Daniel Voigt Godoy - Deep Learning with PyTorch Step-by-Step A Beginner’s Guide-leanpub

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Chapter 8SequencesSpoilersIn this chapter, we will:• learn about the characteristics of sequential data and generate our own• understand the inner workings of recurrent layers• build and train models to perform classification of sequences• understand the importance of the hidden state as the representation of asequence• visualize the journey of a hidden state from beginning to end of a sequence• pre-process variable-length sequences using padding and packing techniques,as well as the collate function• learn how 1D convolutions can be used on sequential dataJupyter NotebookThe Jupyter notebook corresponding to Chapter 8 [134] is part of the official DeepLearning with PyTorch Step-by-Step repository on GitHub. You can also run itdirectly in Google Colab [135] .If you’re using a local installation, open your terminal or Anaconda prompt andnavigate to the PyTorchStepByStep folder you cloned from GitHub. Then, activatethe pytorchbook environment and run jupyter notebook:$ conda activate pytorchbook(pytorchbook)$ jupyter notebookIf you’re using Jupyter’s default settings, this link should open Chapter 8’snotebook. If not, just click on Chapter08.ipynb in your Jupyter’s home page.Spoilers | 587
ImportsFor the sake of organization, all libraries needed throughout the code used in anygiven chapter are imported at its very beginning. For this chapter, we’ll need thefollowing imports:import numpy as npimport torchimport torch.optim as optimimport torch.nn as nnimport torch.nn.functional as Ffrom torch.utils.data import DataLoader, Dataset, random_split, \TensorDatasetfrom torch.nn.utils import rnn as rnn_utilsfrom data_generation.square_sequences import generate_sequencesfrom stepbystep.v4 import StepByStepSequencesIn this third part of the book, we’ll dive into a new kind of input: sequences! So far,each data point has been considered in and of itself; that is, each data point has hada label to call its own. An image of a hand was classified as "rock," "paper," or"scissors" based on its pixel values alone, without paying any attention to otherimages' pixel values. This won’t be the case anymore.In sequence problems, an ordered sequence of data points shares a singlelabel—emphasis on being ordered."Why is ordered so important?"If the data points aren’t ordered, even if they share a single label, they are not asequence, but rather a collection of data points.Let’s think of a slightly contrived example: greyscale images with shuffled pixels.Each pixel has a single value, but a pixel alone doesn’t have a label. It is thecollection of shuffled pixels, the shuffled image, that has a label: a duck, a dog, or acat (labeled before shuffling the pixels, of course).588 | Chapter 8: Sequences
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Deep Learning with PyTorchStep-by-S
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"What I cannot create, I do not und
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Train-Validation-Test Split. . . .
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Random Split. . . . . . . . . . . .
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The Precision Quirk . . . . . . . .
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A REAL Filter . . . . . . . . . . .
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Jupyter Notebook . . . . . . . . .
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Stacked RNN . . . . . . . . . . . .
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Attention Mechanism . . . . . . . .
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4. Positional Encoding. . . . . . .
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Model Configuration & Training . .
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AcknowledgementsFirst and foremost,
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Frequently Asked Questions (FAQ)Why
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There is yet another advantage of f
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• Classes and methods are written
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What’s Next?It’s time to set up
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After choosing a repository, it wil
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1. AnacondaIf you don’t have Anac
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3. PyTorchPyTorch is the coolest de
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(pytorchbook) C:\> conda install py
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(pytorchbook)$ pip install torchviz
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7. JupyterAfter cloning the reposit
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Part IFundamentals| 21
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notebook. If not, just click on Cha
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Also, let’s say that, on average,
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There is one exception to the "alwa
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Random Initialization1 # Step 0 - I
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Batch, Mini-batch, and Stochastic G
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Outputarray([[-2. , -1.94, -1.88, .
