# Preface¶

Just a few years ago, there were no legions of deep learning scientists developing intelligent products and services at major companies and startups. When we entered the field, machine learning did not command headlines in daily newspapers. Our parents had no idea what machine learning was, let alone why we might prefer it to a career in medicine or law. Machine learning was a blue skies academic discipline whose industrial significance was limited to a narrow set of real-world applications, including speech recognition and computer vision. Moreover, many of these applications required so much domain knowledge that they were often regarded as entirely separate areas for which machine learning was one small component. At that time, neural networks—the predecessors of the deep learning methods that we focus on in this book—were generally regarded as outmoded.

In just the past few years, deep learning has taken the world by surprise, driving rapid progress in such diverse fields as computer vision, natural language processing, automatic speech recognition, reinforcement learning, and biomedical informatics. Moreover, the success of deep learning on so many tasks of practical interest has even catalyzed developments in theoretical machine learning and statistics. With these advances in hand, we can now build cars that drive themselves with more autonomy than ever before (and less autonomy than some companies might have you believe), smart reply systems that automatically draft the most mundane emails, helping people dig out from oppressively large inboxes, and software agents that dominate the world’s best humans at board games like Go, a feat once thought to be decades away. Already, these tools exert ever-wider impacts on industry and society, changing the way movies are made, diseases are diagnosed, and playing a growing role in basic sciences—from astrophysics to biology.

## About This Book¶

This book represents our attempt to make deep learning approachable,
teaching you the *concepts*, the *context*, and the *code*.

### One Medium Combining Code, Math, and HTML¶

For any computing technology to reach its full impact, it must be well-understood, well-documented, and supported by mature, well-maintained tools. The key ideas should be clearly distilled, minimizing the onboarding time needing to bring new practitioners up to date. Mature libraries should automate common tasks, and exemplar code should make it easy for practitioners to modify, apply, and extend common applications to suit their needs. Take dynamic web applications as an example. Despite a large number of companies, like Amazon, developing successful database-driven web applications in the 1990s, the potential of this technology to aid creative entrepreneurs has been realized to a far greater degree in the past ten years, owing in part to the development of powerful, well-documented frameworks.

Testing the potential of deep learning presents unique challenges because any single application brings together various disciplines. Applying deep learning requires simultaneously understanding (i) the motivations for casting a problem in a particular way; (ii) the mathematical form of a given model; (iii) the optimization algorithms for fitting the models to data; (iv) the statistical principles that tell us when we should expect our models to generalize to unseen data and practical methods for certifying that they have, in fact, generalized; and (v) the engineering techniques required to train models efficiently, navigating the pitfalls of numerical computing and getting the most out of available hardware. Teaching both the critical thinking skills required to formulate problems, the mathematics to solve them, and the software tools to implement those solutions all in one place presents formidable challenges. Our goal in this book is to present a unified resource to bring would-be practitioners up to speed.

When we started this book project, there were no resources that
simultaneously (i) remained up to date; (ii) covered the breadth of
modern machine learning practices with sufficient technical depth; and
(iii) interleaved exposition of the quality one expects of a textbook
with the clean runnable code that one expects of a hands-on tutorial. We
found plenty of code examples for how to use a given deep learning
framework (e.g., how to do basic numerical computing with matrices in
TensorFlow) or for implementing particular techniques (e.g., code
snippets for LeNet, AlexNet, ResNet, etc.) scattered across various blog
posts and GitHub repositories. However, these examples typically focused
on *how* to implement a given approach, but left out the discussion of
*why* certain algorithmic decisions are made. While some interactive
resources have popped up sporadically to address a particular topic,
e.g., the engaging blog posts published on the website
Distill, or personal blogs, they only covered
selected topics in deep learning, and often lacked associated code. On
the other hand, while several deep learning textbooks have
emerged—e.g., (Goodfellow *et al.*, 2016), which offers
a comprehensive survey on the basics of deep learning—these resources
do not marry the descriptions to realizations of the concepts in code,
sometimes leaving readers clueless as to how to implement them.
Moreover, too many resources are hidden behind the paywalls of
commercial course providers.

