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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

10,580 subscribers

29,627 次观看 • 2 天前 •via X (Twitter)

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hiroko watanabe 的头像
hiroko watanabe1 天前

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

Emmanuel Nwachukwu 💙🥶 的头像
Emmanuel Nwachukwu 💙🥶1 天前

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 的头像
The Chieftain A1 天前

Great video

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Ever wondered what neural networks are and how they work? Systems like ChatGPT use neural networks to work as well as they do. Neural networks are composed of "layers" of neurons, layers with different functions; connections between layers called "weights"; and mathematical functions called "activation functions". If you’re interested in learning about these systems, check the comments. Ultimately, the neural network structure of the model serves to visually demonstrate that it is, in fact, a complex mathematical equation. When companies release the model's weights, they are releasing a key component needed to run the model's complete equation. Without the weights, the equation is incomplete. For the math-minded: the weights of a model are the learned numbers (they are variables during training) that are then used as constants in the mathematical functions that make up the model. Neural networks are ultimately just one big, hyper-complex mathematical function, and when a model is trained, it learns the constants associated with the high-dimensional input.

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50,905 次观看 • 1 年前

Every fundamental law of physics - Newton, Einstein, Quantum Field Theory - is derived from a single equation. Physicists don't propose new laws by writing forces anymore. They write a new Lagrangian and the math produces the physics automatically. The same principle that governs a swinging pendulum governs every quantum field in the universe - and the optimizer inside every LLM training run is solving the same underlying problem. The mechanism is stationary action. A system takes the path where the total action stops changing for any small variation. That condition produces the Euler-Lagrange equation. One equation, any number of variables, any theory of physics. In Quantum Field Theory the variables are fields across all of space and the gradient must vanish at every point simultaneously - exactly the convergence condition gradient descent hunts for across billions of LLM parameters during backpropagation. 20 minutes. Bookmark & watch today. The single equation that every law of physics is secretly a special case of.
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Every fundamental law of physics - Newton, Einstein, Quantum Field Theory - is derived from a single equation. Physicists don't propose new laws by writing forces anymore. They write a new Lagrangian and the math produces the physics automatically. The same principle that governs a swinging pendulum governs every quantum field in the universe - and the optimizer inside every LLM training run is solving the same underlying problem. The mechanism is stationary action. A system takes the path where the total action stops changing for any small variation. That condition produces the Euler-Lagrange equation. One equation, any number of variables, any theory of physics. In Quantum Field Theory the variables are fields across all of space and the gradient must vanish at every point simultaneously - exactly the convergence condition gradient descent hunts for across billions of LLM parameters during backpropagation. 20 minutes. Bookmark & watch today. The single equation that every law of physics is secretly a special case of.

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Does GPT understand the world? Here is what Ilya Sutskever, co-founder of OpenAI, says during a discussion with Jensen Huang, CEO of Nvidia: (1) When we train a large neural network to accurately predict the next word in lots of different texts from the internet, the AI is learning a world model. (2) On the surface, it may look like learning correlations in text, but it turns out that to 'just learn' statistical correlations in text, to compress information really well, what the neural network learns is some representation of the process that produced the text. (3) This text is a projection of the world...what the neural network is learning is aspects of the world, of people, of the human conditions, their hopes, dreams, motivations, their interactions...the situations we are in. The neural network learns a compressed, abstract, usable representation." Do you think learning representations = understanding? Are large language models simply stochastic parrots, or are they much more?

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Backpropagation in Machine Learning In 1970, a Finnish master's student named Seppo Linnainmaa wrote a thesis on tracing a computer's tiny rounding errors backwards through a long calculation, one step at a time. Sixteen years later, David Rumelhart, Geoffrey Hinton and Ronald Williams showed that the same backward trick lets a Neural Network work out how to fix every one of its connections at once, and the world called it 'Backpropagation'. Every big AI model today still learns by passing its mistakes backwards in exactly this way.