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one matrix for each data point, eac
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Sure, different values of b produce
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Output-3.044811379650508 -1.8337537
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each parameter using the chain rule
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What’s the impact of one update o
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gradients, we know we need to take
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Very High Learning RateWait, it may
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true_b = 1true_w = 2N = 100# Data G
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Let’s look at the cross-sections
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Zero Mean and Unit Standard Deviati
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Sure, in the real world, you’ll n
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computing the loss, as shown in the
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• visualizing the effects of usin
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If you’re using Jupyter’s defau
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Notebook Cell 1.1 - Splitting synth
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Step 2# Step 2 - Computing the loss
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Output[0.49671415] [-0.1382643][0.8
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Notebook Cell 1.2 - Implementing gr
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# Sanity Check: do we get the same
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Outputtensor(3.1416)tensor([1, 2, 3
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Outputtensor([[1., 2., 1.],[1., 1.,
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dummy_array = np.array([1, 2, 3])du
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n_cudas = torch.cuda.device_count()
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back_to_numpy = x_train_tensor.nump
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I am assuming you’d like to use y
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Outputtensor([0.1940], device='cuda
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print(error.requires_grad, yhat.req
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Output(tensor([0.], device='cuda:0'
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56 # need to tell it to let it go..
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computation.If you chose "Local Ins
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Figure 1.6 - Now parameter "b" does
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There are many optimizers: SGD is t
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41 optimizer.zero_grad() 34243 prin
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Notebook Cell 1.8 - PyTorch’s los
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Outputarray(0.00804466, dtype=float
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Let’s build a proper (yet simple)
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"What do we need this for?"It turns
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1 Instantiating a model2 What IS th
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In the __init__() method, we create
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LayersA Linear model can be seen as
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There are MANY different layers tha
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We use magic, just like that:%run -
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• Step 1: compute model’s predi
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RecapFirst of all, congratulations
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Chapter 2Rethinking the Training Lo
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Let’s take a look at the code onc
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Higher-Order FunctionsAlthough this
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def exponentiation_builder(exponent
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Apart from returning the loss value
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Our code should look like this; see
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There is no need to load the whole
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but if we want to get serious about
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How does this change our code so fa
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Run - Model Training V2%run -i mode
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piece of code that’s going to be
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for it. We could do the same for th
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EvaluationHow can we evaluate the m
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And then, we update our model confi
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Run - Model Training V4%run -i mode
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Loading Extension# Load the TensorB
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browser, you’ll likely see someth
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model’s graph (not quite the same
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Figure 2.5 - Scalars on TensorBoard
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Define - Model Training V51 %%write
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If, by any chance, you ended up wit
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The procedure is exactly the same,
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soon, so please bear with me for no
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After recovering our model’s stat
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Run - Model Configuration V31 # %lo
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This is the general structure you
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Chapter 2.1Going ClassySpoilersIn t
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# A completely empty (and useless)
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# These attributes are defined here
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# Creates the train_step function f
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# Builds function that performs a s
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setattrThe setattr function sets th
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See? We effectively modified the un
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the random seed as arguments.This s
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The current state of development of
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Lossesdef plot_losses(self):fig = p
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Run - Data Preparation V21 # %load
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Model TrainingWe start by instantia
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Making PredictionsLet’s make up s
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OutputOrderedDict([('0.weight', ten
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Run - Data Preparation V21 # %load
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• defining our StepByStep class
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import numpy as npimport torchimpor
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Next, we’ll standardize the featu
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Equation 3.1 - A linear regression
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The odds ratio is given by the rati
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As expected, probabilities that add
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Sigmoid Functiondef sigmoid(z):retu
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A picture is worth a thousand words
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OutputOrderedDict([('linear.weight'
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The first summation adds up the err
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IMPORTANT: Make sure to pass the pr
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To make it clear: In this chapter,
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argument of nn.BCEWithLogitsLoss().
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It is not that hard, to be honest.
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Figure 3.6 - Training and validatio
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Outputarray([[0.5504593 ],[0.949995
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decision boundary.Look at the expre
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Are my data points separable?That
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model = nn.Sequential()model.add_mo
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It looks like this:Figure 3.10 - Sp
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True and False Positives and Negati
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tpr_fpr(cm_thresh50)Output(0.909090
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The trade-off between precision and
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Figure 3.13 - Using a low threshold
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Figure 3.16 - Trade-offs for two di
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thresholds do not necessarily inclu
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actual data, it is as bad as it can
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If you want to learn more about bot
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Model Training1 n_epochs = 10023 sb
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step in your journey! What’s next
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Chapter 4Classifying ImagesSpoilers
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Data GenerationOur images are quite
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Images and ChannelsIn case you’re
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image_rgb = np.stack([image_r, imag
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That’s fairly straightforward; we
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• Transformations based on Tensor
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position of an object in a picture
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Outputtensor([[[0., 0., 0., 1., 0.]
