Yoshua Bengio的深度学习教材：权威入门指南

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"《深度学习》是由深度学习领域的权威人物Yoshua Bengio与Ian Goodfellow以及Aaron Courville共同编撰的一本教科书。该书是麻省理工学院出版社的作品，专为那些希望进入机器学习领域，特别是深度学习领域的学生和专业人士设计。这本教材具有高度的专业性和实用性，尽管是以英文写作，但因其条理清晰且易于理解，使得非英语母语的学习者也能受益匪浅。在线版的《深度学习》已经完成，并且免费提供访问，这对于全球读者来说是一大福音。纸质版预计即将上市，对最新动态感兴趣的读者可以加入邮件列表获取更新信息。如果你需要引用这本书，建议使用提供的BibTeX引用格式。值得注意的是，由于版权原因，书中并没有可供下载的PDF版本。作者们遵循与MIT Press的合同，限制了电子格式的大规模复制和分发，以保护作品的原创性和完整性。选择HTML格式阅读是出于版权管理的考虑，它作为一种弱形式的数字版权管理，旨在防止未经授权的复制和编辑。对于想将HTML格式打印的读者，官方推荐的打印方式可能会确保最佳的阅读体验。尽管没有明确指出具体方法，通常建议使用支持HTML转换的软件或浏览器选项进行打印，这样可以确保页面布局和格式在印刷品上得到良好呈现。《深度学习》是一本深入浅出的深度学习教程，不仅涵盖了理论知识，还提供了丰富的练习题和演讲稿，为学习者提供了一个全面的学习路径。无论你是初学者还是专业人士，都能在本书中找到适合自己的内容，提升在深度学习领域的理解和实践能力。"

CONTENTS

Calculus

Derivative of with respect toy x

∂y

∂x

Partial derivative of with respect toy x

∇

y Gradient of with respect toy x

∇

y Matrix derivatives of with respect toy X

∇

Tensor containing derivatives of

with respect to

∂f

∂x

Jacobian matrix J ∈ R

m n×

of f : R

→ R

∇

f f f( ) (x or H )( )x The Hessian matrix of at input point x



f d( )x x Deﬁnite integral over the entire domain of x



f d( )x x xDeﬁnite integral with respect to over the set S

Probability and Information Theory

a b The random variables a and b are independent⊥

a b c They are conditionally independent given c⊥ |

P ( )a

A probability distribution over a discrete variable

p( )a

A probability distribution over a continuous vari-

able, or over a variable whose type has not been

speciﬁed

a Random variable a has distribution∼ P P

x∼P

[ ( )] ( ) ( ) ( )f x or Ef x Expectation of f x with respect to P x

Var( ( ))f x Variance of under xf x( ) P ( )

Cov( ( ) ( ))f x , g x Covariance of and under xf x( ) g x( ) P ( )

H( )x Shannon entropy of the random variable x

( )P Q Kullback-Leibler divergence of P and Q

N ( ; )x µ, Σ

Gaussian distribution over

with mean

and

covariance Σ

xiii

CHAPTER 1. INTRODUCTION

concepts are built on top of each other, the graph is deep, with many layers. For

this reason, we call this approach to AI .deep learning

Many of the early successes of AI took place in relatively sterile and formal

environments and did not require computers to have much knowledge about

the world. For example, IBM’s Deep Blue chess-playing system defeated world

champion Garry Kasparov in 1997 ( , ). Chess is of course a very simpleHsu 2002

world, containing only sixty-four locations and thirty-two pieces that can move

in only rigidly circumscribed ways. Devising a successful chess strategy is a

tremendous accomplishment, but the challenge is not due to the diﬃculty of

describing the set of chess pieces and allowable moves to the computer. Chess

can be completely described by a very brief list of completely formal rules, easily

provided ahead of time by the programmer.

