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Home > Data > Deep Learning > Deep Learning with Theano
Deep Learning with Theano
Deep Learning with Theano

Deep Learning with Theano: Perform large-scale numerical and scientific computations efficiently

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Deep Learning with Theano

Chapter 2. Classifying Handwritten Digits with a Feedforward Network

The first chapter presented Theano as a compute engine, with its different functions and specificities. With this knowledge, we'll go through an example and introduce some of the main concepts of deep learning, building three neural networks and training them on the problem of handwritten digit classification.

Deep learning is a field of machine learning in which layers of modules are stacked on top of each of other: this chapter introduces a simple single-linear-layer model, then adds a second layer on top of it to create a multi-layer perceptron (MLP), and last uses multiple convolutional layers to create a Convolutional Neural Network (CNN).

In the meantime, this chapter recaps the basic machine learning concepts, such as overfitting, validation, and loss analysis, for those who are not familiar with data science:

  • Small image classification
  • Handwritten digit recognition challenge
  • Layer design to build a neural...

The MNIST dataset

The Modified National Institute of Standards and Technology (MNIST) dataset is a very well-known dataset of handwritten digits {0,1,2,3,4,5,6,7,8,9} used to train and test classification models.

A classification model is a model that predicts the probabilities of observing a class, given an input.

Training is the task of learning the parameters to fit the model to the data as well as we can so that for any input image, the correct label is predicted. For this training task, the MNIST dataset contains 60,000 images with a target label (a number between 0 and 9) for each example.

To validate that the training is efficient and to decide when to stop the training, we usually split the training dataset into two datasets: 80% to 90% of the images are used for training, while the remaining 10-20% of images will not be presented to the algorithm for training but to validate that the model generalizes well on unobserved data.

There is a separate dataset that the algorithm should never...

Structure of a training program

The structure of a training program always consists of the following steps:

  1. Set the script environment: Such as package imports, the use of the GPU, and so on.
  2. Load data: A data loader class to access the data during training, usually in a random order to avoid too many similar examples of the same class, but sometimes in a precise order, for example, in the case of curriculum learning with simple examples first and complex ones last.
  3. Preprocess the data: A set of transformations, such as swapping dimensions on images, adding blur or noise. It is very common to add some data augmentation transformations, such as random crop, scale, brightness, or contrast jittering to get more examples than the original ones, and reduce the risk of overfitting on data. If the number of free parameters in the model is too important with respect to the training dataset size, the model might learn from the available examples. Also, if the dataset is too small and too many iterations...

Classification loss function

The loss function is an objective function to minimize during training to get the best model. Many different loss functions exist.

In a classification problem, where the target is to predict the correct class among k classes, cross-entropy is commonly used as it measures the difference between the real probability distribution, q, and the predicted one, p, for each class:

Classification loss function

Here, i is the index of the sample in the dataset, n is the number of samples in the dataset, and k is the number of classes.

While the real probability Classification loss function of each class is unknown, it can simply be approximated in practice by the empirical distribution, that is, randomly drawing a sample out of the dataset in the dataset order. The same way, the cross-entropy of any predicted probability, p, can be approximated by the empirical cross-entropy:

Classification loss function

Here, Classification loss function is the probability estimated by the model for the correct class of example Classification loss function.

Accuracy and cross-entropy both evolve in the same direction but measure...

Single-layer linear model

The simplest model is the linear model, where for each class c, the output is a linear combination of the input values:

Single-layer linear model

This output is unbounded.

To get a probability distribution, pi, that sums to 1, the output of the linear model is passed into a softmax function:

Single-layer linear model

Hence, the estimated probability of class c for an input x is rewritten with vectors:

Single-layer linear model

Translated in Python with:

batch_size = 600
n_in = 28 * 28
n_out = 10

x = T.matrix('x')
y = T.ivector('y')
W = theano.shared(
            value=numpy.zeros(
                (n_in, n_out),
                dtype=theano.config.floatX
            ),
            name='W',
            borrow=True
        )
b = theano.shared(
    value=numpy.zeros(
        (n_out,),
        dtype=theano.config.floatX
    ),
    name='b',
    borrow=True
)
model = T.nnet.softmax(T.dot(x, W) + b)

The prediction for a given input is given by the most probable class (maximum probability):

y_pred = T.argmax(model...

