Hands-On Mathematics for Deep Learning

<Hands-On Mathematics for Deep Learning> ▶What You Will Learn
- Understand the key mathematical concepts for building neural network models
- Discover core multivariable calculus concepts
- Improve the performance of deep learning models using optimization techniques
- Cover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizer
- Understand computational graphs and their importance in DL
- Explore the backpropagation algorithm to reduce output error
- Cover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)

▶Key Features
- Understand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networks
- Learn the mathematical concepts needed to understand how deep learning models function
- Use deep learning for solving problems related to vision, image, text, and sequence applications

▶Who This Book Is For
This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required.

▶What this book covers
- Chapter 1, Linear Algebra, will give you an understanding of the inner workings of linear algebra, which is essential for understanding how deep neural networks work. In particular, you will learn about multi-dimensional linear equations, how matrices are multiplied together, and various methods of decomposing/factorizing matrices. These concepts will be critical for developing an intuition for how forward propagation works in neural networks.

- Chapter 2, Vector Calculus, will cover all the main concepts of calculus, where you will start by learning the fundamentals of single variable calculus and build toward an understanding of multi-variable and ultimately vector calculus. The concepts of this chapter will help you better understand the math that underlies the training process of neural networks, particularly how backpropagation works.

- Chapter 3, Probability and Statistics, will teach you the essentials of both probability and statistics and how they are related to each other. In particular, the focus will be on understanding different types of distributions, the importance of the central limit theorem, and how estimations are made. This chapter is critical to developing an understanding of what exactly it is that neural networks are learning.

- Chapter 4, Optimization, will explain what exactly optimization is and several methods of it that are used in practice, such as least squares, gradient descent, Newton's method, and genetic algorithms. The methods covered in this chapter are essential to understanding how neural networks learn during their training phase.

- Chapter 5, Graph Theory, will teach you about graph theory, which is used to model relationships between objects, and will also help in your understanding of the different types of neural network architectures. Later in the book, the concepts from this chapter will be very useful for understanding how graph neural networks work.

- Chapter 6, Linear Neural Networks, will cover the most basic type of neural network and teach you how a model learns to find linear relationships from data through regression. You will also learn that this type of model has limitations, which is where the need for neural networks arises.

- Chapter 7, Feedforward Neural Networks, will show you how all the concepts covered in the previous chapters are brought together to form modern-day neural networks, including coverage of how they are structured, how and what they learn, and what makes them so powerful.

- Chapter 8, Regularization, will show you the various methods of regularization, such as dropout and norm penalties, that are used extensively in practice to help our models to generalize to test data so that they work well once deployed.

- Chapter 9, Convolutional Neural Networks, will explain CNNs, which are a variant of feedforward neural networks and are particularly effective for tasks related to computer vision, as well as time series analysis.

- Chapter 10, Recurrent Neural Networks, will explain RNNs, which are another variant of feedforward neural networks that have recurrent connections, which gives them the ability to learn relationships in sequences such as those in time series and language.

- Chapter 11, Attention Mechanisms, will show a relatively recent breakthrough in deep learning known as attention. This has led to the creation of transformer models, which have resulted in phenomenal results in tasks related to natural language processing.

- Chapter 12, Generative Models, is where the focus will be switched from neural networks that learn to predict classes given data to models that learn to synthetically create data. You will learn about various models, such as autoencoders, GANs, and flow-based networks.

- Chapter 13, Transfer and Meta Learning, will teach you about two separate but related concepts known as transfer learning and meta learning. Their goals respectively are to transfer what one model has learned to another to help it work on a similar task and to create networks that can use existing knowledge to learn new tasks or learn how to learn.

- Chapter 14, Geometric Deep Learning, will explain another relatively new concept in DL, which extends the power of deep neural networks from the Euclidean domain to the non-Euclidean domain.