Book Image

Python Deep Learning - Third Edition

By : Ivan Vasilev
4 (1)
Book Image

Python Deep Learning - Third Edition

4 (1)
By: Ivan Vasilev

Overview of this book

The field of deep learning has developed rapidly recently and today covers a broad range of applications. This makes it challenging to navigate and hard to understand without solid foundations. This book will guide you from the basics of neural networks to the state-of-the-art large language models in use today. The first part of the book introduces the main machine learning concepts and paradigms. It covers the mathematical foundations, the structure, and the training algorithms of neural networks and dives into the essence of deep learning. The second part of the book introduces convolutional networks for computer vision. We’ll learn how to solve image classification, object detection, instance segmentation, and image generation tasks. The third part focuses on the attention mechanism and transformers – the core network architecture of large language models. We’ll discuss new types of advanced tasks they can solve, such as chatbots and text-to-image generation. By the end of this book, you’ll have a thorough understanding of the inner workings of deep neural networks. You'll have the ability to develop new models and adapt existing ones to solve your tasks. You’ll also have sufficient understanding to continue your research and stay up to date with the latest advancements in the field.
Table of Contents (17 chapters)
1
Part 1:Introduction to Neural Networks
5
Part 2: Deep Neural Networks for Computer Vision
8
Part 3: Natural Language Processing and Transformers
13
Part 4: Developing and Deploying Deep Neural Networks

The math of NNs

In the following few sections, we’ll discuss the mathematical principles of NNs. This way, we’ll be able to explain NNs through these very principles in a fundamental and structured way.

Linear algebra

Linear algebra deals with objects such as vectors and matrices, linear transformations, and linear equations such as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>…</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>.

Linear algebra identifies the following mathematical objects:

  • Scalar: A single number.
  • Vector: A one-dimensional array of numbers (also known as components or scalars), where each element has an index. We can denote vectors either with a superscript arrow (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mover><mi>x</mi><mo stretchy="true">→</mo></mover></mrow></math>) or in bold (x), but we’ll mostly use the bold notation throughout the book. The following is an example of a vector:

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" display="block"><mml:mi mathvariant="bold">x</mml:mi><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mfenced open="[" close="]" separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>…</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:math>

We can represent a n-dimensional vector as the coordinates of a point in an n-dimensional Euclidean space, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>. Think of Euclidean space as a coordinate system – the vector starts at the center of that system, and each of the...