We set out to create a resource that could (i) be freely available for
everyone; (ii) offer sufficient technical depth to provide a starting
point on the path to actually becoming an applied machine learning
scientist; (iii) include runnable code, showing readers *how* to solve
problems in practice; (iv) allow for rapid updates, both by us and also
by the community at large; and (v) be complemented by a
forum for interactive discussion of
technical details and to answer questions.

These goals were often in conflict. Equations, theorems, and citations
are best managed and laid out in LaTeX. Code is best described in
Python. And webpages are native in HTML and JavaScript. Furthermore, we
want the content to be accessible both as executable code, as a physical
book, as a downloadable PDF, and on the Internet as a website. No
workflows seemed suited to these demands, so we decided to assemble our
own (Section 20.6). We settled on GitHub to share
the source and to facilitate community contributions; Jupyter notebooks
for mixing code, equations and text; Sphinx as a rendering engine; and
Discourse as a discussion platform. While our system is not perfect,
these choices strike a compromise among the competing concerns. We
believe that *Dive into Deep Learning* might be the first book published
using such an integrated workflow.

### Learning by Doing¶

Many textbooks present concepts in succession, covering each in exhaustive detail. For example, Chris Bishop’s excellent textbook (Bishop, 2006), teaches each topic so thoroughly that getting to the chapter on linear regression requires a non-trivial amount of work. While experts love this book precisely for its thoroughness, for true beginners, this property limits its usefulness as an introductory text.

In this book, we teach most concepts *just in time*. In other words, you
will learn concepts at the very moment that they are needed to
accomplish some practical end. While we take some time at the outset to
teach fundamental preliminaries, like linear algebra and probability, we
want you to taste the satisfaction of training your first model before
worrying about more esoteric concepts.

Aside from a few preliminary notebooks that provide a crash course in
the basic mathematical background, each subsequent chapter introduces
both a reasonable number of new concepts and provides several
self-contained working examples, using real datasets. This presented an
organizational challenge. Some models might logically be grouped
together in a single notebook. And some ideas might be best taught by
executing several models in succession. On the other hand, there is a
big advantage to adhering to a policy of *one working example, one
notebook*: This makes it as easy as possible for you to start your own
research projects by leveraging our code. Just copy a notebook and start
modifying it.

Throughout, we interleave the runnable code with background material as
needed. In general, we err on the side of making tools available before
explaining them fully (often filling in the background later). For
instance, we might use *stochastic gradient descent* before explaining
why it is useful or offering intuitions for why it works. This helps to
give practitioners the necessary ammunition to solve problems quickly,
at the expense of requiring the reader to trust us with some curatorial
decisions.

This book teaches deep learning concepts from scratch. Sometimes, we delve into fine details about models that would typically be hidden from users by modern deep learning frameworks. This comes up especially in the basic tutorials, where we want you to understand everything that happens in a given layer or optimizer. In these cases, we often present two versions of the example: one where we implement everything from scratch, relying only on NumPy-like functionality and automatic differentiation, and a more practical example, where we write succinct code using the high-level APIs of deep learning frameworks. After explaining how some component works, we rely on the high-level API in subsequent tutorials.

### Content and Structure¶

The book can be divided into roughly three parts, focusing on preliminaries, deep learning techniques, and advanced topics focused on real systems and applications (Fig. 1).

**Part 1: Basics and Preliminaries.**Section 1 offers an introduction to deep learning. Then, in Section 2, we quickly bring you up to speed on the prerequisites required for hands-on deep learning, such as how to store and manipulate data, and how to apply various numerical operations based on basic concepts from linear algebra, calculus, and probability. Section 3 and Section 5 cover the most basic concepts and techniques in deep learning, including regression and classification; linear models; multilayer perceptrons; and overfitting and regularization.**Part 2: Modern Deep Learning Techniques.**Section 6 describes the key computational components of deep learning systems and lays the groundwork for our subsequent implementations of more complex models. Next, Section 7 and Section 8 introduce convolutional neural networks (CNNs), powerful tools that form the backbone of most modern computer vision systems. Similarly, Section 9 and Section 10 introduce recurrent neural networks (RNNs), models that exploit sequential (e.g., temporal) structure in data and are commonly used for natural language processing and time series prediction. In Section 11, we introduce a relatively new class of models based on so-called*attention mechanisms*that has displaced RNNs as the dominant architecture for most natural language processing tasks. These sections will bring you up to speed on the most powerful and general tools that are widely used by deep learning practitioners.**Part 3: Scalability, Efficiency, and Applications.**In Section 12, we discuss several common optimization algorithms used to train deep learning models. Next, in Section 13, we examine several key factors that influence the computational performance of deep learning code. Then, in Section 14, we illustrate major applications of deep learning in computer vision. Finally, in Section 15 and Section 16, we demonstrate how to pretrain language representation models and apply them to natural language processing tasks. This part is available online.

