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PyTorch Basics: Tensors & Gradients

Part 1 of "Deep Learning with Pytorch: Zero to GANs"

This tutorial series is a hands-on beginner-friendly introduction to deep learning using PyTorch, an open-source neural networks library. These tutorials take a practical and coding-focused approach. The best way to learn the material is to execute the code and experiment with it yourself. Check out the full series here:

  1. PyTorch Basics: Tensors & Gradients
  2. Gradient Descent & Linear Regression
  3. Working with Images & Logistic Regression
  4. Training Deep Neural Networks on a GPU
  5. Image Classification using Convolutional Neural Networks
  6. Data Augmentation, Regularization and ResNets
  7. Generating Images using Generative Adversarial Networks

This tutorial covers the following topics:

  • Introductions to PyTorch tensors
  • Tensor operations and gradients
  • Interoperability between PyTorch and Numpy
  • How to use the PyTorch documentation site

Prerequisites

If you're just getting started with data science and deep learning, then this tutorial series is for you. You just need to know the following:

We'll cover any additional mathematical and theoretical concepts we need as we go along.

How to run the code

This tutorial is an executable Jupyter notebook hosted on Jovian (don't worry if these terms seem unfamiliar; we'll learn more about them soon). You can run this tutorial and experiment with the code examples in a couple of ways: using free online resources (recommended) or on your computer.

Option 1: Running using free online resources (1-click, recommended)

The easiest way to start executing the code is to click the Run button at the top of this page and select Run on Colab. Google Colab is a free online platform for running Jupyter notebooks using Google's cloud infrastructure. You can also select "Run on Binder" or "Run on Kaggle" if you face issues running the notebook on Google Colab.

Option 2: Running on your computer locally

To run the code on your computer locally, you'll need to set up Python, download the notebook and install the required libraries. We recommend using the Conda distribution of Python. Click the Run button at the top of this page, select the Run Locally option, and follow the instructions.

Jupyter Notebooks: This tutorial is a Jupyter notebook - a document made of cells. Each cell can contain code written in Python or explanations in plain English. You can execute code cells and view the results, e.g., numbers, messages, graphs, tables, files, etc. instantly within the notebook. Jupyter is a powerful platform for experimentation and analysis. Don't be afraid to mess around with the code & break things - you'll learn a lot by encountering and fixing errors. You can use the "Kernel > Restart & Clear Output" or "Edit > Clear Outputs" menu option to clear all outputs and start again from the top.

Before we begin, we need to install the required libraries. The installation of PyTorch may differ based on your operating system / cloud environment. You can find detailed installation instructions here: https://pytorch.org .

In [ ]:
# Uncomment and run the appropriate command for your operating system, if required

# Linux / Binder
# !pip install numpy torch==1.7.0+cpu torchvision==0.8.1+cpu torchaudio==0.7.0 -f https://download.pytorch.org/whl/torch_stable.html

# Windows
# !pip install numpy torch==1.7.0+cpu torchvision==0.8.1+cpu torchaudio==0.7.0 -f https://download.pytorch.org/whl/torch_stable.html

# MacOS
# !pip install numpy torch torchvision torchaudio

Let's import the torch module to get started.

In [2]:
import torch

Tensors

At its core, PyTorch is a library for processing tensors. A tensor is a number, vector, matrix, or any n-dimensional array. Let's create a tensor with a single number.

In [9]:
# Number
t1 = torch.tensor(4.)
t1
Out[9]:
tensor(4.)

4. is a shorthand for 4.0. It is used to indicate to Python (and PyTorch) that you want to create a floating-point number. We can verify this by checking the dtype attribute of our tensor.

In [10]:
t1.dtype
Out[10]:
torch.float32

Let's try creating more complex tensors.

In [11]:
# Vector
t2 = torch.tensor([1., 2, 3, 4])
t2
Out[11]:
tensor([1., 2., 3., 4.])
In [12]:
# Matrix
t3 = torch.tensor([[5., 6], 
                   [7, 8], 
                   [9, 10]])
t3
Out[12]:
tensor([[ 5.,  6.],
        [ 7.,  8.],
        [ 9., 10.]])
In [8]:
# 3-dimensional array
t4 = torch.tensor([
    [[11, 12, 13], 
     [13, 14, 15]], 
    [[15, 16, 17], 
     [17, 18, 19.]]])
t4
Out[8]:
tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])

Tensors can have any number of dimensions and different lengths along each dimension. We can inspect the length along each dimension using the .shape property of a tensor.

