What are "tensor", "vector" and "matrix"?Karakuri of information organization of deep learning
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When studying computer-related things, the appearance of mathematical explanations can be discouraging. In particular, many people may not want to even hear the names of vectors and matrices that high school students are not good at. However, deep learning deals with more esoteric numbers called "tensors". Even if it is not mathematically understandable, if you get an idea of what it is like, you will deepen your understanding of deep learning. This time, I will briefly explain the numerical values handled by deep learning, omitting small and difficult stories.
Freelance writer Naoki Mitsumura
Freelance writer Naoki Mitsumura
Representative of GK Noteip. Writer. He majored in computer science at a university in the United States, and after graduating, engaged in planning and marketing of IT-related products at some listed companies in Japan. After retiring, he has been involved in writing books and articles and creating web content as a writer. In addition to artificial intelligence, he deals with topics related to science, IT, military, and medical care, and also conducts research support activities at research institutes and universities. His books include "Core Technology in the Near Future (Shoeisha)", "Illustration: An Introduction to AI Business (Narumi-do)", and "Artificial Intelligence in Manga (Ikeda Bookstore)".
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- What is a "tensor"?
- Relationship between "tensor" and "vector" "matrix"
- What is the mechanism of translation technology, "vectorizing words"?
In deep learning, a huge number of numbers run around on a complex neural network. The computer can also handle those numbers individually. However, the calculation in the neural network cannot be theorized as it is, and above all, if there is no common understanding about the numerical values handled by each neural network, even if other people read the code of the program, they will not know what is written. However, it becomes difficult to connect to the application and development of technology. The mathematical concept that came to be used there was "tensor". The concept of a tensor is difficult to understand mathematically, but from our point of view it looks like a "collection of many numbers". Basically, a tensor collects a lot of numerical values and expresses them as "one piece of information", which is like "expressing the characteristics of a game character with innumerable stats". The information I want to express is only one existence called "character", but when expressing it numerically, a number of quantified parameters such as "power", "quickness", "physical strength", and "intelligence" are used. .. The difference between a tensor and a simple set of numbers is that it is a huge set of numbers just by adding basic information such as "how many types of numbers (number of dimensions / axes)" and "how many items are there for each type". The point is that you can organize them neatly. And if you use a tensor, you can handle information of special shapes such as "vector" and "matrix" together. For example, a vector can be expressed as "one type (one-dimensional) tensor" because it has only one column of numbers, and a matrix has two types of elements in rows and columns, so it is called "two types (two-dimensional) tensor". Will be. On top of that, adding the number of items for each type, if it is a "tensor with 4 items in 1 type", it will be a "4D vector", and if it is a "tensor with 3 items and 4 items in 2 types", it will be " It is a 3-by-4 matrix. " To put it simply, it's just that the name has changed, but as I learned in high school, various methodologies have been developed for vector and matrix calculations. Therefore, it is (relatively) easier to calculate than a multidimensional tensor with more types and more items. Since it can be processed using an algorithm for calculating vectors and matrices, the image is that I want to make it as simple as a vector or matrix if possible. However, complex and large-scale neural networks use multidimensional tensors that have a large number of dimensions and are difficult to calculate. Calculation of such a large-scale tensor is difficult even on a computer, and it takes time to process with a normal CPU, so GPUs specializing in parallel calculation are used. In recent years, computers and algorithms specializing in tensor calculations have been developed, and the "ability to handle tensors" of computers has dramatically improved. [Next page] What is the mechanism of translation technology, "vectorizing words"?Recommended articles
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