Learn about Tensors and how to use them in one of the most famous machine learning libraries, PyTorch

One of most important libraries in the Deep Learning field (and inclusively, where ChatGPT was built upon) is pytorch. Along with the Tensorflow framework, pytorch is one of the most famous neural network training frameworks available for software developers and data scientists. Apart from its usability and simple API, it excels in flexibility and memory usage, making it extremely fast in multi-dimensional calculus (one of the major components behind backpropagation, the important technique that is used to optimize Neural Network’s weights) — these details make it one of the most sought after libraries by companies when it comes to build Deep Learning models.

In this blog post, we’re going to check some basic operations using pytorch and understand how we can work with the tensor object! Tensors are mathematical representations of data that are commonly addressed by different names:

  • 1 element Tensor: commonly called the scalar, consists of a single mathematical value.
  • 1-Dimensional Tensor: consisting of n examples, they are normally called 1-D vectors and stores different mathematical elements in a single dimension.
  • 2-Dimensional Tensors: commonly called matrices, are able to store data in two dimensions. Think of a normal SQL table or an excel spreadsheet.
  • 3-Dimensional Tensors and beyond: Data organized with this dimensionality are normally harder to visualize and are generally called n-dimensional tensors.

With this small introduction on mathematical concepts, let’s explore how to use pytorch ‘s in Python!

The Tensor object

As we’ve described, the tensor object is a mathematical generalization of n-dimensional objects that can expand to virtually any dimension. Although in the context of Deep Learning, tensors are generally multidimensional, we can also create single element tensors (normally called scalars) using torch (although named pytorch , we use the name torch to manipulate the library in Python).

If tensors are the central object in torch (or pytorch ) , how can we create them in the library?

Super easy! Let’s create our first single-element tensor:

import torch
scalar = torch.tensor(5)

Our scalar object contains a single number — 5. Let’s visualize our tensor below by calling it in the Python console:

scalar object — Image by Author
Fact 1: torch.tensor is used to create tensor objects

Of course, we are not only tied to single element tensors — we can also create 1-dimensional objects with multiple elements. Let’s pass a list inside thetorch.tensor and see how that will go:

vector = torch.tensor([7, 7])
vector object — Image by Author

Our object vector now contains two elements along a single dimension. Think as if this data contains 1 single row or a single column of data.

Having “dimensions” allows us to access interesting properties in our tensor — for example ndim:

ndim of vector object — image by author
Fact 2: tensor.ndim is used to obtain the number of dimensions of a tensor object

In our case, the vector object only has a single dimension. How can we know how many elements our tensor object has? By using another property - shape !

shape of vector object — image by author
Fact 3: tensor.shapeis used to obtain the shape of a tensor object

Our tensor object contains two elements in a single dimension. We’ll see how this output compares to multidimensional objects.

torch tensors also contain a data type attached to it. To know which, we can use:

dtype of vector object — image by author
Fact 4: tensor.dtype outputs the object type of our tensor.

Our tensor contains data in int64 format.

Let’s now expand our object into a 2-D tensor:

matrix = torch.tensor([[10.0, 20.0], 
                       [30.0, 40.0]])

matrix object — image by author

Let’s see some properties about our matrix object:

ndim, shape and dtype of matrix object — image by author

Our matrix object contains data in float32 dtype in two dimensions with 2 elements each.

To finish our exploration on creating tensors, let’s see how we generate random tensors using torch.rand :

torch.rand(size=(4, 4))
random tensor — image by author

For example, in the tensor above, we are generating a 4 by 4 matrix using tensor.rand . This is a very common operation in the context of deep learning (for example, generating random neural network layer weights to optimize later).

Tensor Operations

Let’s now see how we can perform operations with our tensors. If you’re already familiar with numpy , this should be pretty easy! Starting with a simple add operation:

tensor = torch.tensor([1, 2, 3])
tensor + 20
tensor + 10 calculation — Image by Author

Adding a scalar to a tensor is easy — just use the normal mathematical operation! Can you guess how you can multiply a tensor by a scalar?


tensor * 10
tensor * 10 calculation — Image by Author

You can also use the abstraction torch.multiply :

torch.multiply(tensor, 10)
tensor * 10 calculation — Image by Author

Two of the most common operations with tensors are the Hadamard and Dot Product, with the latter being one of the most famous calculations that is widely used in the Attention mechanism.

