Book Image

Hands-On Mathematics for Deep Learning

By : Jay Dawani
Book Image

Hands-On Mathematics for Deep Learning

By: Jay Dawani

Overview of this book

Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL.
Table of Contents (19 chapters)
1
Section 1: Essential Mathematics for Deep Learning
7
Section 2: Essential Neural Networks
13
Section 3: Advanced Deep Learning Concepts Simplified

Linear Algebra

In this chapter, we will be covering the main concepts of linear algebra, and the concepts learned here will serve as the backbone on which we will learn all the concepts in the chapters to come, so it is important that you pay attention.

It is very important for you to know that these chapters cannot be substituted for an education in mathematics; they exist merely to help you better grasp the concepts of deep learning and how various architectures work and to develop an intuition for why that is, so you can become a better practitioner in the field.

At its core, algebra is nothing more than the study of mathematical symbols and the rules for manipulating these symbols. The field of algebra acts as a unifier for all of mathematics and provides us with a way of thinking. Instead of using numbers, we use letters to represent variables.

Linear algebra, however, concerns only linear transformations and vector spaces. It allows us to represent information through vectors, matrices, and tensors, and having a good understanding of linear algebra will take you a long way on your journey toward getting a very strong understanding of deep learning. It is said that a mathematical problem can only be solved if it can be reduced to a calculation in linear algebra. This speaks to the power and usefulness of linear algebra.

This chapter will cover the following topics:

  • Comparing scalars and vectors
  • Linear equations
  • Matrix operations
  • Vector spaces and subspaces
  • Linear maps
  • Matrix decompositions