"""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.

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

"""

from __future__ import print_function

import os

import sys

import timeit

import numpy

import theano

import theano.tensor as T

from theano.tensor.signal import pool

from theano.tensor.nnet import conv2d

from logistic_sgd import LogisticRegression, load_data

from mlp import HiddenLayer

class LeNetConvPoolLayer(object):

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

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

"""

Allocate a LeNetConvPoolLayer with shared variable internal parameters.

:type rng: numpy.random.RandomState

:param rng: a random number generator used to initialize weights

:type input: theano.tensor.dtensor4

:param input: symbolic image tensor, of shape image_shape

:type filter_shape: tuple or list of length 4

:param filter_shape: (number of filters, num input feature maps,

filter height, filter width)

:type image_shape: tuple or list of length 4

:param image_shape: (batch size, num input feature maps,

image height, image width)

:type poolsize: tuple or list of length 2

:param poolsize: the downsampling (pooling) factor (#rows, #cols)

"""

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 = conv2d(

input=input,

filters=self.W,

filter_shape=filter_shape,

input_shape=image_shape

)

# pool each feature map individually, using maxpooling

pooled_out = pool.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

self.params = [self.W, self.b]

# keep track of model input

self.input = input

def evaluate_lenet5(learning_rate=0.1, n_epochs=200,

dataset='mnist.pkl.gz',

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

""" Demonstrates lenet on MNIST dataset

:type learning_rate: float

:param learning_rate: learning rate used (factor for the stochastic

gradient)

:type n_epochs: int

:param n_epochs: maximal number of epochs to run the optimizer

:type dataset: string

:param dataset: path to the dataset used for training /testing (MNIST here)

:type nkerns: list of ints

:param nkerns: number of kernels on each layer

"""

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

# start-snippet-1

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

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

# 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

# (28, 28) is the size of MNIST images.

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 (batch_size, 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 (batch_size, nkerns[1] * 4 * 4),

# or (500, 50 * 4 * 4) = (500, 800) with the default values.

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 = [

(param_i, param_i - learning_rate * grad_i)

for param_i, grad_i in zip(params, grads)

]

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]

}

)

# end-snippet-1

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

# 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_validation_loss = numpy.inf

best_iter = 0

test_score = 0.

start_time = timeit.default_timer()

epoch = 0

done_looping = False

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

epoch = epoch + 1

for minibatch_index in range(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 range(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 range(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 = timeit.default_timer()

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(('The code for file ' +

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

' ran for %.2fm' % ((end_time - start_time) / 60.)), file=sys.stderr)

if __name__ == '__main__':

evaluate_lenet5()

def experiment(state, channel):

evaluate_lenet5(state.learning_rate, dataset=state.dataset)