### Code¶

Most sections of this book feature executable code. We believe that some intuitions are best developed via trial and error, tweaking the code in small ways and observing the results. Ideally, an elegant mathematical theory might tell us precisely how to tweak our code to achieve a desired result. However, deep learning practitioners today must often tread where no solid theory provides guidance. Despite our best attempts, formal explanations for the efficacy of various techniques are still lacking, both because the mathematics to characterize these models can be so difficult, because the explanation likely depends on properties of the data that currently lack clear definitions, and because serious inquiry on these topics has just recently kicked into high gear. We are hopeful that as the theory of deep learning progresses, each future edition of this book will provide insights that eclipse those presently available.

To avoid unnecessary repetition, we encapsulate some of our most
frequently imported and used functions and classes in the `d2l`

package. Throughout, we mark blocks of code (such as functions, classes,
or collection of import statements) with `#@save`

to indicate that
they will be accessed later via the `d2l`

package. We offer a detailed
overview of these functions and classes in Section 20.8. The
`d2l`

package is lightweight and only requires the following
dependencies:

```
#@save
import collections
import hashlib
import inspect
import math
import os
import random
import re
import shutil
import sys
import tarfile
import time
import zipfile
from collections import defaultdict
import pandas as pd
import requests
from IPython import display
from matplotlib import pyplot as plt
from matplotlib_inline import backend_inline
d2l = sys.modules[__name__]
```

Most of the code in this book is based on PyTorch, an extremely popular
open-source framework that has been enthusiastically embraced by the
deep learning research community. All of the code in this book has
passed tests under the latest stable version of PyTorch. However, due to
the rapid development of deep learning, some code *in the print edition*
may not work properly in future versions of PyTorch. We plan to keep the
online version up-to-date. In case you encounter any problems, please
consult Installation to update your code and runtime
environment.

Here is how we import modules from PyTorch.

```
#@save
import numpy as np
import torch
import torchvision
from PIL import Image
from torch import nn
from torch.nn import functional as F
from torch.utils import data
from torchvision import transforms
```

```
#@save
import collections
import hashlib
import inspect
import math
import os
import random
import re
import shutil
import sys
import tarfile
import time
import zipfile
from collections import defaultdict
import pandas as pd
import requests
from IPython import display
from matplotlib import pyplot as plt
from matplotlib_inline import backend_inline
d2l = sys.modules[__name__]
```

Most of the code in this book is based on Apache MXNet, an open-source
framework for deep learning that is the preferred choice of AWS (Amazon
Web Services), as well as many colleges and companies. All of the code
in this book has passed tests under the newest MXNet version. However,
due to the rapid development of deep learning, some code *in the print
edition* may not work properly in future versions of MXNet. We plan to
keep the online version up-to-date. In case you encounter any problems,
please consult Installation to update your code and
runtime environment.

Here is how we import modules from MXNet.

```
#@save
from mxnet import autograd, context, gluon, image, init, np, npx
from mxnet.gluon import nn, rnn
```

```
#@save
import collections
import hashlib
import inspect
import math
import os
import random
import re
import shutil
import sys
import tarfile
import time
import zipfile
from collections import defaultdict
import pandas as pd
import requests
from IPython import display
from matplotlib import pyplot as plt
from matplotlib_inline import backend_inline
d2l = sys.modules[__name__]
```

Most of the code in this book is based on TensorFlow, an open-source
framework for deep learning that is widely adopted in industry and
popular among researchers. All of the code in this book has passed tests
under the latest stable version TensorFlow. However, due to the rapid
development of deep learning, some code *in the print edition* may not
work properly in future versions of TensorFlow. We plan to keep the
online version up-to-date. In case you encounter any problems, please
consult Installation to update your code and runtime
environment.

