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Getting started with linear algebra
I'd like to introduce a series of blog posts and their corresponding Python Notebooks gathering notes on the Deep Learning Book from Ian Goodfellow, Yoshua B...
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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Why isn’t the fundamental theorem of arithmetic obvious? (2011)
The fundamental theorem of arithmetic states that every positive integer can be factorized in one way as a product of prime numbers. This statement has to be appropriately interpreted: we count the…
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When did computer science theory get so hard?
I posted on When did Math get so hard? a commenter pointed out that one can also ask When did Computer Science Theory Get so Hard? For t...
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The exponential function is a miracle
From the highly eclectic blog of Mark Dominus
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Perceptually lossless (talking head) video compression at 22kbit/s
Achieving extreme video compression rates using the LivePortrait model for talking head videos.
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It’s not just p=0.048 vs. p=0.052
Peter Dorman points to this post on statistical significance and p-values by Timothy Taylor, editor of the Journal of Economic Perspectives, a highly influential publication of the American Economic Association.
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A study of musical scales (2017)
PREFACE. This essay was written in 2009. Since then, a few errata have been corrected and I embedded the youtube videos, but there have been no substantial additions. I think it still holds up fairly well, but if I were to rewrite it today, I would change some things. My main regret is using the criteria of maximum…
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Knuth reward check
Twenty years ago I got a reward check from Donald Knuth.
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The Largest Black Hole in the Known Universe
It’s a huge surprise, and shows up in the most unlikely of places!
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Parallel Curves of Cubic Béziers
Blog of Raph Levien.
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Matrices as Tensor Network Diagrams
In the previous post, I described a simple way to think about matrices, namely as bipartite graphs. Today I'd like to share a different way to picture matrices—one which is used not only in mathematics, but also in physics and machine learning. Here's the basic idea. An $m\times n$ matrix $M$ with real entries…
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Why formalize mathematics – more than catching errors
I read a good post by one of the authors of the Isabelle theorem prover, that got me thinking. The author, Lawrence Paulson, observed that most math proofs are trivial, but writing them (preferably with a proof assistant) is a worthwhile activity, for reasons similar to safety checklists - “Not every obvious statement…
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The Missing 11th of the Month (2015)
Personal website of David R Hagen, scientific software engineer
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What is the inverse of a circle?
In this post we’ll try to make sense of what we’re seeing, and try to understand what it means to invert a circle!
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Who Can Name the Bigger Number?
[This essay in Spanish] [This essay in French] [This essay in Chinese] In an old joke, two noblemen vie to name the bigger number. The first, after ruminating for hours, triumphantly announces "Eighty-three!" The second, mightily impressed, replies "You win." A biggest number contest is clearly pointless when the…
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Is the reversal curse in LLMs real?
A recent paper The Reversal Curse points out an apparent failure in large large language models like GPT-4. From the abstract: We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is
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The Fermi Paradox
The Fermi Paradox: There should be 100,000 intelligent alien civilizations in our galaxy — so why haven't we found any of them?
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What does 0^0 equal? Why do mathematicians and high school teachers disagree?
Clever student: I know! $latex x^{0}$ = $latex x^{1-1}$ = $latex x^{1} x^{-1}$ = $latex \frac{x}{x}$ = $latex 1$. Now we just plug in x=0, and we see that zero to the zero is one! Cleverer …
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Diffusion Is Spectral Autoregression
A deep dive into spectral analysis of diffusion models of images, revealing how they implicitly perform a form of autoregression in the frequency domain.
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Show HN: Solving Rush Hour, the 6x6 Sliding Block Puzzle
Rush Hour is a 6x6 sliding block puzzle invented by Nob Yoshigahara in the 1970s. It was first sold in the United States in 1996.
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A Formula for the Number of Days in Each Month
Recently, after being awake for longer than I should have, I started thinking about methods of remembering the number of days in each month of the year. There is a rhyme for it, and a way to count on your knuckles, but these didn’t satisfy me. I wondered if there was a mathematical formula for the problem, and upon…
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Deriving the piano keyboard from biological principles using clustering
Once upon a time we were creatures in the wilderness and we evolved the ability to hear sounds. Now here's an interesting thing, if you hear a sound of frequency f and others of frequency 2f, 3f, etc then there's a good chance these sounds come from the same object, due to the physical principle of resonance . And so…
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Interview on ”Bayesian Statistics the Fun Way”
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
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My Prime Factorization Sweater
I wore my Prime Factorization Sweater to KidlitCon09 , and it shows up in all my pictures, so I think it’s time for me to explain it.
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Understanding the math behind 0x5f3759df and the fast inverse square root (2012)
This post is about the magic constant 0x5f3759df and an extremely neat hack, fast inverse square root, which is where the constant comes from.
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An interactive intro to quadtrees
An interactive exploration of quadtrees. Start with brute-force spatial search, build recursive space partitioning step by step, then use it for point lookups, range queries, nearest-neighbor search, collision detection, and image compression.