Deep Learning and Scientific Computing with R torch (Chapman & Hall/CRC The R Series)

414 Pages·2023·10.655 MB·English

by  Sigrid Keydana

Deep Learning and
Scientific Computing
with R torch
torch is an R port of PyTorch, one of the two most-employed deep learning
frameworks in industry and research. It is also an excellent tool to use in scientific
computations. It is written entirely in R and C/C++.
Though still “young” as a project, R torch already has a vibrant community of
users and developers. Experience shows that torch users come from a broad
range of different backgrounds. This book aims to be useful to (almost) everyone.
Globally speaking, its purposes are threefold:
- Provide a thorough introduction to torch basics – both by carefully explaining
underlying concepts and ideas, and showing enough examples for the reader
to become “fluent” in torch.
- Again with a focus on conceptual explanation, show how to use torch in
deep-learning applications, ranging from image recognition over time series
prediction to audio classification.
- Provide a concepts-first, reader-friendly introduction to selected scientific-
computation topics (namely, matrix computations, the Discrete Fourier
Transform, and wavelets), all accompanied by torch code you can play with.
Deep Learning and Scientific Computing with R torch is written with first-hand
technical expertise and in an engaging, fun-to-read way.
Chapman & Hall/CRC
The R Series
Series Editors
John M. Chambers, Department of Statistics, Stanford University, California, USA
Torsten Hothorn, Division of Biostatistics, University of Zurich, Switzerland
Duncan Temple Lang, Department of Statistics, University of California, Davis, USA
Hadley Wickham, RStudio, Boston, Massachusetts, USA
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CRC-The-R-Series/book-series/CRCTHERSER
Deep Learning and
Scientific Computing
with R torch
Sigrid Keydana
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rel-sciurus-vulgaris-looking-2070311126
First edition published 2023
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© 2023 Sigrid Keydana
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ISBN: 978-1-032-23138-9 (hbk)
ISBN: 978-1-032-23139-6 (pbk)
ISBN: 978-1-003-27592-3 (ebk)
DOI: 10.1201/9781003275923
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Publisher’s note: This book has been prepared from camera-ready copy provided by the
authors.
Contents
List of Figures xi
Preface xv
Author Biography xix
I Getting Familiar with Torch 1
1 Overview 3
2 On torch, and How to Get It 5
2.1 In torch World . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Installing and Running torch . . . . . . . . . . . . . . . . . 6
3 Tensors 7
3.1 What’s in a Tensor? . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Creating Tensors . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.1 Tensors from values . . . . . . . . . . . . . . . . . . . 9
3.2.2 Tensors from specifications . . . . . . . . . . . . . . . 12
3.2.3 Tensors from datasets . . . . . . . . . . . . . . . . . . 14
3.3 Operations on Tensors . . . . . . . . . . . . . . . . . . . . . . 19
3.3.1 Summary operations . . . . . . . . . . . . . . . . . . . 21
3.4 Accessing Parts of a Tensor . . . . . . . . . . . . . . . . . . 23
3.4.1 “Think R” . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Reshaping Tensors . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5.1 Zero-copy reshaping vs. reshaping with copy. . . . . . 27
3.6 Broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6.1 Broadcasting rules . . . . . . . . . . . . . . . . . . . . 31
4 Autograd 33
4.1 Why Compute Derivatives? . . . . . . . . . . . . . . . . . . . 33
4.2 Automatic Differentiation Example . . . . . . . . . . . . . . 35
4.3 Automatic Differentiation with torch autograd . . . . . . . . 36
5 Function Minimization with autograd 41
5.1 An Optimization Classic . . . . . . . . . . . . . . . . . . . . 41
5.2 Minimization from Scratch . . . . . . . . . . . . . . . . . . . 42
v
vi Contents
6 A Neural Network from Scratch 47
6.1 Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.2 Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.3 Activation Functions . . . . . . . . . . . . . . . . . . . . . . . 49
6.4 Loss Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.5.1 Generate random data . . . . . . . . . . . . . . . . . . 52
