We explain tensors in simple terms, where they came from, and why they’re so important to machine learning models, specifically within deep learning.
Tensors are used in Machine Learning to represent input and output data and are central to Machine Learning models. In isolation, tensors are numbers configured to a specific shape and rank based on dimensionality, enabling one to calculate arithmetic operations.
What is a Tensor?
A tensor is an algebraic object that describes the relationship between specific mathematical objects relative to a vector space. Similarly to a vector, a tensor has geometric meaning and is a way of calculating arithmetic operations.
In terms of their representation, a tensor is shown as several numbers arranged on a grid with variable numbers of axis.
Tensor notation is similar to matrix notation, beginning with a capital letter representing tensor and lowercase letters with subscript integers representing scalar values within.
Widely used in mathematics, physics, and engineering, tensors are critical to machine learning, as well as in the training and operation of deep learning models, as explained below.
What is Deep Learning?
To understand tensors, you need to grasp the concept of deep learning, which itself is a subset of machine learning. Specifically, deep learning is a field concerned with learning and improving independently based on an examination of computer algorithms.
Deep learning works with artificial neural networks designed to conceptualize and imitate human thinking and learning.
The likes of TensorFlow and PyTorch are typical examples of deep learning frameworks.
The relationship between tensors and deep learning is vital, as tensors store the data structures used by machine learning systems.
As such, it’s essential to understand that the two go hand-in-hand.
Are Tensors Used in Machine Learning?
Yes, tensors are used in machine learning and are everywhere you look in modern machine learning systems.
As well as the aforementioned neural networks, tensors exist in videos and fMRI data and play a crucial role in a machine’s performance.
Often regarded as the future of deep learning, tensor methods enable developers to preserve and leverage systems and structures even further, adding individual layers of whole networks to programs.
Developers regard tensors as integral in the current generation of AI algorithms.
They are likely to play a massive part in the development of future structures such as home DIY machines like Cameo due to their unique design and the fact that they can be manipulated differently.
Why are Tensors Important in Machine Learning?
Tensors have become integral to physics as they provide a concise mathematical framework for formulating and solving problems.
Developers who utilize tensor methods within deep learning see multiple benefits, including:
- Improved performance and generalization as a result of enhanced inductive biases.
- Enhanced robustness.
- Significant reduction in the number of required parameters, resulting in economical models.
- Increased computational speeds.
It’s also important to understand that tensors are dynamic, meaning that they transform when they interact with other mathematical models.
This differentiates tensors from matrices, as the latter don’t usually have this property.
This characteristic ensures that tensors are fundamental to machine learning, as machines cannot learn without the relevant datasets.
Due to the multidimensional nature of current data, tensors play a vital role in machine learning by encoding multifaceted data.
Who Invented Tensors?
Credit for the invention of the tensor is usually attributed to the great Italian mathematician Gregorio Ricci-Curbastro.
His early work focused on mathematical physics, and by 1900, Curbastro had developed a framework for his theory of tensor calculus.
The initial theory was an extension of vector calculus to tensor fields, and he developed and honed his theory with the help of a student – Tullio Levi-Civita.
Their theory was one of a number than enabled Einstein to develop his theory of general relativity, and the two met in Padua in 1921.
Of course, tensors have come a long way since the start of the 1900s, and in the modern day, their use is fuelling the growth and potential of machine learning and AI.
If only the Italian geniuses could see what their theory has become!
Conclusion
As explained, tensors are mathematical formations configured to a specific shape that enable machine learning and contribute to the progression and success of AI.
They’re essential to machine learning because they play a vital role in learning by encoding multidimensional data.
The theory of tensors and an understanding of their use has been widely known since the early 1900s.
It’s fair to say that their use in modern-day AI systems and frameworks has made them of fundamental importance to developers and everyone involved in machine learning systems.