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Folks, we have the best π
And some novel ideas for bicycle wheel design.
New
The latest blog posts to take off on Hacker News. 2,851 posts.
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Language models pack billions of concepts into 12k dimensions
In a recent 3Blue1Brown video series on transformer models, Grant Sanderson posed a fascinating question: How can a relatively modest embedding space of 12,288 dimensions (GPT-3) accommodate millions of distinct real-world concepts? The answer lies at the intersection of high-dimensional geometry and a remarkable…
273
Many hard LeetCode problems are easy constraint problems
Use the right tool for the job.
274
Hashed sorting is typically faster than hash tables
Benchmarks and theoretical explanation of why and when hashed radix sort beats hash tables.
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How many dimensions is this?
A degree in mathematics might not save you from stacking boxes for a living.
276
A Random Walk in 10 Dimensions (2021)
The geometry of random walks in high dimensions provides the power behind deep learning and may be the secret to intelligence.
277
John Coltrane's Tone Circle
An article about the John Coltrane Tone Circle, a 5-octave Circle of Fifths and a double-ring Hexatonic Circle as well. Interpretation, explanation ...
278
The maths you need to start understanding LLMs
A quick refresher on the maths behind LLMs: vectors, matrices, projections, embeddings, logits and softmax.
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Minesweeper thermodynamics
You know how sometimes you start a game of Minesweeper and immediately get stuck?
280
Inverting the Xorshift128 random number generator
CVE-2025-7783 is a very recent vulnerability affecting a lot of applications in the Node.js ecosystem including those which use axios or the deprecated request library. In all honesty, this vulnera…
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Why haven't quantum computers factored 21 yet?
Craig Gidney's computer science blog
282
From multi-head to latent attention: The evolution of attention mechanisms
From Multi-Head to Latent Attention: The Evolution of Attention Mechanisms What is attention? In any autoregressive model, the prediction of the future tokens is based on some preceding context …
283
God created the real numbers
W. Jherek Swanger writes in his introduction to Camillo 7 Agrippa's "A Treatise on the Science of Arms, with a philosophical Dialogue (1553)" that:
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The Math Behind GANs (2020)
Generative Adversarial Networks refer to a family of generative models that seek to discover the underlying distribution behind a certain data generating process. This distribution is discovered through an adversarial competition between a generator and a discriminator. As we saw in an earlier introductory post on…
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Important machine learning equations
A reference guide to fundamental machine learning equations with correct implementations and clear explanations of how they connect to each other.
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A visual introduction to big O notation
A visual introduction to big O notation.
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Everything is correlated (2014–23)
Anthology of sociology, statistical, or psychological papers discussing the observation that all real-world variables have non-zero correlations and the implications for statistical theory such as ‘null hypothesis testing’.
289
A statistical analysis of Rotten Tomatoes
Can Hollywood's stamp of artistic excellence still be trusted?
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CRDT: Text Buffer
Collaboratively editing strings of text is a common desire in peer-to-peer applications. For example, a note-taking app might represent each document as a single collaboratively-edited string of text.
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The Block Stacking Problem
John D. Norton Department of History and Philosophy of Science University of Pittsburgh https://sites.pitt.edu/~jdnorton/jdnorton.html
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Derivatives, Gradients, Jacobians and Hessians
This article explains how these four things fit together and shows some examples of what they are used for. Derivatives Derivatives are the most fundamental concept in calculus. If you have a funct…
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Tversky Neural Networks
Psychologically Plausible Deep Learning with Differentiable Tversky Similarity
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Simulating and Visualising the Central Limit Theorem
Update: this post was discussed on Hacker News I completed a Computer Science degree at uni, and bundled a lot of maths subjects in as electives: partial differential equations, vector calculus, discrete maths, linear algebra.
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Is chain-of-thought AI reasoning a mirage?
Reading research papers and articles about chain-of-thought reasoning makes me frustrated. There are many interesting questions to ask about chain-of-thought…
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500 days of math
I recently crossed 500 days of practicing math daily with Math Academy. I wrote about my experience after 100 days here. TL;DR: I am still very impressed by the Math Academy system and highly…
297
Perfecting anti-aliasing on signed distance functions
Doing anti-aliasing on SDF is not as straightforward as it seems. Most of the time, we see people use a smoothstep with hardcoded constants, sometimes with screen space information, sometimes cryptic or convoluted formulas. Even if SDFs have the perfect mathematical properties needed for a clean anti-aliasing, the…
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Monte Carlo Crash Course: Quasi-Monte Carlo
We’ve learned how to define and apply Monte Carlo integration—fundamentally, it’s the only tool we need. In the remaining chapters, we’ll explore ways to reduce variance and successfully sample difficult distributions.
299
Compressing Icelandic name declension patterns into a 3.27 kB trie
How I used a compressed trie data structure to encode Icelandic declension data.
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