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Outputtensor([[[-1., -1., -1., 1.,
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We can convert the former into the
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composer = Compose([RandomHorizonta
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Output<torch.utils.data.dataset.Sub
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train_composer = Compose([RandomHor
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The minority class should have the
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train_loader = DataLoader(dataset=t
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implemented in Chapter 2.1? Let’s
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Let’s take one mini-batch of imag
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What does our model look like? Visu
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Model TrainingLet’s train our mod
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preceding hidden layer to compute i
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fig = sbs_nn.plot_losses()Figure 4.
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Equation 4.2 - Equivalence of deep
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w_nn_equiv = w_nn_output.mm(w_nn_hi
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Weights as PixelsDuring data prepar
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is only 0.25 (for z = 0) and that i
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nn.Tanh()(dummy_z)Outputtensor([-0.
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dummy_z = torch.tensor([-3., 0., 3.
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As you can see, in PyTorch the coef
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Figure 4.16 - Deep model (for real)
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Figure 4.18 - Losses (before and af
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Equation 4.3 - Activation functions
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Helper Function #41 def index_split
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Model Configuration1 # Sets learnin
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Bonus ChapterFeature SpaceThis chap
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Affine TransformationsAn affine tra
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Figure B.3 - Annotated model diagra
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Figure B.5 - In the beginning…But
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OK, now we can clearly see a differ
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In the model above, the sigmoid fun
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the more dimensions, the more separ
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import randomimport numpy as npfrom
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identity = np.array([[[[0, 0, 0],[0
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Figure 5.4 - Striding the image, on
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Output-----------------------------
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Outputtensor([[[[9., 5., 0., 7.],[0
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OutputParameter containing:tensor([
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Moreover, notice that if we were to
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In code, as usual, PyTorch gives us
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Outputtensor([[[[5., 5., 0., 8., 7.
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edge = np.array([[[[0, 1, 0],[1, -4
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A pooling kernel of two-by-two resu
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Outputtensor([[22., 23., 11., 24.,
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Figure 5.15 - LeNet-5 architectureS
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• second block: produces 16-chann
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Transformed Dataset1 class Transfor
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LossNew problem, new loss. Since we
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Outputtensor([4.0000, 1.0000, 0.500
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The loss only considers the predict
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Outputtensor([[-1.5229, -0.3146, -2
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IMPORTANT: I can’t stress this en
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figures at the beginning of this ch
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The three units in the output layer
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StepByStep Method@staticmethoddef _
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The meow() method is totally indepe
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StepByStep Methoddef visualize_filt
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dummy_model = nn.Linear(1, 1)dummy_
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dummy_listOutput[(Linear(in_feature
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Output{Conv2d(1, 1, kernel_size=(3,
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will be the externally defined vari
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Removing Hookssbs_cnn1.remove_hooks
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return figsetattr(StepByStep, 'visu
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Figure 5.22 - Feature maps (classif
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classification: The predicted class
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convolutional layers to our model a
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Capturing Outputsfeaturizer_layers
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the filters learned by the model pr
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given chapter are imported at its v
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Data PreparationThe data preparatio
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model anyway. We’ll use it to com
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StepByStep Method@staticmethoddef m
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"What’s wrong with the colors?"Th
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three_channel_filter = np.array([[[
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Fancier Model (Constructor)class CN
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Fancier Model (Classifier)def class
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torch.manual_seed(44)dropping_model
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Outputtensor([0.1000, 0.2000, 0.300
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Figure 6.8 - Output distribution fo
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Adaptive moment estimation (Adam) u
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torch.manual_seed(13)# Model Config
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Outputtorch.Size([5, 3, 3, 3])Its s
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Choosing a learning rate that works
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Higher-Order Learning Rate Function
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Perfect! Now let’s build the actu
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ax.set_xlabel('Learning Rate')ax.se
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LRFinderThe function we’ve implem
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value in our moving average has an
