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Google's first rule for machine learning: don't use machine learning. A 3-line PID equation beats a neural network at balancing a robot. Proportional error, integral of accumulated error, derivative of error change rate - three terms, hand-tuned gains, no training data. The same control theory running inside every GPU...

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Eron

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51,808 views • 5 days ago •via X (Twitter)

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hiroko watanabe5 days ago

@0xEronn Great Video, indeed. Very interesting and understandable, not easy of course, but quite helpful to learn physics.

Emmanuel Nwachukwu 💙🥶's profile picture
Emmanuel Nwachukwu 💙🥶5 days ago

Good reminder that a simple rule can beat a complex model. As a beginner I like seeing the basics get respect before the fancy stuff.

The Chieftain A's profile picture
The Chieftain A5 days ago

Great video

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109,764 views • 1 year ago

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117,748 views • 1 year ago

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13,116 views • 8 days ago

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31,497 views • 1 month ago

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15,057 views • 6 months ago

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26,204 views • 3 months ago

Neural networks sometimes memorize training data perfectly for thousands of steps - then suddenly generalize. Physicists call this a phase transition. The same math that explains why water freezes explains why an LLM stops cheating and starts understanding. The key is weight decay acting like pressure on a thermodynamic system. Memorization requires large, fragile weights. A real rule requires smaller, more structured ones. As training continues, the balance shifts until the rule-based solution becomes cheaper to maintain - and the model snaps into it. 14 minutes. Bookmark & watch today. The physics behind the most mysterious thing AI does.
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Neural networks sometimes memorize training data perfectly for thousands of steps - then suddenly generalize. Physicists call this a phase transition. The same math that explains why water freezes explains why an LLM stops cheating and starts understanding. The key is weight decay acting like pressure on a thermodynamic system. Memorization requires large, fragile weights. A real rule requires smaller, more structured ones. As training continues, the balance shifts until the rule-based solution becomes cheaper to maintain - and the model snaps into it. 14 minutes. Bookmark & watch today. The physics behind the most mysterious thing AI does.

Eron

26,222 views • 2 months ago

MIT FILMED THE LECTURE WHERE THEIR MOST LEGENDARY LINEAR ALGEBRA PROFESSOR EXPLAINS WHY EVERY GPS SIGNAL EVERY MEDICAL SCAN AND EVERY AI MODEL ON EARTH IS SECRETLY SOLVING A PROBLEM THAT HAS NO SOLUTION This is Gilbert Strang, MIT, 18.06 Linear Algebra, lecture 15. The professor whose textbooks sit in over 3,000 universities across 135 countries and whose course has been watched by millions of engineers and mathematicians worldwide. He opens with one claim - when equations have no solution, you do not give up. You solve the closest problem that can be solved. He starts with a vector b and a line through a. The projection of b onto that line is the point closest to b that actually lives on the line. The key is a right angle. The error - the gap between b and its projection - must be perpendicular to a. That one geometric fact produces the entire formula. The projection is a times a transpose b divided by a transpose a. One fraction. The numerator is a matrix. The denominator is a number. Then the projection matrix. Every projection is carried out by a matrix P that multiplies b and lands on the line. That matrix has two properties that define all projections everywhere. First, P transpose equals P - the matrix is symmetric. Second, P squared equals P - project twice and you stay where you are. The first projection moves you onto the line. The second leaves you there. Then higher dimensions. Instead of projecting onto a line, project onto a plane. Instead of one vector a, you have a matrix A with two columns spanning the plane. The error vector must now be perpendicular to both columns - perpendicular to the entire plane. That condition produces one matrix equation. A transpose times the error equals zero. The error lives in the null space of A transpose, which is exactly perpendicular to the column space of A. The four fundamental subspaces appear without being called. Then the formula for n dimensions. The projection matrix is A times A transpose A inverse times A transpose. Strang warns the room not to simplify it by canceling A inverse against A - A is not square, it has no inverse, and the formula cannot be pulled apart. The only case where it simplifies to the identity is when A spans the whole space and the projection is b itself. Watch the moment he applies the formula to fitting a line through three points that no line can pass through. Three equations, two unknowns, no solution. He writes the matrix, writes the right-hand side, and shows that multiplying both sides by A transpose produces an equation that always has a solution. That equation is the foundation of least squares, GPS triangulation, and every regression model trained in 2026. A data scientist I know rewatched this lecture before building a recommendation system from scratch. Said it was the first time the normal equations felt like geometry rather than a formula someone handed down to memorize. Free on YouTube, MIT OpenCourseWare, filmed over 20 years ago. bookmark this and watch later - after this lecture every unsolvable equation you meet will feel like a projection waiting to be found
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MIT FILMED THE LECTURE WHERE THEIR MOST LEGENDARY LINEAR ALGEBRA PROFESSOR EXPLAINS WHY EVERY GPS SIGNAL EVERY MEDICAL SCAN AND EVERY AI MODEL ON EARTH IS SECRETLY SOLVING A PROBLEM THAT HAS NO SOLUTION This is Gilbert Strang, MIT, 18.06 Linear Algebra, lecture 15. The professor whose textbooks sit in over 3,000 universities across 135 countries and whose course has been watched by millions of engineers and mathematicians worldwide. He opens with one claim - when equations have no solution, you do not give up. You solve the closest problem that can be solved. He starts with a vector b and a line through a. The projection of b onto that line is the point closest to b that actually lives on the line. The key is a right angle. The error - the gap between b and its projection - must be perpendicular to a. That one geometric fact produces the entire formula. The projection is a times a transpose b divided by a transpose a. One fraction. The numerator is a matrix. The denominator is a number. Then the projection matrix. Every projection is carried out by a matrix P that multiplies b and lands on the line. That matrix has two properties that define all projections everywhere. First, P transpose equals P - the matrix is symmetric. Second, P squared equals P - project twice and you stay where you are. The first projection moves you onto the line. The second leaves you there. Then higher dimensions. Instead of projecting onto a line, project onto a plane. Instead of one vector a, you have a matrix A with two columns spanning the plane. The error vector must now be perpendicular to both columns - perpendicular to the entire plane. That condition produces one matrix equation. A transpose times the error equals zero. The error lives in the null space of A transpose, which is exactly perpendicular to the column space of A. The four fundamental subspaces appear without being called. Then the formula for n dimensions. The projection matrix is A times A transpose A inverse times A transpose. Strang warns the room not to simplify it by canceling A inverse against A - A is not square, it has no inverse, and the formula cannot be pulled apart. The only case where it simplifies to the identity is when A spans the whole space and the projection is b itself. Watch the moment he applies the formula to fitting a line through three points that no line can pass through. Three equations, two unknowns, no solution. He writes the matrix, writes the right-hand side, and shows that multiplying both sides by A transpose produces an equation that always has a solution. That equation is the foundation of least squares, GPS triangulation, and every regression model trained in 2026. A data scientist I know rewatched this lecture before building a recommendation system from scratch. Said it was the first time the normal equations felt like geometry rather than a formula someone handed down to memorize. Free on YouTube, MIT OpenCourseWare, filmed over 20 years ago. bookmark this and watch later - after this lecture every unsolvable equation you meet will feel like a projection waiting to be found

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