Introduction to Vectorization

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  "title": "Introduction to Vectorization",
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  "url": "https://thepalindrome.org/p/an-introduction-to-vectorization"
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{
  "author": "Tivadar Danka",
  "date": "2024-05-01T18:43:46.000Z",
  "description": "Making expressions do more, faster",
  "image": "https://substackcdn.com/image/fetch/w_1200,h_600,c_fill,f_jpg,q_auto:good,fl_progressive:steep,g_auto/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6da44dba-3100-46eb-81a8-aaba677c920b_1400x1000.png",
  "logo": null,
  "publisher": "The Palindrome",
  "title": "Vectorization in theory",
  "url": "https://thepalindrome.org/p/an-introduction-to-vectorization"
}

{
  "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...",
  "links": [
    "https://thepalindrome.org/p/an-introduction-to-vectorization"
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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><div><figure><a target=\"_blank\" href=\"https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png\"><div><picture><source type=\"image/webp\" srcset=\"https://substackcdn.com/image/fetch/w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 424w, https://substackcdn.com/image/fetch/w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 848w, https://substackcdn.com/image/fetch/w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 1272w, https://substackcdn.com/image/fetch/w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 1456w\" sizes=\"100vw\"></source><img src=\"https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png\" srcset=\"https://substackcdn.com/image/fetch/w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 424w, https://substackcdn.com/image/fetch/w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 848w, https://substackcdn.com/image/fetch/w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 1272w, https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc3365c26-6173-4e4f-87a8-ef27f69701fd_1920x700.png 1456w\" /></picture></div></a></figure></div><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>",
  "author": "Tivadar Danka",
  "favicon": "https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9730ef35-6aae-4efc-9168-f780f058566a%2Ffavicon-48x48.png",
  "source": "thepalindrome.org",
  "published": "2024-05-01t18:43:46+00:00",
  "ttr": 34,
  "type": "article"
}