AMVITABLE® @amvitable

How CNNs see images. Tensors, filters, feature maps, stride, padding, channels, pooling, receptive fields, mental model.

keyboard_arrow_left Previous keyboard_arrow_right Next

Así funciona el algoritmo de Dijkstra

Karl Weierstrass (31 Oct 1815 – 19 Feb 1897) constructed what a function looks like that’s continuous everywhere but has no derivative at any point: f(x) = ∑_{n=0}^∞ aⁿ cos(bⁿ π x). The magnified inset reveals its fractal self-similarity at every scale. “A mathematician who is not also something of a poet will never be a complete mathematician.” Today this function underpins fractal geometry and models irregular real-world phenomena; from coastlines and turbulent flows in physics to stock-price volatility in finance and rough signals in engineering.

This 17 page pdf reveals the same technique Hedge Funds like Jim Simons' Renaissance Technologies use to find signal through noise. Stanford released the complete Hidden Markov Model framework for everyone to use it. Bookmark it before someone takes it down:

Two math olympiad champions wrote a training manual in 1993 on two old Macintosh computers, and every American kid who has won a major math competition in the last decade learned to think from it. Their names are Sandor Lehoczky and Richard Rusczyk. The book is called The Art of Problem Solving. Most people in math know it as AoPS. Since 2015, every single member of the US International Math Olympiad team has been an AoPS student. Not most of them. Every one. That statistic sounds impossible until you understand what the book actually does. Lehoczky and Rusczyk were not professors. They were competitors. Lehoczky earned the sole perfect AIME score in 1990 and led the national first place team. Rusczyk was a USA Mathematical Olympiad winner and a perfect AIME scorer in 1989. They had both survived the same brutal selection process the book was designed to train students for. And the first thing they decided was that almost every existing math textbook was teaching the wrong thing. School math gives you formulas. You memorize them. You apply them. You pass the test. Then you sit down in front of a real competition problem and the formula does not apply, and you have nothing underneath it. That is the gap. The gap is not knowledge. It is thinking. The entire premise of AoPS is that problem-solving is a transferable skill, not a bag of memorized tricks. A student who genuinely understands why a technique works can adapt it, combine it with something else, and deploy it in a context they have never seen before. A student who only memorized the technique freezes the moment the problem looks different. The book teaches the difference between a formula and a method. A formula tells you what to compute. A method tells you how to see. The students who win olympiads are not the ones who know more formulas. They are the ones who have trained themselves to look at an unfamiliar problem and recognize its structure. To see that this problem is secretly asking the same question as a problem they solved three weeks ago, just dressed differently. Rusczyk calls this "learning to read the problem." Not reading the words. Reading what the problem is actually asking underneath the words. The second thing they built into the book is tolerance for being stuck. Most students treat confusion as a signal to stop. The book treats confusion as the starting point. Every chapter pushes students past the point where the obvious approach runs out. That moment of running out is not failure. That is where the actual thinking begins. Lehoczky once described it this way. If you can solve a problem quickly, you are not learning. You are performing. Learning only happens when you are past the edge of what you already know. The book was written on old Macintosh computers in 1993. Rusczyk launched the AoPS website in 2003. Today the community has over one million users. Thousands of students enroll in AoPS online courses every year. Most winners of every major American math competition are AoPS alumni. A platform built by two kids who were good at math competitions has become the infrastructure that produces the next generation of mathematicians, engineers, and scientists who are good at thinking. The formulas you memorized in school will eventually be obsolete. The thinking you trained will not. What is one problem in your life right now that you have been avoiding because you do not yet know the right formula to solve it?

Integration by parts turns products of functions into simpler integrals. If u(x) and v(x) are continuously differentiable, then ∫u dv = uv − ∫v du. Use the ILATE rule to pick u: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential. Example: ∫(log x)⋅1 dx = x log x − x + C. Engineers rely on it to compute work from variable forces in physics and to solve signals in electrical and mechanical systems.

This 277-page PDF unlocks the secrets of Large Language Models. Here's what's inside: 🧵

🏆The Kaggle Book — Master Data Analysis and Data Science Competitions with Machine Learning, GenAI, and LLMs [2nd Ed.]: amzn.to/4pxJpTC v/ @PacktDataML Table of Contents: 🔶Introducing Data Science Competition 🔷Organizing Data with Datasets 🔶Work & Learn with Kaggle Notebooks 🔷Kaggle Models 🔶Leveraging Discussion Forums 🔷Detailing Competition Tasks & Metrics 🔶Designing Good Validation Schemes 🔷Modeling for Tabular Competitions 🔶Hyperparameter Optimization 🔷Ensembling & Stacking Solutions 🔶Modeling Image Classification & Segmentation My Review (on Amazon): This 700-page masterpiece of writing covers everything you need—start to finish—to be a competitive coder, specifically for Kaggle data science competitions. The book covers the mechanics of the competitions (platform, resources, rankings, leaderboards), then the infrastructure (notebooks, GitHub, data sets, frameworks, discussion forums), and then nearly 500 pages devoted to "Elevating Your Game" (in-depth coverage of modeling techniques, evaluation metrics, validation strategies, hyperparameter optimization, ensembles, stacking, and various categories of competitions: tabular data, computer vision, NLP, Gen AI, simulations). The book concludes with a valuable section on building your Kaggle portfolio for career advancement and new opportunities. This is an outstanding data science / AI / Machine Learning training resource for anyone, even if you are not into the competitions, though especially if you are a dedicated Kaggler.

Check out AMVITABLE's video! #TikTok vt.tiktok.com/ZSx2hXGN4/

"Mathematical Theory of Deep Learning" is an excellent free resource for anyone interested in the mathematical structure underlying modern deep learning systems. The book introduces the theory of deep neural networks through approximation theory, optimization theory, and statistical learning theory, three of the central pillars of the field. What makes it particularly interesting is its attempt to balance rigor with accessibility, focusing on the essential ideas needed to understand modern AI systems without sacrificing mathematical depth. Despite this clarity of exposition, the book is clearly oriented toward a specialized audience. It is also an enormous cultural contribution and an extremely valuable free resource for students, researchers, and anyone interested in studying deep learning more rigorously. arxiv.org/abs/2407.18384

instagram.com/reel/DVwVc6YEV…

👀👀👀 "Geometric bifurcation theory: Fisher information geometry applied to dynamical and complex systems"

"'It's a naive model, doesn't take into account much about what real neurons are like. Nevertheless, it is a model, and we can ask what we can do with it.' Turns out you can do quite a bit." MIT 6.034 Artificial Intelligence, Fall 2010 Instructor: Patrick Winston

instagram.com/stories/nelson…

Download 242-page PDF “Introduction to Neural Networks” ➡️ dkriesel.com/en/science/neu… ————— #DataScience #AI #Algorithms #ML #MachineLearning #DeepLearning #Mathematics #Calculus #DataScientist

You can't engineer luck. Cleanest phrasing of P vs NP I've heard. NP is the magical computer that always tells you which path to take. P is what current silicon can do. Tetris is NP-complete. Chess is EXP-complete. MIT 6.006 Introduction to Algorithms, Fall 2011.

instagram.com/amvitable/live…

The most important equation in statistics is the Normal Equations AᵀA x̂ = Aᵀb. It's the foundation of linear regression. Professor Gilbert Strang, MIT.

Delete 99.87% of your digital footprint from the internet. Here is a step -by -step guide:

A visualization showing how gravity curves spacetime [🎞️ Daniel Ibarra]