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Figure 6.15 - Distribution of weigh
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In code, the implementation of the
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As expected, the EWMA without corre
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optimizer = optim.Adam(model.parame
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IMPORTANT: The logging function mus
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Output{'state': {140601337662512: {
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different optimizer, set them to ca
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• dampening: dampening factor for
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Figure 6.20 - Paths taken by SGD (w
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Equation 6.16 - Looking aheadOnce N
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Figure 6.22 - Path taken by each SG
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for epoch in range(4):# training lo
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course) up to a given number of epo
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Next, we create a protected method
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Mini-Batch SchedulersThese schedule
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Schedulers in StepByStep — Part I
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Scheduler PathsBefore trying out a
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After applying each scheduler to SG
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Data Preparation1 # Loads temporary
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Figure 6.31 - LossesEvaluationprint
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[96] http://www.samkass.com/theorie
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ImportsFor the sake of organization
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ILSVRC-2012The 2012 edition [111] o
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remained unchanged.ResNet (MSRA Tea
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Transfer Learning in PracticeIn Cha
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dropout. You’re already familiar
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OutputDownloading: "https://downloa
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Replacing the "Top" of the Model1 a
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Model Size Classifier Layer(s) Repl
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Model TrainingWe have everything se
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"Removing" the Top Layer1 alex.clas
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torch.save(train_preproc.tensors, '
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Outputtensor([[109, 124],[124, 124]
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Model Configuration1 optimizer_mode
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Figure 7.4 - 1x1 convolutionThe inp
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The weights used by PIL are 0.299 f
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• reduce the number of output cha
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The constructor method defines the
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Does it sound familiar? That’s wh
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and w to represent these parameters
Page 562 and 563: A mini-batch of size 64 is small en
Page 564 and 565: normed1 = batch_normalizer(batch1[0
Page 566 and 567: OutputOrderedDict([('running_mean',
Page 568 and 569: OutputOrderedDict([('running_mean',
Page 570 and 571: batch_normalizer = nn.BatchNorm2d(n
Page 572 and 573: torch.manual_seed(23)dummy_points =
Page 574 and 575: np.concatenate([dummy_points[:5].nu
Page 576 and 577: Another advantage of these shortcut
Page 578 and 579: It should be pretty clear, except f
Page 580 and 581: Data Preparation1 # ImageNet statis
Page 582 and 583: Data Preparation — Preprocessing1
Page 584 and 585: • freezing the layers of the mode
Page 586 and 587: Extra ChapterVanishing and Explodin
Page 588 and 589: discussing it, let me illustrate it
Page 590 and 591: Model Configuration (2)1 loss_fn =
Page 592 and 593: weights. If done properly, the init
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Page 596 and 597: Figure E.3 - The effect of batch no
Page 598 and 599: Model Configuration1 torch.manual_s
Page 600 and 601: torch.manual_seed(42)parm = nn.Para
Page 602 and 603: (and only if) the norm exceeds the
Page 604 and 605: if callable(self.clipping): 1self.c
Page 606 and 607: Moreover, let’s use a ten times h
Page 608 and 609: Clipping with HooksFirst, we reset
Page 610 and 611: • visualizing the difference betw
Page 614 and 615: Before shuffling, the pixels were o
Page 616 and 617: And then let’s visualize the firs
Page 618 and 619: sequence so far, and a data point f
Page 620 and 621: Considering this, the not "unrolled
Page 622 and 623: linear_input = nn.Linear(n_features
Page 624 and 625: Outputtensor([[0.3924, 0.8146]], gr
Page 626 and 627: Now we’re talking! The last hidde
Page 628 and 629: Let’s take a look at the RNN’s
Page 630 and 631: ◦ The initial hidden state, which
Page 632 and 633: batch_first argument to True so we
Page 634 and 635: OutputOrderedDict([('weight_ih_l0',
Page 636 and 637: out, hidden = rnn_stacked(x)out, hi
Page 638 and 639: _l0_reverse).Once again, let’s cr
Page 640 and 641: For bidirectional RNNs, the last el
Page 642 and 643: Model Configuration1 class SquareMo
Page 644 and 645: StepByStep.loader_apply(test_loader
Page 646 and 647: Figure 8.14 - Final hidden states f
Page 648 and 649: Figure 8.16 - Transforming the hidd
Page 650 and 651: Since the RNN cell has both of them
Page 652 and 653: Every gate worthy of its name will
Page 654 and 655: • For r=0 and z=0, the cell becom
Page 656 and 657: In code, we can use split() to get
Page 658 and 659: Let’s pause for a moment here. Fi
Page 660 and 661: Square Model II — The QuickeningT
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Outputtensor([[53, 53],[75, 75]])Th
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Figure 8.22 - Transforming the hidd
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Equation 8.9 - LSTM—candidate hid
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Now, let’s visualize the internal
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OutputOrderedDict([('weight_ih', te
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def forget_gate(h, x):thf = f_hidde
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Outputtensor([[-5.4936e-02, -8.3816
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1 First change: from RNN to LSTM2 S
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Like the GRU, the LSTM presents fou
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Output-----------------------------
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Before moving on to packed sequence
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column-wise fashion, from top to bo
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does match the last output.• No,
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So, to actually get the last output
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Data Preparation1 class CustomDatas
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OutputPackedSequence(data=tensor([[
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Model Configuration & TrainingWe ca
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size = 5weight = torch.ones(size) *
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torch.manual_seed(17)conv_seq = nn.
