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Introduction
Tensors have become the foundational element in modern machine learning. From natural language processing models like GPT to computer vision models such as convolutional neural networks, tensors play a crucial role in nearly all cutting-edge algorithms. However, despite their central importance, the concept of tensors is often abstracted away by frameworks such as PyTorch, TensorFlow, and JAX, leaving many to misunderstand their true potential. In this article, we will explore tensors in-depth, aiming to demystify their nature and provide a robust framework for understanding them both mathematically and computationally.
Tensors Explained: From Basic Equations to Advanced Concepts
In linear algebra, we often start by looking at a basic linear equation, such as $ax + by + cz$. This equation is straightforward to compute when we know the values for $a$, $b$, $c$, and $x$, $y$, $z$. For instance, if $a = 1$, $b = 2$, $c = 3$, and $x = 4$, $y = 5$, $z = 6$, the result of the equation would be:
$$
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