Cost function and errors

The cost function given the predicted probabilities by the model is as follows:

cost = -T.mean(T.log(model)[T.arange(y.shape[0]), y])

The error is the number of predictions that are different from the true class, averaged by the total number of values, which can be written as a mean:

error = T.mean(T.neq(y_pred, y))

On the contrary, accuracy corresponds to the number of correct predictions divided by the total number of predictions. The sum of error and accuracy is one.

For other types of problems, here are a few other loss functions and implementations:

Categorical cross entropy

An equivalent implementation of ours

 

T.nnet.categorical_crossentropy(model, y_true).mean()

Binary cross entropy

For the case when output can take only two values {0,1}

Typically used after a sigmoid activation predicting the probability, p

T.nnet.binary_crossentropy(model, y_true).mean()

Mean squared error

L2 norm for regression problems

T.sqr(model – y_true).mean()

Mean absolute...

The MNIST dataset

The Modified National Institute of Standards and Technology (MNIST) dataset is a very well-known dataset of handwritten digits {0,1,2,3,4,5,6,7,8,9} used to train and test classification models.

A classification model is a model that predicts the probabilities of observing a class, given an input.

Training is the task of learning the parameters to fit the model to the data as well as we can so that for any input image, the correct label is predicted. For this training task, the MNIST dataset contains 60,000 images with a target label (a number between 0 and 9) for each example.

To validate that the training is efficient and to decide when to stop the training, we usually split the training dataset into two datasets: 80% to 90% of the images are used for training, while the remaining 10-20% of images will not be presented to the algorithm for training but to validate that the model generalizes well on unobserved data.

There is a separate dataset that the algorithm should never...

Structure of a training program

The structure of a training program always consists of the following steps:

  1. Set the script environment: Such as package imports, the use of the GPU, and so on.

  2. Load data: A data loader class to access the data during training, usually in a random order to avoid too many similar examples of the same class, but sometimes in a precise order, for example, in the case of curriculum learning with simple examples first and complex ones last.

  3. Preprocess the data: A set of transformations, such as swapping dimensions on images, adding blur or noise. It is very common to add some data augmentation transformations, such as random crop, scale, brightness, or contrast jittering to get more examples than the original ones, and reduce the risk of overfitting on data. If the number of free parameters in the model is too important with respect to the training dataset size, the model might learn from the available examples. Also, if the dataset is too small and too many iterations...

Classification loss function

The loss function is an objective function to minimize during training to get the best model. Many different loss functions exist.

In a classification problem, where the target is to predict the correct class among k classes, cross-entropy is commonly used as it measures the difference between the real probability distribution, q, and the predicted one, p, for each class:

Here, i is the index of the sample in the dataset, n is the number of samples in the dataset, and k is the number of classes.

While the real probability of each class is unknown, it can simply be approximated in practice by the empirical distribution, that is, randomly drawing a sample out of the dataset in the dataset order. The same way, the cross-entropy of any predicted probability, p, can be approximated by the empirical cross-entropy:

Here, is the probability estimated by the model for the correct class of example .

Accuracy and cross-entropy both evolve in the same direction but measure...

Single-layer linear model

The simplest model is the linear model, where for each class c, the output is a linear combination of the input values:

This output is unbounded.