Here is how we import modules from TensorFlow.

```
#@save
import numpy as np
import tensorflow as tf
```

### Target Audience¶

This book is for students (undergraduate or graduate), engineers, and researchers, who seek a solid grasp of the practical techniques of deep learning. Because we explain every concept from scratch, no previous background in deep learning or machine learning is required. Fully explaining the methods of deep learning requires some mathematics and programming, but we will only assume that you come in with some basics, including modest amounts of linear algebra, calculus, probability, and Python programming. Just in case you forget the basics, the Appendix provides a refresher on most of the mathematics you will find in this book. Most of the time, we will prioritize intuition and ideas over mathematical rigor. If you would like to extend these foundations beyond the prerequisites to understand our book, we happily recommend some other terrific resources: Linear Analysis by Bela Bollobas (Bollobás, 1999) covers linear algebra and functional analysis in great depth. All of Statistics (Wasserman, 2013) provides a marvelous introduction to statistics. Joe Blitzstein’s books and courses on probability and inference are pedagogical gems. And if you have not used Python before, you may want to peruse this Python tutorial.

### Forum¶

Associated with this book, we have launched a discussion forum, located at discuss.d2l.ai. When you have questions on any section of the book, you can find a link to the associated discussion page at the end of each notebook.

## Acknowledgments¶

We are indebted to the hundreds of contributors for both the English and the Chinese drafts. They helped improve the content and offered valuable feedback. Specifically, we thank every contributor of this English draft for making it better for everyone. Their GitHub IDs or names are (in no particular order): alxnorden, avinashingit, bowen0701, brettkoonce, Chaitanya Prakash Bapat, cryptonaut, Davide Fiocco, edgarroman, gkutiel, John Mitro, Liang Pu, Rahul Agarwal, Mohamed Ali Jamaoui, Michael (Stu) Stewart, Mike Müller, NRauschmayr, Prakhar Srivastav, sad-, sfermigier, Sheng Zha, sundeepteki, topecongiro, tpdi, vermicelli, Vishaal Kapoor, Vishwesh Ravi Shrimali, YaYaB, Yuhong Chen, Evgeniy Smirnov, lgov, Simon Corston-Oliver, Igor Dzreyev, Ha Nguyen, pmuens, Andrei Lukovenko, senorcinco, vfdev-5, dsweet, Mohammad Mahdi Rahimi, Abhishek Gupta, uwsd, DomKM, Lisa Oakley, Bowen Li, Aarush Ahuja, Prasanth Buddareddygari, brianhendee, mani2106, mtn, lkevinzc, caojilin, Lakshya, Fiete Lüer, Surbhi Vijayvargeeya, Muhyun Kim, dennismalmgren, adursun, Anirudh Dagar, liqingnz, Pedro Larroy, lgov, ati-ozgur, Jun Wu, Matthias Blume, Lin Yuan, geogunow, Josh Gardner, Maximilian Böther, Rakib Islam, Leonard Lausen, Abhinav Upadhyay, rongruosong, Steve Sedlmeyer, Ruslan Baratov, Rafael Schlatter, liusy182, Giannis Pappas, ati-ozgur, qbaza, dchoi77, Adam Gerson, Phuc Le, Mark Atwood, christabella, vn09, Haibin Lin, jjangga0214, RichyChen, noelo, hansent, Giel Dops, dvincent1337, WhiteD3vil, Peter Kulits, codypenta, joseppinilla, ahmaurya, karolszk, heytitle, Peter Goetz, rigtorp, Tiep Vu, sfilip, mlxd, Kale-ab Tessera, Sanjar Adilov, MatteoFerrara, hsneto, Katarzyna Biesialska, Gregory Bruss, Duy–Thanh Doan, paulaurel, graytowne, Duc