Introduction to Vectorization

https://thepalindrome.org/p/an-introduction-to-vectorization

There’s a pattern in machine learning that blows my mind every time, even though I’ve seen it more than I can count.

Look at this expression:

Yes, I know. You are more than familiar with linear regression; we are not here to discuss that. I want to share a wonderful mathematical principle with you, learning through the example of linear regression.

Depending on what we understand by a, x, b, +, and ·, the expression “ax + b” can either be the very first machine learning model a student encounters or the main component of a powerful neural network.

Its evolution from basic to state-of-the-art was shaped by the two great forces of mathematics:

generalizing the meaning of simple symbols such as + and · to make them do more,
and then abstracting the complex symbols into a-s, b-s, and x-es to keep them simple.

This dance of generalization and abstraction is the essence of mathematics; it’s why we can treat functions as vectors, use matrices as exponents, build the foundations of mathematics by dr…

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  "author": "Tivadar Danka",
  "date": "2024-05-01T18:43:46.000Z",
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  "url": "https://thepalindrome.org/p/an-introduction-to-vectorization",
  "title": "Vectorization in theory",
  "description": "There’s a pattern in machine learning that blows my mind every time, even though I’ve seen it more than I can count.Look at this expression:Yes, I know. You are more than familiar with linear regression; we...",
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  "content": "<div><p>There’s a pattern in machine learning that blows my mind every time, even though I’ve seen it more than I can count.</p><p>Look at this expression:</p><p>Yes, I know. You are more than familiar with linear regression; we are not here to discuss that. I want to share a wonderful mathematical principle with you, learning through the example of linear regression.</p><p><span>Depending on what we understand by </span><em>a</em><span>, </span><em>x</em><span>, </span><em>b</em><span>, +, and ·, the expression “</span><em>ax</em><span> + </span><em>b</em><span>” can either be the very first machine learning model a student encounters or the main component of a powerful neural network.</span></p><p>Its evolution from basic to state-of-the-art was shaped by the two great forces of mathematics:</p><ul><li><p>generalizing the meaning of simple symbols such as + and · to make them do more,</p></li><li><p><span>and then abstracting the complex symbols into </span><em>a</em><span>-s, </span><em>b</em><span>-s, and </span><em>x</em><span>-es to keep them simple.</span></p></li></ul><p>This dance of generalization and abstraction is the essence of mathematics; it’s why we can treat functions as vectors, use matrices as exponents, build the foundations of mathematics by dr…</p></div>",
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