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

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• dampening: dampening factor for momentum• nesterov: enables Nesterov momentum, which is a smarter version of theregular momentum, and also has its own sectionThat’s the perfect moment to dive deeper into momentum (sorry, I really cannot missa pun!).MomentumOne of SGD’s tricks is called momentum. At first sight, it looks very much like usingan EWMA for gradients, but it isn’t. Let’s compare EWMA’s beta formulation withmomentum’s:Equation 6.11 - Momentum vs EWMASee the difference? It does not average the gradients; it runs a cumulative sum of"discounted" gradients. In other words, all past gradients contribute to the sum,but they are "discounted" more and more as they grow older. The "discount" isdriven by the beta parameter. We can also write the formula for momentum likethis:Equation 6.12 - Compounding momentumThe disadvantage of this second formula is that it requires the full history ofgradients, while the previous one depends only on the gradient’s current value andmomentum’s latest value. "What about the dampening factor?" Learning Rates | 471
The dampening factor is a way to, well, dampen the effect of the latest gradient.Instead of having its full value added, the latest gradient gets its contribution tomomentum reduced by the dampening factor. So, if the dampening factor is 0.3,only 70% of the latest gradient gets added to momentum. Its formula is given by:Equation 6.13 - Momentum with dampening factorIf the dampening factor equals the momentum factor (beta), itbecomes a true EWMA!Similar to Adam, SGD with momentum keeps the value of momentum for eachparameter. The beta parameter is stored there as well (momentum). We can take apeek at it using the optimizer’s state_dict():{'state': {139863047119488: {'momentum_buffer': tensor([[-0.0053]])},139863047119168: {'momentum_buffer': tensor([-0.1568])}},'param_groups': [{'lr': 0.1,'momentum': 0.9,'dampening': 0,'weight_decay': 0,'nesterov': False,'params': [139863047119488, 139863047119168]}]}Even though old gradients slowly fade away, contributing less and less to the sum,very recent gradients are taken almost at their face value (assuming a typicalvalue of 0.9 for beta and no dampening). This means that, given a sequence of allpositive (or all negative) gradients, their sum, that is, the momentum, is going upreally fast (in absolute value). A large momentum gets translated into a largeupdate since momentum replaces gradients in the parameter update:Equation 6.14 - Parameter updateThis behavior can be easily visualized in the path taken by SGD with momentum.472 | Chapter 6: Rock, Paper, Scissors
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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
Page 446 and 447: model anyway. We’ll use it to com
Page 448 and 449: StepByStep Method@staticmethoddef m
Page 450 and 451: "What’s wrong with the colors?"Th
Page 452 and 453: three_channel_filter = np.array([[[
Page 454 and 455: Fancier Model (Constructor)class CN
Page 456 and 457: Fancier Model (Classifier)def class
Page 458 and 459: torch.manual_seed(44)dropping_model
Page 460 and 461: Outputtensor([0.1000, 0.2000, 0.300
Page 462 and 463: Figure 6.8 - Output distribution fo
Page 464 and 465: Adaptive moment estimation (Adam) u
Page 466 and 467: torch.manual_seed(13)# Model Config
Page 468 and 469: Outputtorch.Size([5, 3, 3, 3])Its s
Page 470 and 471: Choosing a learning rate that works
Page 472 and 473: Higher-Order Learning Rate Function
Page 474 and 475: Perfect! Now let’s build the actu
Page 476 and 477: ax.set_xlabel('Learning Rate')ax.se
Page 478 and 479: LRFinderThe function we’ve implem
Page 480 and 481: value in our moving average has an
Page 482 and 483: Figure 6.15 - Distribution of weigh
Page 484 and 485: In code, the implementation of the
Page 486 and 487: As expected, the EWMA without corre
Page 488 and 489: optimizer = optim.Adam(model.parame
Page 490 and 491: IMPORTANT: The logging function mus
Page 492 and 493: Output{'state': {140601337662512: {
Page 494 and 495: different optimizer, set them to ca
Page 498 and 499: Figure 6.20 - Paths taken by SGD (w
Page 500 and 501: Equation 6.16 - Looking aheadOnce N
Page 502 and 503: Figure 6.22 - Path taken by each SG
Page 504 and 505: for epoch in range(4):# training lo
Page 506 and 507: course) up to a given number of epo
Page 508 and 509: Next, we create a protected method
Page 510 and 511: Mini-Batch SchedulersThese schedule
Page 512 and 513: Schedulers in StepByStep — Part I
Page 514 and 515: Scheduler PathsBefore trying out a
Page 516 and 517: After applying each scheduler to SG
Page 518 and 519: Data Preparation1 # Loads temporary
Page 520 and 521: Figure 6.31 - LossesEvaluationprint
Page 522 and 523: [96] http://www.samkass.com/theorie
Page 524 and 525: ImportsFor the sake of organization
Page 526 and 527: ILSVRC-2012The 2012 edition [111] o
Page 528 and 529: remained unchanged.ResNet (MSRA Tea
Page 530 and 531: Transfer Learning in PracticeIn Cha
Page 532 and 533: dropout. You’re already familiar
Page 534 and 535: OutputDownloading: "https://downloa
Page 536 and 537: Replacing the "Top" of the Model1 a
Page 538 and 539: Model Size Classifier Layer(s) Repl
Page 540 and 541: Model TrainingWe have everything se
Page 542 and 543: "Removing" the Top Layer1 alex.clas
Page 544 and 545: 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
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A mini-batch of size 64 is small en
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normed1 = batch_normalizer(batch1[0
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OutputOrderedDict([('running_mean',
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OutputOrderedDict([('running_mean',
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batch_normalizer = nn.BatchNorm2d(n
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torch.manual_seed(23)dummy_points =
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np.concatenate([dummy_points[:5].nu
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Another advantage of these shortcut
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It should be pretty clear, except f
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Data Preparation1 # ImageNet statis
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Data Preparation — Preprocessing1
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• freezing the layers of the mode
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Extra ChapterVanishing and Explodin
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discussing it, let me illustrate it
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Model Configuration (2)1 loss_fn =
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weights. If done properly, the init
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just did), or, if you are training
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Figure E.3 - The effect of batch no
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Model Configuration1 torch.manual_s
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torch.manual_seed(42)parm = nn.Para
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(and only if) the norm exceeds the
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if callable(self.clipping): 1self.c
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Moreover, let’s use a ten times h
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Clipping with HooksFirst, we reset
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• visualizing the difference betw
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Chapter 8SequencesSpoilersIn this c
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Before shuffling, the pixels were o
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And then let’s visualize the firs
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sequence so far, and a data point f
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Considering this, the not "unrolled
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linear_input = nn.Linear(n_features
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Outputtensor([[0.3924, 0.8146]], gr
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Now we’re talking! The last hidde
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Let’s take a look at the RNN’s
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◦ The initial hidden state, which
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batch_first argument to True so we
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OutputOrderedDict([('weight_ih_l0',
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out, hidden = rnn_stacked(x)out, hi
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_l0_reverse).Once again, let’s cr
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For bidirectional RNNs, the last el
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Model Configuration1 class SquareMo
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StepByStep.loader_apply(test_loader
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Figure 8.14 - Final hidden states f
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Figure 8.16 - Transforming the hidd
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Since the RNN cell has both of them
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Every gate worthy of its name will
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• For r=0 and z=0, the cell becom
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In code, we can use split() to get
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Let’s pause for a moment here. Fi
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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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