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Understanding Deep Learning

Simon J.D. Prince

December 15, 2022

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

https://mitpress.mit.edu, which will be releasing the nal version to the public in 2024. All

inquiries regarding rights should be addressed to the MIT Press, Rights and 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 mail

suggestions, factual inaccuracies, ambiguities, questions, and errata to

udlbookmail@gmail.com.

Contents

Contents 1

1 Introduction 11

1.1 Supervised learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.1.1 Regression and classication problems . . . . . . . . . . . . . . . . 12

1.1.2 Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.1.3 Machine learning models . . . . . . . . . . . . . . . . . . . . . . . . 14

1.1.4 Deep neural networks . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.1.5 Structured outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.2 Unsupervised learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.2.1 Generative models . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.2.2 Latent variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2.3 Connecting supervised and unsupervised learning . . . . . . . . . . 21

1.3 Reinforcement learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.3.1 Two examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.4 Structure of book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.5 Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.6 Other books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.7 How to read this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 Supervised learning 27

2.1 Supervised learning overview . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2 Linear regression example . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2.1 1D linear regression model . . . . . . . . . . . . . . . . . . . . . . . 29

2.2.2 Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2.3 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.4 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 Shallow neural networks 35

3.1 Neural network example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 Neural network intuition . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.2 Depicting neural networks . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Universal approximation theorem . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 Multivariate inputs and outputs . . . . . . . . . . . . . . . . . . . . . . . . 40

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

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