To get a probability distribution, pi, that sums to 1, the output of the linear model is passed into a softmax function:

Hence, the estimated probability of class c for an input x is rewritten with vectors:

Translated in Python with:

batch_size = 600
n_in = 28 * 28
n_out = 10

x = T.matrix('x')
y = T.ivector('y')
W = theano.shared(
            value=numpy.zeros(
                (n_in, n_out),
                dtype=theano.config.floatX
            ),
            name='W',
            borrow=True
        )
b = theano.shared(
    value=numpy.zeros(
        (n_out,),
        dtype=theano.config.floatX
    ),
    name='b',
    borrow=True
)
model = T.nnet.softmax(T.dot(x, W) + b)

The prediction for a given input is given by the most probable class (maximum probability):

y_pred = T.argmax(model, axis=1)

In this model with a single linear...

Cost function and errors

The cost function given the predicted probabilities by the model is as follows:

cost = -T.mean(T.log(model)[T.arange(y.shape[0]), y])

The error is the number of predictions that are different from the true class, averaged by the total number of values, which can be written as a mean:

error = T.mean(T.neq(y_pred, y))

On the contrary, accuracy corresponds to the number of correct predictions divided by the total number of predictions. The sum of error and accuracy is one.

For other types of problems, here are a few other loss functions and implementations:

Categorical cross entropy

An equivalent implementation of ours

 

T.nnet.categorical_crossentropy(model, y_true).mean()

Binary cross entropy

For the case when output can take only two values {0,1}

Typically used after a sigmoid activation predicting the probability, p

T.nnet.binary_crossentropy(model, y_true).mean()

Mean squared error

L2 norm for regression problems

T.sqr(model – y_true).mean()

Mean absolute...

Backpropagation and stochastic gradient descent

Backpropagation, or the backward propagation of errors, is the most commonly used supervised learning algorithm for adapting the connection weights.

Considering the error or the cost as a function of the weights W and b, a local minimum of the cost function can be approached with a gradient descent, which consists of changing weights along the negative error gradient:

Here, is the learning rate, a positive constant defining the speed of a descent.

The following compiled function updates the variables after each feedforward run:

g_W = T.grad(cost=cost, wrt=W)
g_b = T.grad(cost=cost, wrt=b)

learning_rate=0.13
index = T.lscalar()

train_model = theano.function(
    inputs=[index],
    outputs=[cost,error],
    updates=[(W, W - learning_rate * g_W),(b, b - learning_rate * g_b)],
    givens={
        x: train_set_x[index * batch_size: (index + 1) * batch_size],
        y: train_set_y[index * batch_size: (index + 1) * batch_size]
    }
)

The input variable...

Multiple layer model

A multi-layer perceptron (MLP) is a feedforward net with multiple layers. A second linear layer, named hidden layer, is added to the previous example:

Having two linear layers following each other is equivalent to having a single linear layer.

With a non-linear function or non-linearity or transfer function between the linearities, the model does not simplify into a linear one any more, and represents more possible functions in order to capture more complex patterns in the data:

Activation functions helps saturating (ON-OFF) and reproduces the biological neuron activations.

The Rectified Linear Unit (ReLU) graph is given as follows:

(x + T.abs_(x)) / 2.0

The Leaky Rectifier Linear Unit (Leaky ReLU) graph is given as follows:

( (1 + leak) * x + (1 – leak) * T.abs_(x) ) / 2.0

Here, leak is a parameter that defines the slope in the negative values. In leaky rectifiers, this parameter is fixed.

The activation named PReLU considers the leak parameter to be learned.

More generally...

Convolutions and max layers

A great improvement in image classification has been achieved with the invention of the convolutional layers on the MNIST database:

While previous fully-connected layers perform a computation with all input values (pixels in the case of an image) of the input, a 2D convolution layer will consider only a small patch or window or receptive field of NxN pixels of the 2D input image for each output unit. The dimensions of the patch are named kernel dimensions, N is the kernel size, and the coefficients/parameters are the kernel.

At each position of the input image, the kernel produces a scalar, and all position values will lead to a matrix (2D tensor) called a feature map. Convolving the kernel on the input image as a sliding window creates a new output image. The stride of the kernel defines the number of pixels to shift the patch/window over the image: with a stride of 2, the convolution with the kernel is computed every 2 pixels.