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13,116 次观看 • 4 天前

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109,764 次观看 • 1 年前

a playlist of 30 youtube videos to learn machine learning fundamentals from scratch if you're struggling on where to start learning ML, this list goes this "Machine Learning: Teach by Doing" is a solid choice to learn both theory and code. (1) Introduction to Machine Learning Teach by Doing: (2) What is Machine Learning? History of Machine Learning: (3) Types of ML Models: (4) 6 steps of any ML project: (5) Install Python and VSCode and run your first code: (6) Linear Classifiers Part 1: (7) Linear Classifiers Part 2: (8) Jupyter Notebook, Numpy and Scikit-Learn: (9) Running the Random Linear Classifier Algorithm in Python: (10) The oldest ML model - Perceptron: (11) Coding the Perceptron: (12) Perceptron Convergence Theorem: (13) Magic of features in Machine Learning: (14) One hot encoding: (15) Logistic Regression Part 1: (16) Cross Entropy Loss: (17) How gradient descent works: (18) Logistic Regression from scratch in Python: (19) Introduction to Regularization: (20) Implementing Regularization in Python: (21) Linear Regression Introduction: (22) Ordinary Least Squares step by step implementation: (23) Ridge regression fundamentals and intuition: (24) Regression recap for interviews: (25) Neural network architecture in 30 minutes: (26) Backpropagation intuition: (27) Neural network activation functions: (28) Momentum in gradient descent: (29) Hands on neural network training in Python: (30) Introduction to Convolutional Neural Networks (CNNs):
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117,748 次观看 • 1 年前

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RAI Institute

15,057 次观看 • 5 个月前

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Ten million people have watched an MIT professor teach a course whose first lecture is literally titled "What is a Derivative?" Almost none have written down the two-line answer. He filmed the lecture once in the fall of 2007 and it has been on YouTube ever since. Math tutors charge $200 an hour to teach a diluted version of what he covered in 50 minutes for free. His name is David Jerison. He is a professor of mathematics at MIT and the instructor of 18.01 Single Variable Calculus, one of the most-watched math courses in the history of the internet. The 50-minute clip in this video is Lecture 1, filmed at MIT in the fall of 2007. Jerison is deriving the definition of a derivative from a single tangent line. The whole framework fits on a napkin. A derivative is just how much y changes when x moves a tiny bit. Draw a tangent line to any curve at any point. The slope of that line is the derivative. Memorize one formula, the power rule, and you can differentiate every polynomial on earth in your head. Chain that with a handful of exceptions and you can differentiate almost every function humanity has ever written down. That single set of rules is what every neural network runs on gradient descent, what every rocket landing at SpaceX solves in real time, and what every options desk at Goldman Sachs is running behind every quote you see on the screen. "In mathematics you don't understand things. You just get used to them." That is John von Neumann, the mathematician who helped design the atomic bomb and invent the modern computer. Jerison returns to the same idea in every lecture. Almost no student giving up on calculus has heard von Neumann say it out loud. Every quant fund on Wall Street pays entry-level analysts $250,000 to know the same power rule Jerison derives on the board. Every AI bootcamp charges tens of thousands to teach a diluted version of the same equation on a laptop. The lecture is free on MIT OpenCourseWare. The textbook is under sixty dollars. Almost none of the millions who watched have ever taken the power rule and applied it to their own numbers on their own paper. The math is free. The willingness to actually take one derivative before your next model, trade, or engineering trade-off is the entire edge.

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31,497 次观看 • 1 个月前

Since Newton, every law of physics has been written as a differential equation. The same math that describes a pendulum swinging is what makes AI training unstable when learning rates are too large. Differential equations are hard not because the concepts are complex, but because most of them simply cannot be solved exactly. This video shows why - and how phase space diagrams let you understand them anyway without solving anything. 25 minutes. Bookmark & watch today. The chaos theory connection at the end alone is worth it.
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Since Newton, every law of physics has been written as a differential equation. The same math that describes a pendulum swinging is what makes AI training unstable when learning rates are too large. Differential equations are hard not because the concepts are complex, but because most of them simply cannot be solved exactly. This video shows why - and how phase space diagrams let you understand them anyway without solving anything. 25 minutes. Bookmark & watch today. The chaos theory connection at the end alone is worth it.

Eron

26,204 次观看 • 3 个月前

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.
17:24

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 次观看 • 2 个月前

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

Lupen

24,677 次观看 • 2 个月前