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Figure 8.32 - Applying dilated filt
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Model Configuration1 torch.manual_s
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We can actually find an expression
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Data Preparation1 def pack_collate(
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and variable-length sequences.Model
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• generating variable-length sequ
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import copyimport numpy as npimport
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Figure 9.3 - Sequence datasetThe co
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coordinates of a "perfect" square a
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Let’s pretend for a moment that t
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to initialize the hidden state and
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predictions in previous steps have
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the second set of predicted coordin
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Let’s create an instance of the m
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Model Configuration & TrainingThe m
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Sure, we can!AttentionHere is a (no
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based on "the" and "zone," I’ve j
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Figure 9.12 - Matching a query to t
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Outputtensor([[[ 0.0832, -0.0356],[
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utmost importance for the correct i
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Its formula is:Equation 9.3 - Cosin
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second hidden state contributes to
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Outputtensor([[[ 0.5475, 0.0875, -1
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alphas = F.softmax(scaled_products,
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Outputtensor([[[ 0.2138, -0.3175]]]
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Attention Mechanism1 class Attentio
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"Why would I want to force it to do
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1 Sets attention module and adjusts
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encdec = EncoderDecoder(encoder, de
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fig = sbs_seq_attn.plot_losses()Fig
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Figure 9.20 - Attention scoresSee?
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Wide vs Narrow AttentionThis mechan
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"What’s so special about it?"Even
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Once again, the affine transformati
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Next, we shift our focus to the sel
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Encoder + Self-Attention1 class Enc
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Figure 9.27 - Encoder with self- an
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The figure below depicts the self-a
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shifted_seq = torch.cat([source_seq
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Equation 9.17 - Decoder’s (masked
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At evaluation / prediction time we
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Outputtensor([[[0.4132, 0.3728],[0.
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Figure 9.33 - Encoder + decoder + a
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64 return outputsThe encoder-decode
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Figure 9.34 - Losses—encoder + de
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curse. On the one hand, it makes co
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"Are we done now? Is this good enou
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Figure 9.46 - Consistent distancesA
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Let’s recap what we’ve already
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Let’s see it in code:max_len = 10
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Let’s put it all together into a
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Outputtensor([[[-1.0000, 0.0000],[-
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Decoder with Positional Encoding1 c
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Visualizing PredictionsLet’s plot
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Next, we’re moving on to the thre
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Data Generation & Preparation1 # Tr
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59 self.trg_masks)60 else:61 # Deco
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Model Configuration1 class EncoderS
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1617 @property18 def alphas(self):1
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Output(0.016193246061448008, 0.0341
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sequential order of the data• fig
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following imports:import copyimport
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Figure 10.2 - Chunking: the wrong a
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chunks to compute the other half of
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67 # N, L, n_heads, d_k68 context =
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dummy_points = torch.randn(16, 2, 4
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Stacking Encoders and DecodersLet
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"… with great depth comes great c
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Transformer EncoderWe’ll be repre
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Let’s see it in code, starting wi
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Transformer Encoder1 class EncoderT
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of the encoder-decoder (or Transfor
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In PyTorch, the decoder "layer" is
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In PyTorch, the decoder is implemen
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Equation 10.7 - Data points' means
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layer_norm = nn.LayerNorm(d_model)n
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Figure 10.10 - Layer norm vs batch
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Outputtensor([[[ 1.4636, 2.3663],[
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The TransformerLet’s start with t
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"values") in the decoder.• decode
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Data Preparation1 # Generating trai
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Figure 10.15 - Losses—Transformer
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• First, and most important, PyTo
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decode(), with a single one, encode
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46 for i in range(self.target_len):
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Figure 10.18 - Losses - PyTorch’s
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Figure 10.20 - Sample image—label
