh)

# classify the values of the fully-connected sigmoidal layer

layer3 = LogisticRegression(input=layer2.output, n_in=500, n_out=10)

# the cost we minimize during training is the NLL of the model

cost = layer3.negative_log_likelihood(y)

# create a function to compute the mistakes that are made by the model

test_model = theano.function([index], layer3.errors(y),

givens={

x: test_set_x[index * batch_size: (index + 1) * batch_size],

y: test_set_y[index * batch_size: (index + 1) * batch_size]})

validate_model = theano.function([index], layer3.errors(y),

givens={

x: valid_set_x[index * batch_size: (index + 1) * batch_size],

y: valid_set_y[index * batch_size: (index + 1) * batch_size]})

# create a list of all model parameters to be fit by gradient descent

params = layer3.params + layer2.params + layer1.params + layer0.params

# create a list of gradients for all model parameters

grads = T.grad(cost, params)

# train_model is a function that updates the model parameters by

# SGD Since this model has many parameters, it would be tedious to

# manually create an update rule for each model parameter. We thus

# create the updates list by automatically looping over all

# (params[i],grads[i]) pairs.

updates = []

for param_i, grad_i in zip(params, grads):

updates.append((param_i, param_i - learning_rate * grad_i))

train_model = theano.function([index], cost, updates=updates,

givens={

x: train_set_x[index * batch_size: (index + 1) * batch_size],

y: train_set_y[index * batch_size: (index + 1) * batch_size]})

###############

# TRAIN MODEL #

###############

print '... training'

# early-stopping parameters

patience = 10000 # look as this many examples regardless

patience_increase = 2 # wait this much longer when a new best is

# found

improvement_threshold = 0.995 # a relative improvement of this much is

# considered significant

validation_frequency = min(n_train_batches, patience / 2)

# go through this many

# minibatche before checking the network

# on the validation set; in this case we

# check every epoch

best_params = None

best_validation_loss = numpy.inf

best_iter = 0

test_score = 0.

start_time = time.clock()

epoch = 0

done_looping = False

while (epoch < n_epochs) and (not done_looping):

epoch = epoch + 1

for minibatch_index in xrange(n_train_batches):

iter = (epoch - 1) * n_train_batches + minibatch_index

if iter % 100 == 0:

print 'training @ iter = ', iter

cost_ij = train_model(minibatch_index)

if (iter + 1) % validation_frequency == 0:

# compute zero-one loss on validation set

validation_losses = [validate_model(i) for i

in xrange(n_valid_batches)]

this_validation_loss = numpy.mean(validation_losses)

print('epoch %i, minibatch %i/%i, validation error %f %%' % \

(epoch, minibatch_index + 1, n_train_batches, \

this_validation_loss * 100.))

# if we got the best validation score until now

if this_validation_loss < best_validation_loss:

#improve patience if loss improvement is good enough

if this_validation_loss < best_validation_loss * \

improvement_threshold:

patience = max(patience, iter * patience_increase)

# save best validation score and iteration number

best_validation_loss = this_validation_loss

best_iter = iter

# test it on the test set

test_losses = [test_model(i) for i in xrange(n_test_batches)]

test_score = numpy.mean(test_losses)

print((' epoch %i, minibatch %i/%i, test error of best '

'model %f %%') %

(epoch, minibatch_index + 1, n_train_batches,

test_score * 100.))

if patience <= iter:

done_looping = True

break

end_time = time.clock()

print('Optimization complete.')

print('Best validation score of %f %% obtained at iteration %i,'\

'with test performance %f %%' %

(best_validation_loss * 100., best_iter + 1, test_score * 100.))

print >> sys.stderr, ('The code for file ' +

os.path.split(__file__)[1] +