Pham, sl7423, Jaedong Hwang, Yida Wang, cys4, clhm, Jean Kaddour, austinmw, trebeljahr, tbaums, Cuong V. Nguyen, pavelkomarov, vzlamal, NotAnotherSystem, J-Arun-Mani, jancio, eldarkurtic, the-great-shazbot, doctorcolossus, gducharme, cclauss, Daniel-Mietchen, hoonose, biagiom, abhinavsp0730, jonathanhrandall, ysraell, Nodar Okroshiashvili, UgurKap, Jiyang Kang, StevenJokes, Tomer Kaftan, liweiwp, netyster, ypandya, NishantTharani, heiligerl, SportsTHU, Hoa Nguyen, manuel-arno-korfmann-webentwicklung, aterzis-personal, nxby, Xiaoting He, Josiah Yoder, mathresearch, mzz2017, jroberayalas, iluu, ghejc, BSharmi, vkramdev, simonwardjones, LakshKD, TalNeoran, djliden, Nikhil95, Oren Barkan, guoweis, haozhu233, pratikhack, Yue Ying, tayfununal, steinsag, charleybeller, Andrew Lumsdaine, Jiekui Zhang, Deepak Pathak, Florian Donhauser, Tim Gates, Adriaan Tijsseling, Ron Medina, Gaurav Saha, Murat Semerci, Lei Mao, Levi McClenny, Joshua Broyde, jake221, jonbally, zyhazwraith, Brian Pulfer, Nick Tomasino, Lefan Zhang, Hongshen Yang, Vinney Cavallo, yuntai, Yuanxiang Zhu, amarazov, pasricha, Ben Greenawald, Shivam Upadhyay, Quanshangze Du, Biswajit Sahoo, Parthe Pandit, Ishan Kumar, HomunculusK, Lane Schwartz, varadgunjal, Jason Wiener, Armin Gholampoor, Shreshtha13, eigen-arnav, Hyeonggyu Kim, EmilyOng, Bálint Mucsányi, Chase DuBois, Juntian Tao, Wenxiang Xu, Lifu Huang, filevich, quake2005, nils-werner, Yiming Li, Marsel Khisamutdinov, Francesco “Fuma” Fumagalli, Peilin Sun, Vincent Gurgul, qingfengtommy, Janmey Shukla, Mo Shan, Kaan Sancak, regob, AlexSauer, Gopalakrishna Ramachandra, Tobias Uelwer, Chao Wang, Tian Cao, Nicolas Corthorn, akash5474, kxxt, zxydi1992, Jacob Britton, Shuangchi He, zhmou, krahets, Jie-Han Chen, Atishay Garg, Marcel Flygare, adtygan, Nik Vaessen, bolded, Louis Schlessinger, Balaji Varatharajan, atgctg, Kaixin Li, Victor Barbaros, Riccardo Musto, Elizabeth Ho, azimjonn, Guilherme Miotto, Alessandro Finamore, Joji Joseph, Anthony Biel, Zeming Zhao.

We thank Amazon Web Services, especially Swami Sivasubramanian, Peter DeSantis, Adam Selipsky, and Andrew Jassy for their generous support in writing this book. Without the available time, resources, discussions with colleagues, and continuous encouragement, this book would not have happened.

## Summary¶

Deep learning has revolutionized pattern recognition, introducing technology that now powers a wide range of technologies, in such diverse fields as computer vision, natural language processing, and automatic speech recognition. To successfully apply deep learning, you must understand how to cast a problem, the basic mathematics of modeling, the algorithms for fitting your models to data, and the engineering techniques to implement it all. This book presents a comprehensive resource, including prose, figures, mathematics, and code, all in one place. To ask (or answer) questions related to this book, visit our forum at https://discuss.d2l.ai/. All of our notebooks are available for download on the D2L.ai website and on GitHub.

## Exercises¶

Register an account on the discussion forum of this book discuss.d2l.ai.

Install Python on your computer.

Follow the links at the bottom of the section to the forum, where you will be able to seek out help and discuss the book and find answers to your questions by engaging the authors and broader community.