6.5.2 Build the network . . . . . . . . . . . . . . . . . . . . 52
6.5.3 Train the network . . . . . . . . . . . . . . . . . . . . 53
7 Modules 57
7.1 Built-in nn_module()s . . . . . . . . . . . . . . . . . . . . . 57
7.2 Building up a Model . . . . . . . . . . . . . . . . . . . . . . . 60
7.2.1 Models as sequences of layers: nn_sequential()
index{nn_sequential()} . . . . . . . . . . . . . . . . 60
7.2.2 Models with custom logic . . . . . . . . . . . . . . . . 61
8 Optimizers 63
8.1 Why Optimizers? . . . . . . . . . . . . . . . . . . . . . . . . 63
8.2 Using built-in torch Optimizers . . . . . . . . . . . . . . . . 64
8.3 Parameter Update Strategies . . . . . . . . . . . . . . . . . . 65
8.3.1 Gradient descent (a.k.a. steepest descent, a.k.a.
stochastic gradient descent (SGD)) . . . . . . . . . . . 66
8.3.2 Things that matter . . . . . . . . . . . . . . . . . . . . 67
8.3.3 Staying on track: Gradient descent with momentum . 68
8.3.4 Adagrad . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.3.5 RMSProp . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.3.6 Adam . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
9 Loss Functions 75
9.1 torch Loss Functions . . . . . . . . . . . . . . . . . . . . . . 75
9.2 What Loss Function Should I Choose? . . . . . . . . . . . . . 76
9.2.1 Maximum likelihood . . . . . . . . . . . . . . . . . . . 76
9.2.2 Regression. . . . . . . . . . . . . . . . . . . . . . . . . 76
9.2.3 Classification . . . . . . . . . . . . . . . . . . . . . . . 77
10 Function Minimization with L-BFGS 83
10.1 Meet L-BFGS . . . . . . . . . . . . . . . . . . . . . . . . . . 83
10.1.1 Changing slopes . . . . . . . . . . . . . . . . . . . . . 83
10.1.2 Exact Newton method . . . . . . . . . . . . . . . . . . 84
10.1.3 Approximate Newton: BFGS and L-BFGS . . . . . . . 85
10.1.4 Line search . . . . . . . . . . . . . . . . . . . . . . . . 85
10.2 Minimizing the Rosenbrock Function with optim_lbfgs() . . 86
10.2.1 optim_lbfgs() default behavior . . . . . . . . . . . . 87
10.2.2 optim_lbfgs() with line search . . . . . . . . . . . . 89
Contents vii
11 Modularizing the Neural Network 91
11.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
11.2 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
11.3 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
11.4 What’s to Come . . . . . . . . . . . . . . . . . . . . . . . . . 93
II Deep Learning with torch 95
12 Overview 97
13 Loading Data 99
13.1 Datavs.dataset()vs.dataloader()–What’stheDifference? 99
13.2 Using dataset()s . . . . . . . . . . . . . . . . . . . . . . . . 100
13.2.1 A self-built dataset() . . . . . . . . . . . . . . . . . . 101
13.2.2 tensor_dataset() . . . . . . . . . . . . . . . . . . . . 102
13.2.3 torchvision::mnist_dataset() . . . . . . . . . . . . 103
13.3 Using dataloader()s . . . . . . . . . . . . . . . . . . . . . . 104
14 Training with luz 107
14.1 Que haya luz – Que haja luz – Let there be Light . . . . . . 107
14.2 Porting the Toy Example . . . . . . . . . . . . . . . . . . . . 108
14.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
14.2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
14.2.3 Training . . . . . . . . . . . . . . . . . . . . . . . . . . 109
14.3 A More Realistic Scenario . . . . . . . . . . . . . . . . . . . . 111
14.3.1 Integrating training, validation, and test . . . . . . . . 111
14.3.2 Using callbacks to “hook” into the training process . . 114
14.3.3 How luz helps with devices . . . . . . . . . . . . . . . 116
14.4 Appendix: A Train-Validate-Test Workflow Implemented by
Hand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
15 A First Go at Image Classification 121
15.1 What does It Take to Classify an Image? . . . . . . . . . . . 121
15.2 Neural Networks for Feature Detection and Feature Emergence 122
15.2.1 Detecting low-level features with cross-correlation . . 122
15.2.2 Build up feature hierarchies . . . . . . . . . . . . . . . 128
15.3 Classification on Tiny Imagenet . . . . . . . . . . . . . . . . 134
15.3.1 Data pre-processing . . . . . . . . . . . . . . . . . . . 135
15.3.2 Image classification from scratch . . . . . . . . . . . . 137
16 Making Models Generalize 141
16.1 The Royal Road: more – and More Representative! – Data . 142
16.2 Pre-processing Stage: Data Augmentation . . . . . . . . . . . 142
16.2.1 Classic data augmentation . . . . . . . . . . . . . . . . 142
16.2.2 Mixup . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
16.3 Modeling Stage: Dropout and Regularization . . . . . . . . . 151
viii Contents
16.3.1 Dropout . . . . . . . . . . . . . . . . . . . . . . . . . . 151
16.3.2 Regularization . . . . . . . . . . . . . . . . . . . . . . 153
16.4 Training Stage: Early Stopping . . . . . . . . . . . . . . . . . 154
17 Speeding up Training 157
17.1 Batch Normalization . . . . . . . . . . . . . . . . . . . . . . 157
17.2 Dynamic Learning Rates . . . . . . . . . . . . . . . . . . . . 159