Ironically, abstract and formal tasks that are among the most diﬃcult mental

undertakings for a human being are among the easiest for a computer. Computers

have long been able to defeat even the best human chess player, but are only

recently matching some of the abilities of average human beings to recognize objects

or speech. A person’s everyday life requires an immense amount of knowledge

about the world. Much of this knowledge is subjective and intuitive, and therefore

diﬃcult to articulate in a formal way. Computers need to capture this same

knowledge in order to behave in an intelligent way. One of the key challenges in

artiﬁcial intelligence is how to get this informal knowledge into a computer.

Several artiﬁcial intelligence projects have sought to hard-code knowledge about

the world in formal languages. A computer can reason about statements in these

formal languages automatically using logical inference rules. This is known as the

knowledge base

approach to artiﬁcial intelligence. None of these projects has led

to a major success. One of the most famous such projects is Cyc ( ,Lenat and Guha

1989). Cyc is an inference engine and a database of statements in a language

called CycL. These statements are entered by a staﬀ of human supervisors. It is an

unwieldy process. People struggle to devise formal rules with enough complexity

to accurately describe the world. For example, Cyc failed to understand a story

about a person named Fred shaving in the morning ( , ). Its inferenceLinde 1992

engine detected an inconsistency in the story: it knew that people do not have

electrical parts, but because Fred was holding an electric razor, it believed the

entity “FredWhileShaving” contained electrical parts. It therefore asked whether

Fred was still a person while he was shaving.

The diﬃculties faced by systems relying on hard-coded knowledge suggest

that AI systems need the ability to acquire their own knowledge, by extracting

patterns from raw data. This capability is known as

machine learning

. The

CHAPTER 1. INTRODUCTION

introduction of machine learning allowed computers to tackle problems involving

knowledge of the real world and make decisions that appear subjective. A simple

machine learning algorithm called

logistic regression

can determine whether to

recommend cesarean delivery (Mor-Yosef 1990et al., ). A simple machine learning

algorithm called naive Bayes can separate legitimate e-mail from spam e-mail.

The performance of these simple machine learning algorithms depends heavily

on the

representation

of the data they are given. For example, when logistic

regression is used to recommend cesarean delivery, the AI system does not examine

the patient directly. Instead, the doctor tells the system several pieces of relevant

information, such as the presence or absence of a uterine scar. Each piece of

information included in the representation of the patient is known as a

feature

Logistic regression learns how each of these features of the patient correlates with

various outcomes. However, it cannot inﬂuence the way that the features are

deﬁned in any way. If logistic regression was given an MRI scan of the patient,

rather than the doctor’s formalized report, it would not be able to make useful

predictions. Individual pixels in an MRI scan have negligible correlation with any

complications that might occur during delivery.

This dependence on representations is a general phenomenon that appears

throughout computer science and even daily life. In computer science, opera-

tions such as searching a collection of data can proceed exponentially faster if

the collection is structured and indexed intelligently. People can easily perform

arithmetic on Arabic numerals, but ﬁnd arithmetic on Roman numerals much

more time-consuming. It is not surprising that the choice of representation has an

enormous eﬀect on the performance of machine learning algorithms. For a simple

visual example, see ﬁgure .1.1

Many artiﬁcial intelligence tasks can be solved by designing the right set of

features to extract for that task, then providing these features to a simple machine

learning algorithm. For example, a useful feature for speaker identiﬁcation from

sound is an estimate of the size of speaker’s vocal tract. It therefore gives a strong

clue as to whether the speaker is a man, woman, or child.

However, for many tasks, it is diﬃcult to know what features should be extracted.

For example, suppose that we would like to write a program to detect cars in

photographs. We know that cars have wheels, so we might like to use the presence

of a wheel as a feature. Unfortunately, it is diﬃcult to describe exactly what a

wheel looks like in terms of pixel values. A wheel has a simple geometric shape but

its image may be complicated by shadows falling on the wheel, the sun glaring oﬀ

the metal parts of the wheel, the fender of the car or an object in the foreground

obscuring part of the wheel, and so on.

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