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4041 # Builds a weighted random sam
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Figure 10.23 - Sample image—split
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Einops"There is more than one way t
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Figure 10.26 - Two patch embeddings
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Now each sequence has ten elements,
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It takes an instance of a Transform
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Putting It All TogetherIn this chap
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1. Encoder-DecoderThe encoder-decod
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This is the actual encoder-decoder
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3. DecoderThe Transformer decoder h
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5. Encoder "Layer"The encoder "laye
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7. "Sub-Layer" WrapperThe "sub-laye
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8. Multi-Headed AttentionThe multi-
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Model Configuration & TrainingModel
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• training the Transformer to tac
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Part IVNatural Language Processing|
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Additional SetupThis is a special c
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"Down the Yellow Brick Rabbit Hole"
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The actual texts of the books are c
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"What is this punkt?"That’s the P
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14 # If there is a configuration fi
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Sentence Tokenization in spaCyBy th
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AttributesThe Dataset has many attr
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Output{'labels': 1,'sentence': 'The
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elements from the text. But preproc
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Data AugmentationLet’s briefly ad
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The corpora’s dictionary is not a
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Finally, if we want to convert a li
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Once we’re happy with the size an
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from transformers import BertTokeni
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"What about the separation token?"T
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The last output, attention_mask, wo
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Outputtensor([[ 3, 27, 1, ..., 0, 0
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vector, right? And our vocabulary i
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Maybe you filled this blank in with
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Continuous Bag-of-Words (CBoW)In th
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That’s a fairly simple model, rig
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Figure 11.13 - Continuous bag-of-wo
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Figure 11.15 - Reviewing restaurant
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You got that right—arithmetic—r
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There we go, 50 dimensions! It’s
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Equation 11.1 - Embedding arithmeti
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Only 82 out of 50,802 words in the
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Now we can use its encode() method
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Model I — GloVE + ClassifierData
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Pre-trained PyTorch EmbeddingsThe e
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Model Configuration & TrainingLet
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6 self.encoder = encoder7 self.mlp
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Figure 11.20 - Losses—Transformer
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Outputtensor([[[2.6334e-01, 6.9912e
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I want to introduce you to…ELMoBo
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OutputToken: 32 watchThe get_token(
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Helper Function to Retrieve Embeddi
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Output(tensor(-0.5047, device='cuda
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torch.all(new_flair_sentences[0].to
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Outputtensor(0.3504, device='cuda:0
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We can leverage this fact to slight
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We can easily get the embeddings fo
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Figure 11.24 - Losses—simple clas
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We can inspect the pre-trained mode
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Every word piece is prefixed with #
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far, our models used these embeddin
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position_ids = torch.arange(512).ex
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Pre-training TasksMasked Language M
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Then, let’s create an instance of
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If these two sentences were the inp
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The BERT model may take many other
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The contextual word embeddings are
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Model Configuration1 class BERTClas
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"Which BERT is that? DistilBERT?!"D
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Well, you probably don’t want to
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set num_labels=1 as argument.If you
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Output{'attention_mask': [1, 1, 1,
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OutputTrainingArguments(output_dir=
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Method for Computing Accuracy1 def
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loaded_model = (AutoModelForSequenc
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logits.logits.argmax(dim=1)Outputte
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For a complete list of available ta
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[215]. For a demo of GPT-2’s capa
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in Chapter 9, and I reproduce it be
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Data Preparation1 auto_tokenizer =
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Data Preparation1 lm_train_dataset
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The training arguments are roughly
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device_index = (model.device.indexi
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• learning that a language model
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[167] https://huggingface.co/docs/d
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