For example, on a 224 x 224 input...

Training

In order to get a good measure of how the model behaves on data that's unseen during training, the validation dataset is used to compute a validation loss and accuracy during training.

The validation dataset enables us to choose the best model, while the test dataset is only used at the end to get the final test accuracy/error of the model. The training, test, and validation datasets are discrete datasets, with no common examples. The validation dataset is usually 10 times smaller than the test dataset to slow the training process as little as possible. The test dataset is usually around 10-20% of the training dataset. Both the training and validation datasets are part of the training program, since the first one is used to learn, and the second is used to select the best model on unseen data at training time.

The test dataset is completely outside the training process and is used to get the accuracy of the produced model, resulting from training and model selection.

If the model overfits...

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Key benefits

  • Learn Theano basics and evaluate your mathematical expressions faster and in an efficient manner
  • Learn the design patterns of deep neural architectures to build efficient and powerful networks on your datasets
  • Apply your knowledge to concrete fields such as image classification, object detection, chatbots, machine translation, reinforcement agents, or generative models.

Description

This book offers a complete overview of Deep Learning with Theano, a Python-based library that makes optimizing numerical expressions and deep learning models easy on CPU or GPU. The book provides some practical code examples that help the beginner understand how easy it is to build complex neural networks, while more experimented data scientists will appreciate the reach of the book, addressing supervised and unsupervised learning, generative models, reinforcement learning in the fields of image recognition, natural language processing, or game strategy. The book also discusses image recognition tasks that range from simple digit recognition, image classification, object localization, image segmentation, to image captioning. Natural language processing examples include text generation, chatbots, machine translation, and question answering. The last example deals with generating random data that looks real and solving games such as in the Open-AI gym. At the end, this book sums up the best -performing nets for each task. While early research results were based on deep stacks of neural layers, in particular, convolutional layers, the book presents the principles that improved the efficiency of these architectures, in order to help the reader build new custom nets.

Who is this book for?

This book is indented to provide a full overview of deep learning. From the beginner in deep learning and artificial intelligence, to the data scientist who wants to become familiar with Theano and its supporting libraries, or have an extended understanding of deep neural nets. Some basic skills in Python programming and computer science will help, as well as skills in elementary algebra and calculus.

What you will learn

  • Get familiar with Theano and deep learning
  • Provide examples in supervised, unsupervised, generative, or reinforcement learning.
  • Discover the main principles for designing efficient deep learning nets: convolutions, residual connections, and recurrent connections.
  • Use Theano on real-world computer vision datasets, such as for digit classification and image classification.
  • Extend the use of Theano to natural language processing tasks, for chatbots or machine translation
  • Cover artificial intelligence-driven strategies to enable a robot to solve games or learn from an environment
  • Generate synthetic data that looks real with generative modeling
  • Become familiar with Lasagne and Keras, two frameworks built on top of Theano
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Publication date : Jul 31, 2017
Length: 300 pages
Edition : 1st
Language : English
ISBN-13 : 9781786465825
Vendor :
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Category :
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Concepts :
Deep Learning
Tools :
Theano

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Length: 300 pages
Edition : 1st
Language : English
ISBN-13 : 9781786465825
Vendor :
Google
Category :
Data
Concepts :
Deep Learning
Tools :
Theano