In [ ]:
print(t1)
t1.shape
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print(t2)
t2.shape
In [ ]:
print(t3)
t3.shape
In [ ]:
print(t4)
t4.shape

Note that it's not possible to create tensors with an improper shape.

In [ ]:
# Matrix
t5 = torch.tensor([[5., 6, 11], 
                   [7, 8], 
                   [9, 10]])
t5

A ValueError is thrown because the lengths of the rows [5., 6, 11] and [7, 8] don't match.

Tensor operations and gradients

We can combine tensors with the usual arithmetic operations. Let's look at an example:

In [4]:
# Create tensors.
x = torch.tensor(3.)
w = torch.tensor(4., requires_grad=True)
b = torch.tensor(5., requires_grad=True)
print(x, w, b)
tensor(3.) tensor(4., requires_grad=True) tensor(5., requires_grad=True)

We've created three tensors: x, w, and b, all numbers. w and b have an additional parameter requires_grad set to True. We'll see what it does in just a moment.

Let's create a new tensor y by combining these tensors.

In [5]:
# Arithmetic operations
y = w * x + b
y
Out[5]:
tensor(17., grad_fn=<AddBackward0>)

As expected, y is a tensor with the value 3 * 4 + 5 = 17. What makes PyTorch unique is that we can automatically compute the derivative of y w.r.t. the tensors that have requires_grad set to True i.e. w and b. This feature of PyTorch is called autograd (automatic gradients).

To compute the derivatives, we can invoke the .backward method on our result y.

In [ ]:
# Compute derivatives
y.backward()

The derivatives of y with respect to the input tensors are stored in the .grad property of the respective tensors.

In [ ]:
# Display gradients
print('dy/dx:', x.grad)
print('dy/dw:', w.grad)
print('dy/db:', b.grad)

As expected, dy/dw has the same value as x, i.e., 3, and dy/db has the value 1. Note that x.grad is None because x doesn't have requires_grad set to True.

The "grad" in w.grad is short for gradient, which is another term for derivative. The term gradient is primarily used while dealing with vectors and matrices.

Tensor functions

Apart from arithmetic operations, the torch module also contains many functions for creating and manipulating tensors. Let's look at some examples.

In [6]:
# Create a tensor with a fixed value for every element
t6 = torch.full((3, 2), 42)
t6
Out[6]:
tensor([[42, 42],
        [42, 42],
        [42, 42]])
In [13]:
# Concatenate two tensors with compatible shapes
t7 = torch.cat((t3, t6))
t7
Out[13]:
tensor([[ 5.,  6.],
        [ 7.,  8.],
        [ 9., 10.],
        [42., 42.],
        [42., 42.],
        [42., 42.]])
In [14]:
# Compute the sin of each element
t8 = torch.sin(t7)
t8
Out[14]:
tensor([[-0.9589, -0.2794],
        [ 0.6570,  0.9894],
        [ 0.4121, -0.5440],
        [-0.9165, -0.9165],
        [-0.9165, -0.9165],
        [-0.9165, -0.9165]])
In [17]:
# Change the shape of a tensor
t9 = t8.reshape(2, 3, 2)
t9
Out[17]:
tensor([[[-0.9589, -0.2794],
         [ 0.6570,  0.9894],
         [ 0.4121, -0.5440]],

        [[-0.9165, -0.9165],
         [-0.9165, -0.9165],
         [-0.9165, -0.9165]]])

You can learn more about tensor operations here: https://pytorch.org/docs/stable/torch.html . Experiment with some more tensor functions and operations using the empty cells below.

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Interoperability with Numpy

Numpy is a popular open-source library used for mathematical and scientific computing in Python. It enables efficient operations on large multi-dimensional arrays and has a vast ecosystem of supporting libraries, including:

  • Pandas for file I/O and data analysis
  • Matplotlib for plotting and visualization
  • OpenCV for image and video processing

If you're interested in learning more about Numpy and other data science libraries in Python, check out this tutorial series: https://jovian.ai/aakashns/python-numerical-computing-with-numpy .

Instead of reinventing the wheel, PyTorch interoperates well with Numpy to leverage its existing ecosystem of tools and libraries.

Here's how we create an array in Numpy:

In [ ]:
import numpy as np

x = np.array([[1, 2], [3, 4.]])
x

We can convert a Numpy array to a PyTorch tensor using torch.from_numpy.

In [ ]:
# Convert the numpy array to a torch tensor.
y = torch.from_numpy(x)
y

Let's verify that the numpy array and torch tensor have similar data types.

In [ ]:
x.dtype, y.dtype

We can convert a PyTorch tensor to a Numpy array using the .numpy method of a tensor.

In [ ]:
# Convert a torch tensor to a numpy array
z = y.numpy()
z

The interoperability between PyTorch and Numpy is essential because most datasets you'll work with will likely be read and preprocessed as Numpy arrays.

You might wonder why we need a library like PyTorch at all since Numpy already provides data structures and utilities for working with multi-dimensional numeric data. There are two main reasons:

  1. Autograd: The ability to automatically compute gradients for tensor operations is essential for training deep learning models.
  2. GPU support: While working with massive datasets and large models, PyTorch tensor operations can be performed efficiently using a Graphics Processing Unit (GPU). Computations that might typically take hours can be completed within minutes using GPUs.

We'll leverage both these features of PyTorch extensively in this tutorial series.

Save and upload your notebook

Whether you're running this Jupyter notebook online or on your computer, it's essential to save your work from time to time. You can continue working on a saved notebook later or share it with friends and colleagues to let them execute your code. Jovian offers an easy way of saving and sharing your Jupyter notebooks online.

First, you need to install the Jovian python library if it isn't already installed.

In [ ]:
!pip install jovian --upgrade --quiet
In [ ]:
import jovian
In [ ]:
jovian.commit(project='01-pytorch-basics')

The first time you run jovian.commit, you may be asked to provide an API Key to securely upload the notebook to your Jovian account. You can get the API key from your Jovian profile page after logging in / signing up.

jovian.commit uploads the notebook to your Jovian account, captures the Python environment, and creates a shareable link for your notebook, as shown above. You can use this link to share your work and let anyone (including you) run your notebooks and reproduce your work. Jovian also includes a powerful commenting interface, so you can discuss & comment on specific parts of your notebook:

https://jovian.ai/docs/user-guide/upload.html

You can do a lot more with the jovian Python library. Visit the documentation site to learn more: https://jovian.ai/docs/index.html

Summary and Further Reading

Try out this assignment to learn more about tensor operations in PyTorch: https://jovian.ai/aakashns/01-tensor-operations

This tutorial covers the following topics:

  • Introductions to PyTorch tensors
  • Tensor operations and gradients
  • Interoperability between PyTorch and Numpy

You can learn more about PyTorch tensors here: https://pytorch.org/docs/stable/tensors.html.

The material in this series is inspired by:

With this, we complete our discussion of tensors and gradients in PyTorch, and we're ready to move on to the next topic: Gradient Descent & Linear Regression.

Questions for Review

Try answering the following questions to test your understanding of the topics covered in this notebook:

  1. What is PyTorch?
  2. What is a Jupyter notebook?
  3. What is Google Colab?
  4. How do you install PyTorch?
  5. How do you import the torch module?
  6. What is a vector? Give an example.
  7. What is a matrix? Give an example.
  8. What is a tensor?
  9. How do you create a PyTorch tensor? Illustrate with examples.
  10. What is the difference between a tensor and a vector or a matrix?
  11. Is every tensor a matrix?
  12. Is every matrix a tensor?
  13. What does the dtype property of a tensor represent?
  14. Is it possible to create a tensor with elements of different data types?
  15. How do you inspect the number of dimensions of a tensor and the length along each dimension?
  16. Is it possible to create a tensor with the values [[1, 2, 3], [4, 5]]? Why or why not?
  17. How do you perform arithmetic operations on tensors? Illustrate with examples?
  18. What happens if you specify requires_grad=True while creating a tensor? Illustrate with an example.
  19. What is autograd in PyTorch? How is it useful?
  20. What happens when you invoke the backward method of a tensor?
  21. How do you check the derivates of a result tensor w.r.t. the tensors used to compute its value?
  22. Give some examples of functions available in the torch module for creating tensors.
  23. Give some examples of functions available in the torch module for performing mathematical operations on tensors.
  24. Where can you find the list of tensor operations available in PyTorch?
  25. What is Numpy?
  26. How do you create a Numpy array?
  27. How do you create a PyTorch tensor using a Numpy array?
  28. How do you create a Numpy array using a PyTorch tensor?
  29. Why is interoperability between PyTorch and Numpy important?
  30. What is the purpose of a library like PyTorch if Numpy already provides data structures and utilities to with multi-dimensional numeric data?
  31. What is Jovian?
  32. How do you upload your notebooks to Jovian using jovian.commit ?
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