17.2.1 Learning rate finder . . . . . . . . . . . . . . . . . . . 160
17.2.2 Learning rate schedulers . . . . . . . . . . . . . . . . . 163
17.3 Transfer Learning . . . . . . . . . . . . . . . . . . . . . . . . 164
18 Image Classification, Take Two: Improving Performance 169
18.1 Data Input (Common for all) . . . . . . . . . . . . . . . . . . 170
18.2 Run 1: Dropout . . . . . . . . . . . . . . . . . . . . . . . . . 171
18.3 Run 2: Batch Normalization . . . . . . . . . . . . . . . . . . 174
18.4 Run 3: Transfer Learning . . . . . . . . . . . . . . . . . . . . 177
19 Image Segmentation 181
19.1 Segmentation vs. Classification . . . . . . . . . . . . . . . . . 181
19.2 U-Net, a “classic” in image segmentation . . . . . . . . . . . 182
19.3 U-Net – a torch implementation . . . . . . . . . . . . . . . . 183
19.3.1 Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . 183
19.3.2 Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . 186
19.3.3 The “U” . . . . . . . . . . . . . . . . . . . . . . . . . . 190
19.3.4 Top-level module . . . . . . . . . . . . . . . . . . . . . 191
19.4 Dogs and Cats . . . . . . . . . . . . . . . . . . . . . . . . . . 192
20 Tabular Data 201
20.1 Types of Numerical Data, by Example . . . . . . . . . . . . . 201
20.2 A torch dataset for Tabular Data . . . . . . . . . . . . . . 204
20.3 Embeddings in Deep Learning: The Idea . . . . . . . . . . . 208
20.4 Embeddings in deep learning: Implementation . . . . . . . . 209
20.5 Model and Model Training . . . . . . . . . . . . . . . . . . . 211
20.6 Embedding-generated Representations by Example . . . . . 214
21 Time Series 219
21.1 Deep Learning for Sequences: The Idea . . . . . . . . . . . . 219
21.2 A Basic Recurrent Neural Network . . . . . . . . . . . . . . . 221
21.2.1 Basic rnn_cell() . . . . . . . . . . . . . . . . . . . . 221
21.2.2 Basic rnn_module() . . . . . . . . . . . . . . . . . . . 222
21.3 Recurrent Neural Networks in torch . . . . . . . . . . . . . 225
21.4 RNNs in Practice: GRU and LSTM . . . . . . . . . . . . . . 226
21.5 Forecasting Electricity Demand . . . . . . . . . . . . . . . . 228
21.5.1 Data inspection . . . . . . . . . . . . . . . . . . . . . . 229
21.5.2 Forecasting the very next value . . . . . . . . . . . . . 231
21.5.3 Forecasting multiple time steps ahead . . . . . . . . . 239
Contents ix
22 Audio Classification 247
22.1 Classifying Speech Data . . . . . . . . . . . . . . . . . . . . . 247
22.2 Two Equivalent Representations . . . . . . . . . . . . . . . . 250
22.3 Combining Representations: The Spectrogram . . . . . . . . 251
22.4 Training a Model for Audio Classification . . . . . . . . . . . 254
22.4.1 Baseline setup: Training a convnet on spectrograms . 254
22.4.2 Variation one: Use a Mel-scale spectrogram instead . . 261
22.4.3 Variation two: Complex-valued spectograms . . . . . . 267
III Other Things to do with torch: Matrices,
Fourier Transform, and Wavelets 273
23 Overview 275
24 Matrix Computations: Least-squares Problems 277
24.1 Five Ways to do Least Squares . . . . . . . . . . . . . . . . . 277
24.2 Regression for Weather Prediction . . . . . . . . . . . . . . . 278
24.2.1 Least squares (I): Setting expectations with lm() . . . 280
24.2.2 Least squares (II): Using linalg_lstsq() . . . . . . . 282
24.2.3 Interlude: What if we hadn’t standardized the data? . 283
24.2.4 Least squares (III): The normal equations . . . . . . . 287
24.2.5 Least squares (IV): Cholesky decomposition . . . . . . 289
24.2.6 Least squares (V): LU factorization. . . . . . . . . . . 292
24.2.7 Least squares (VI): QR factorization . . . . . . . . . . 293
24.2.8 Least squares (VII): Singular Value Decomposition
(SVD) . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
24.2.9 Checking execution times . . . . . . . . . . . . . . . . 296
24.3 A Quick Look at Stability . . . . . . . . . . . . . . . . . . . . 299
25 Matrix Computations: Convolution 305
25.1 Why Convolution? . . . . . . . . . . . . . . . . . . . . . . . . 305
25.2 Convolution in One Dimension . . . . . . . . . . . . . . . . . 306
25.2.1 Two ways to think about convolution. . . . . . . . . . 307
25.2.2 Implementation . . . . . . . . . . . . . . . . . . . . . . 310
25.3 Convolution in Two Dimensions . . . . . . . . . . . . . . . . 311
25.3.1 How it works (output view) . . . . . . . . . . . . . . . 312
25.3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . 313
26 Exploring the Discrete Fourier Transform (DFT) 319
26.1 Understanding the Output of torch_fft_fft() . . . . . . . 319
26.1.1 Starting point: A cosine of frequency 1 . . . . . . . . . 320
26.1.2 Reconstructing the magic . . . . . . . . . . . . . . . . 324
26.1.3 Varying frequency . . . . . . . . . . . . . . . . . . . . 327
26.1.4 Varying amplitude . . . . . . . . . . . . . . . . . . . . 330
26.1.5 Adding phase . . . . . . . . . . . . . . . . . . . . . . . 330
26.1.6 Superposition of sinusoids . . . . . . . . . . . . . . . . 333