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Table of Contents

14 Chapters
1. Theano Basics Chevron down icon Chevron up icon
1. Theano Basics
The need for tensors
Installing and loading Theano
Tensors
Graphs and symbolic computing
Operations on tensors
Memory and variables
Functions and automatic differentiation
Loops in symbolic computing
Configuration, profiling and debugging
Summary
2. Classifying Handwritten Digits with a Feedforward Network Chevron down icon Chevron up icon
2. Classifying Handwritten Digits with a Feedforward Network
The MNIST dataset
Structure of a training program
Classification loss function
Single-layer linear model
Cost function and errors
Backpropagation and stochastic gradient descent
Multiple layer model
Convolutions and max layers
Training
Dropout
Inference
Optimization and other update rules
Related articles
Summary
3. Encoding Word into Vector Chevron down icon Chevron up icon
3. Encoding Word into Vector
Encoding and embedding
Dataset
Continuous Bag of Words model
Training the model
Visualizing the learned embeddings
Evaluating embeddings – analogical reasoning
Evaluating embeddings – quantitative analysis
Application of word embeddings
Weight tying
Further reading
Summary
4. Generating Text with a Recurrent Neural Net Chevron down icon Chevron up icon
4. Generating Text with a Recurrent Neural Net
Need for RNN
A dataset for natural language
Simple recurrent network
Metrics for natural language performance
Training loss comparison
Example of predictions
Applications of RNN
Related articles
Summary
5. Analyzing Sentiment with a Bidirectional LSTM Chevron down icon Chevron up icon
5. Analyzing Sentiment with a Bidirectional LSTM
Installing and configuring Keras
Preprocessing text data
Designing the architecture for the model
Compiling and training the model
Evaluating the model
Saving and loading the model
Running the example
Further reading
Summary
6. Locating with Spatial Transformer Networks Chevron down icon Chevron up icon
6. Locating with Spatial Transformer Networks
MNIST CNN model with Lasagne
A localization network
Unsupervised learning with co-localization
Region-based localization networks
Further reading
Summary
7. Classifying Images with Residual Networks Chevron down icon Chevron up icon
7. Classifying Images with Residual Networks
Natural image datasets
Residual connections
Stochastic depth
Dense connections
Multi-GPU
Data augmentation
Further reading
Summary
8. Translating and Explaining with Encoding – decoding Networks Chevron down icon Chevron up icon
8. Translating and Explaining with Encoding – decoding Networks
Sequence-to-sequence networks for natural language processing
Seq2seq for translation
Seq2seq for chatbots
Improving efficiency of sequence-to-sequence network
Deconvolutions for images
Multimodal deep learning
Further reading
Summary
9. Selecting Relevant Inputs or Memories with the Mechanism of Attention Chevron down icon Chevron up icon
9. Selecting Relevant Inputs or Memories with the Mechanism of Attention
Differentiable mechanism of attention
Store and retrieve information in Neural Turing Machines
Memory networks
Further reading
Summary
10. Predicting Times Sequences with Advanced RNN Chevron down icon Chevron up icon
10. Predicting Times Sequences with Advanced RNN
Dropout for RNN
Deep approaches for RNN
Stacked recurrent networks
Deep transition recurrent network
Highway networks design principle
Recurrent Highway Networks
Further reading
Summary
11. Learning from the Environment with Reinforcement Chevron down icon Chevron up icon
11. Learning from the Environment with Reinforcement
Reinforcement learning tasks
Simulation environments
Q-learning
Deep Q-network
Training stability
Policy gradients with REINFORCE algorithms
Related articles
Summary
12. Learning Features with Unsupervised Generative Networks Chevron down icon Chevron up icon
12. Learning Features with Unsupervised Generative Networks
Generative models
Semi-supervised learning
Further reading
Summary
13. Extending Deep Learning with Theano Chevron down icon Chevron up icon
13. Extending Deep Learning with Theano
Theano Op in Python for CPU
Theano Op in Python for the GPU
Theano Op in C for CPU
Theano Op in C for GPU
Coalesced transpose via shared memory, NVIDIA parallel for all
The future of artificial intelligence
Further reading
Summary
Index Chevron down icon Chevron up icon
Index

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RAG-Driven Generative AI
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Hands-On Reinforcement Learning with Python
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Customer reviews

