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Understanding Deep Learning

Simon J.D. Prince

July 2, 2024

If you enjoy this book, here are four ways you can help me:

1. Spread the word via social media. Posts in languages other than English par-

ticularly welcome. Tag me on LinkedIn or X and I’ll probably say hi.

2. Write me an Amazon review. Preferably positive, but all publicity is good

publicity...

3. Send me comments (see bottom of this page). I reply to everything eventually.

4. Buy a copy. I took 18 months completely o work to write this book and ideally

I’d like to make minimum wage (or better) for this time. Also, I’d like to write

a second edition, but I need to sell enough copies to do this. Thanks!

The most recent version of this document can be found at http://udlbook.com.

Copyright in this work has been licensed exclusively to The MIT Press,

https://mitpress.mit.edu, which released the nal version to the public in December 2023.

Inquiries regarding rights should be addressed to the MIT Press, Rights & Permissions

Department.

This work is subject to a Creative Commons CC-BY-NC-ND license.

I would really appreciate help improving this document. No detail too small! Please contact

me with suggestions, factual inaccuracies, ambiguities, questions, and errata via github or by

e-mail at udlbookmail@gmail.com.

Contents

Preface ix

Acknowledgements xi

1 Introduction 1

1.1 Supervised learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Unsupervised learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Reinforcement learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 Structure of book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6 Other books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.7 How to read this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Supervised learning 17

2.1 Supervised learning overview . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Linear regression example . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Shallow neural networks 25

3.1 Neural network example . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Universal approximation theorem . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Multivariate inputs and outputs . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 Shallow neural networks: general case . . . . . . . . . . . . . . . . . . . . 33

3.5 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Deep neural networks 41

4.1 Composing neural networks . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 From composing networks to deep networks . . . . . . . . . . . . . . . . 43

4.3 Deep neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4 Matrix notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.5 Shallow vs. deep neural networks . . . . . . . . . . . . . . . . . . . . . . 49

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Draft: please send errata to udlbookmail@gmail.com.

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