After Google’s TensorFlow machine learning framework, tensors became well-known in IT. Tensors are the primary unit of calculation for them. Although the terms are similar, they are not identical. Tensors in programming and tensors in mathematics are not the same thing. They just inherit some of their characteristics. They use some of their representation strategies.
They are simply expressed as arrays of arrays or lists of lists in this case. In machine learning, these representations may be changed in a variety of ways, and they are not bound by the tight coordinating transformation principles imposed by mathematics and physics. As a result, it is not equal to mathematical tensors, although it does inherit some of their mathematical features.
Every tensor in Tensorflow has a shape attribute that represents it. Every tensor has a shape(x,y), where x is the tensor’s length and y is the dimension of matrices or lists/arrays inside the tensor in this example. It must be the same for each list/array within.
Meaning of Tensor
When it comes to representing data for machine learning, we usually have to do it mathematically. This is performed using a data repository known as the tensor, especially when it comes to neural network data representation.
So, what does it mean to be a tensor? A tensor is a container that can hold N dimensions of data. Tensors are extensions of matrices to N-dimensional space and are frequently and incorrectly used interchangeably with the matrix (which is precisely a 2-dimensional tensor).
Tensors, on the other hand, are more than just a data container in mathematics. Tensors provide descriptions of valid linear transformations between tensors in addition to numeric data.
The cross product and the dot product are two examples of such transformations or relations. Tensors can be thought of as things in an object-oriented sense, rather than just as data structures, from a computer science perspective.
Tensor and Machine Learning
While everything preceding is correct, there is a distinction between what tensors are formally and what we refer to as tensors in machine learning applications. If we take tensors to be nothing more than data structures, we can see where they fit in with scalars, vectors, and matrices, as well as some basic code that shows how they may be used to produce each of these data types.
A scalar is defined as a single number. A scalar is a tensor with zero dimensions. As a result, it has 0 axes and is ranked 0.
And here’s where the intricacy enters in: just because a single number may be written as a tensor doesn’t mean it should be, or even that it is in general. Although there are compelling reasons to be able to regard them as such (which will become clear when we explore tensor operations), this ability can be perplexing as a storage method.
A vector is a one-dimensional (1D) tensor, which is more generally referred to as an array in computer science. A vector is a set of integers with a single axis and a rank of one.
A matrix is a rank 2 tensor, which means it has two axes. You’ve seen them in a variety of places. A matrix is a two-dimensional (2D) tensor that is organized as a grid of integers (imagine rows and columns).
While all of the above structures are genuine tensors in theory, when we talk about tensors, we’re referring to the generalization of the idea of a matrix to N 3 dimensions. To prevent misunderstanding, we would generally refer to tensors with three dimensions or more as tensors.
Tensor and Deep Learning
Machine learning includes deep learning as a subset. It is a field that is focused on computer algorithms learning and developing on its own. Deep learning employs artificial neural networks, which are supposed to mimic how people think and learn, as opposed to machine learning, which uses simpler principles. TensorFlow and PyTorch are well-known deep learning frameworks.
Machine learning systems employ sensors as a data structure, and understanding them is a crucial ability to develop early on.
A tensor is a numerical data container. It is the method through which we will store the data that we will utilize in our system.
A tensor is defined by three fundamental characteristics: rank, data type, and shape.
Matrix is used to represent tensors. It makes representing data in an array so much easier. Consider a picture with a Y x Y resolution. The pixel data of the photos may be expressed in an array with ease. The same may be stated for video frames. The representation becomes a lot less difficult. As a result, the key lesson is that we may obtain such a precise representation of data that it can be deemed almost identical to the natural representation of those items.
This is why, despite the fact that there are many alternative frameworks available, TensorFlow is popular among engineers and many other firms are adopting it.