Rating distribution
Full star icon Full star icon Full star icon Half star icon Empty star icon 3.7
(3 Ratings)
5 star 66.7%
4 star 0%
3 star 0%
2 star 0%
1 star 33.3%
Coquard Aurélien Oct 10, 2017
Full star icon Full star icon Full star icon Full star icon Full star icon 5
Don't know where to start with Neural Networks and Deep Learning? Well, here is a perfect starting point, and more ... The walkthrough all Theano concepts is illustrated with really relevant examples and algorithms. Great book! Every student in the domain should have it.
Amazon Verified review Amazon
David Oct 08, 2017
Full star icon Full star icon Full star icon Full star icon Full star icon 5
The dean from my data science graduate program told me about this book, as I am huge fan of PackT publishing. This book provides excellent resources for implementing deep learning algorithms using the Theano library in python. Plus, at the end of each chapter the author has taken the extra step of listing resent articles and publications that are relevant to that particular area of deep learning in each chapter. This one has everything that I needed to prepare to execute a deep learning computer program. It is a great resource, and so far outside of just the technical guide for Theano, there is no other book like it.
Amazon Verified review Amazon
Maciek Aug 03, 2018
Full star icon Empty star icon Empty star icon Empty star icon Empty star icon 1
This book is horrible even by Packt standards. It's full of errors, it's poorly written to the point of being barely comprehensible in some places. It almost feels like this text has been generated by a neural network rather than being written by a human author.
Amazon Verified review Amazon

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About the author

Profile icon Bourez
Bourez
Christopher Bourez graduated from Ecole Polytechnique and Ecole Normale Suprieure de Cachan in Paris in 2005 with a Master of Science in Math, Machine Learning and Computer Vision (MVA). For 7 years, he led a company in computer vision that launched Pixee, a visual recognition application for iPhone in 2007, with the major movie theater brand, the city of Paris and the major ticket broker: with a snap of a picture, the user could get information about events, products, and access to purchase. While working on missions in computer vision with Caffe, TensorFlow or Torch, he helped other developers succeed by writing on a blog on computer science. One of his blog posts, a tutorial on the Caffe deep learning technology, has become the most successful tutorial on the web after the official Caffe website. On the initiative of Packt Publishing, the same recipes that made the success of his Caffe tutorial have been ported to write this book on Theano technology. In the meantime, a wide range of problems for Deep Learning are studied to gain more practice with Theano and its application.
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Shipping Details

USA:

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Economy: Delivery to most addresses in the US within 10-15 business days

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UK:

Economy: Delivery to most addresses in the U.K. within 7-9 business days.
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Add one extra business day for deliveries to Northern Ireland and Scottish Highlands and islands

EU:

Premium: Trackable delivery to most EU destinations within 4-9 business days.

Australia:

Economy: Can deliver to P. O. Boxes and private residences.
Trackable service with delivery to addresses in Australia only.
Delivery time ranges from 7-9 business days for VIC and 8-10 business days for Interstate metro
Delivery time is up to 15 business days for remote areas of WA, NT & QLD.

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Premium: Delivery to most Indian addresses within 5-6 business days

Rest of the World:

Premium: Countries in the American continent: Trackable delivery to most countries within 4-7 business days

Asia:

Premium: Delivery to most Asian addresses within 5-9 business days

Disclaimer:
All orders received before 5 PM U.K time would start printing from the next business day. So the estimated delivery times start from the next day as well. Orders received after 5 PM U.K time (in our internal systems) on a business day or anytime on the weekend will begin printing the second to next business day. For example, an order placed at 11 AM today will begin printing tomorrow, whereas an order placed at 9 PM tonight will begin printing the day after tomorrow.


Unfortunately, due to several restrictions, we are unable to ship to the following countries:

  1. Afghanistan
  2. American Samoa
  3. Belarus
  4. Brunei Darussalam
  5. Central African Republic
  6. The Democratic Republic of Congo
  7. Eritrea
  8. Guinea-bissau
  9. Iran
  10. Lebanon
  11. Libiya Arab Jamahriya
  12. Somalia
  13. Sudan
  14. Russian Federation
  15. Syrian Arab Republic
  16. Ukraine
  17. Venezuela