Let’s create two 2-D tensors to check these operations:

tensor_1 = torch.tensor([[1,2,3],[2,3,4]])
tensor_2 = torch.tensor([[1,2],[2,3],[3,4]])
tensor_1, a 2 by 3 tensor — Image by Author
tensor_2, a 3 by 2 tensor — Image by Author

To perform the Hadamard product, the tensor shapes must match. Let’s perform a calculation of tensor_1 with itself:

# Hadamard product
tensor_1 * tensor_1
tensor_1 times tensor_1 — Image by Author

In case of the dot product, the inner dimensions of the tensors must match. Let’s multiply tensor_1 (a 2x3 tensor) by tensor_2 (a 3x2 tensor):

torch.matmul(tensor_1, tensor_2)
dot product of tensor_1 with tensor_2 — Image by Author

We can also use the elegant @ operation, that does just the same:

tensor_1 @ tensor_2
dot product of tensor_1 with tensor_2 — Image by Author

Tensor Indexing

For our final examples, let’s see how we can pluck certain elements from our tensors. For these examples, we’ll use:

indexing_example = torch.tensor([[10,20,30],[40,50,60],[70,80,90]])
2-D Tensor example — Image by Author

Indexing in pytorch is similar to other Python objects — let’s try to index the first column:

1st Row Example — Image by Author

Using 0 index on the [] will give us the ability to extract the first row of the object. The : symbol enables us to extract all elements from a certain dimension. In our case, we want all elements from the columns (2nd dimension).

Can you guess how to extract the first column? Just switch the position of the indices!

1st Column Example — Image by Author

For more complex objects, we can also use the same logic. Let’s try to index an element from a 3D tensor:

indexing_example_3d = torch.tensor([[[10,20,30],[40,50,60],[70,80,90]], [[100,200,300],[400,500,600],[700,800,900]]])
3D Tensor — Image by Author

How can we extract the element “100” from this tensor? Let’s see, we want:

  • First row
  • First column
  • Second matrix

Using indexing logic, we can do this easily:

100 element from indexing_example_3d— Image by Author

In torch, the index ordering for 3d objects is the following: matrix, row, column.

Can you try to index a 4D object?

Bonus —Where is the tensor stored?

One of the advantages of using torch over other array libraries (such as numpy ) is the ability to save our tensors in the gpu — this will be particularly useful if we need to speed up neural network calculations.

By default, your tensors are stored on the cpu (and most computers only have a cpu available) but you can send your tensors to your gpu by doing the following:

device = "cuda" if torch.cuda.is_available() else "cpu"

If torch.cuda.is_available() finds a specific NVIDIA gpu in your machine, it will let you send your tensor to it.

Imagining you have a tensor stored in a tensor named object, you can use the .to method to send it to the device:

tensor_on_gpu = tensor.to(device)


Thank you for taking the time to read this post! Working with tensors is extremely fun and definitely give you a solid foundation to work with advanced neural networks.

The torch API is extremely elegant and easy to visualize. Later, you can use these tensors to train Neural Networks (something I’ll show in the next blog posts of this series). Additionally, learning a bit of linear algebra as you go will be extremely helpful to learn some other Data Science and Machine Learning Algorithms.

The inspiration for this post came from


— this is an excellent free course on the Pytorch topic and I definitely recommend it. At DareData, we’ve been involved with a lot of Deep Learning projects and I can’t stress how important this course has been to train our people into learning this Machine Learning paradigm and all frameworks associated with it.

In the next post, we’ll take a look into training a Linear Regression using torch — stay tuned!

If you would like to know more about how we use torch  in our projects, or would like to capacitate your team, contact me at ivo@daredata.engineering - looking to speaking to you!