PyTorch Basics: Tensors and Gradients
Part 1 of “PyTorch: Zero to GANs”
This post is the first in a series of tutorials on building deep learning models with PyTorch, an open source neural networks library developed and maintained by Facebook. Check out the full series:
- PyTorch Basics: Tensors & Gradients (this post)
- Linear Regression & Gradient Descent
- Coming soon.. (logistic regression, neural networks, CNNs, RNNs, GANs etc.)
This series attempts to make PyTorch a bit more approachable for people starting out with deep learning and neural networks. In this post, we’ll cover the basic building blocks of PyTorch models: tensors and gradients.
This tutorial takes a code-first approach towards learning PyTorch, and you should try to follow along by running and experimenting with the code yourself. We’ll use the Anaconda distribution of Python to install libraries and manage virtual environments. For interactive coding and experimentation, we’ll use Jupyter notebooks. All the tutorials in this series are available as Jupyter notebooks hosted on Jovian: a sharing and collaboration platform for Jupyter. The notebook for this post is available here:
Share Juptyer notebooks instantly. Jovian makes Jupyter notebooks shareable, commentable and reproducible.jvn.io
Jovian makes it easy to share Jupyter notebooks on the cloud by running a single command directly within Jupyter. It also captures the Python environment and libraries required to run your notebook, so anyone (including you) can reproduce your work.
Here’s what you need to do to get started:
1. Install Anaconda by following the instructions given here. You might also need to add Anaconda binaries to your system PATH to be able to run the
conda command line tool.
2. Install the
jovian Python library by the running the following command (without the
$) on your Mac/Linux terminal or Windows command prompt:
$ pip install jovian --upgrade
3. Download the notebook for this tutorial using the
jovian clone command:
$ jovian clone e5cfe043873f4f3c9287507016747ae5
This creates a directory
01-pytorch-basics containing a Jupyter notebook and and Anaconda environment file.
$ ls 01-pytorch-basics
4. Now we can enter the directory and install the required Python libraries (Jupyter, PyTorch etc.) with a single command using
$ cd 01-pytorch-basics
$ conda env update
conda reads the
environment.yml file, creates a virtual environment with the name
01-pytorch-basics and installs all the required libraries inside the environment, to avoid modifying your system-wide installation of Python.
5. Activate the virtual environment by running
$ conda activate 01-pytorch-basics
For older installations of conda, you might need to run the command:
source activate 01-pytorch-basics.
6. Once the virtual environment is active, we can start Jupyter by running
$ jupyter notebook
7. You can now access Jupyter’s web interface by clicking the link that shows up on the terminal or by visiting http://localhost:8888 on your browser.
At this point, you can click on the notebook
01-pytorch-basics.ipynb to open it and run the code. If you want to type out the code yourself, you can also create a new notebook using the ‘New’ button.
We begin by importing PyTorch:
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:
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:
Let’s try creating slightly more complex tensors:
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.
Tensor operations and gradients
We can combine tensors with the usual arithmetic operations. Let’s look an example:
We’ve created 3 tensors
b, all numbers.
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:
y is a tensor with the value
3 * 4 + 5 = 17. What makes PyTorch special is that we can automatically compute the derivative of
y w.r.t. the tensors that have
requires_grad set to
b. To compute the derivatives, we can call the
.backward method on our result
The derivates of
y w.r.t the input tensors are stored in the
.grad property of the respective tensors.
dy/dw has the same value as
dy/dbhas the value
1. Note that
x doesn't have
requires_grad set to
True. The “grad” in
w.grad stands for gradient, which is another term for derivative, used mainly when dealing with matrices.
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 large ecosystem of supporting libraries:
- Matplotlib for plotting and visualization
- OpenCV for image and video processing
- Pandas for file I/O and data analysis
Instead of reinventing the wheel, PyTorch interoperates really well with Numpy to leverage its existing ecosystem of tools and libraries.
Here’s how we create an array in Numpy:
We can convert a Numpy array to a PyTorch tensor using
Let’s verify that the Numpy array and PyTorch tensor have similar data types.
We can convert a PyTorch tensor to a Numpy array using the
.to_numpymethod of a tensor.
The interoperability between PyTorch and Numpy is really important because most datasets you’ll work with will likely be read and preprocessed as Numpy arrays.
Commit and upload the notebook
As a final step, we can save and commit our work using the
Jovian uploads the notebook to https://jvn.io, captures the Python environment and creates a sharable link for your notebook as shown above. You can use this link to share your work and let anyone reproduce it easily with the
jovian clone command. Jovian also includes a powerful commenting interface, so you (and others) can discuss & comment on specific parts of your notebook:
Tensors in PyTorch support a variety of operations, and what we’ve covered here is by no means exhaustive. You can learn more about tensors and tensor operations here:
When data is a tensor x, reads out 'the data' from whatever it is passed, and constructs a leaf variable. Therefore…pytorch.org
You can take advantage of the interactive Jupyter environment to experiment with tensors and try different combinations of operations discussed above. Here are some things to try out:
- What if one or more “x”, “w” or “b” were matrices, instead of numbers, in the above example? What would the result “y” and the gradients
b.gradlook like in this case?
- What if “y” was a matrix created using
torch.tensor, with each element of the matrix expressed as a combination of numeric tensors “x”, “w” and “b”?
- What if we had a chain of operations instead of just one i.e.
y = x * w + b,
z = l * y + m,
e =c * z + dand so on? What would calling
If you’re interested, you can learn more about matrix derivates on Wikipedia (although it’s not necessary for following along with this series of tutorials):
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of…en.wikipedia.org
With this, we complete our discussion of tensors and gradients in PyTorch, and we’re ready to move on to the next topic: Linear regression.
The material in this series is heavily inspired by the following resources: