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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…
New
The latest blog posts to take off on Hacker News. 238 posts.
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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…
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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.
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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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Revisiting Moneyball
Data, sports, payrolls, and memes
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Scarcity, Inventory, and Inequity: A Deep Dive into Airline Fare Buckets
Airline pricing may seem mystifying, but behind every airfare is a complex system of fare buckets and inventory controls. Airlines don't just sell seats - they manage a dynamic inventory of fares, divided into booking classes (fare buckets) with different prices and rules. For the technically curious, understanding…
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Gemini with Deep Think achieves gold-medal standard at the IMO
The International Mathematical Olympiad (“IMO”) is the world’s most prestigious competition for young mathematicians, and has been held annually since 1959. Each country taking part is represented by six elite, pre-university mathematicians who compete to solve six exceptionally difficult problems in algebra…
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“Dynamic programming” is not referring to “computer programming”
When seeing the phrase “dynamic programming” in an algorithms class or leetcode study guide, the first question people ask is “what does ‘dynamic’ mean in this context?”.
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All AI models might be the same
what can language model embeddings tell us about whales speech, and decoding ancient texts? (on The Platonic Representation Hypothesis and the idea of *universality* in AI models)
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To be a better programmer, write little proofs in your head
This is a brief write-up of a trick I learned that helps me write code faster and more accurately. I say "trick", but it's really something I started to do without noticing as I moved further into my career. When you're working on something difficult, sketch a
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Algorithms for making interesting organic simulations
Article explaining simulation algorithms that produce complex organic behaviours, starting with the classic physarum algorithm from Jeff Jones.
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Introduction to Digital Filters (2024)
INTRODUCTION TO DIGITAL FILTERS WITH AUDIO APPLICATIONS
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Lossless Float Image Compression
Back in 2021 I looked at OpenEXR lossless compression options (and I think my findings led a change of the default zip compression level , as well as change of the compression library from zlib to libdeflate . Yay blogging about things!) . Then in 2023 I looked at losslessly compressing a bunch of floating point data…
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Optimizing a Math Expression Parser in Rust
Optimizing a math expression parser for speed and memory.
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Million Times Million
Is a million times a million a billion or is it a trillion ? For my entire childhood, it was a billion, only for me to grow up and realise, as an adult, that it had better be a trillion!
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Bloom Filters by Example
A Bloom filter is a data structure designed to tell you, rapidly and memory-efficiently, whether an element is present in a set.
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People Keep Inventing Prolly Trees
A novel data structure has been invented four times now, with three different names. We think that's a good sign.
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BusyBeaver(6) Is Quite Large
For overdetermined reasons, I’ve lately found the world an increasingly terrifying and depressing place. It’s gotten harder and harder to concentrate on research, or even popular scienc…
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Graph Theory Applications in Video Games
A detailed look at Graph Theory and how it can be applied to video games.
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Normalizing Flows Are Capable Generative Models
Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density…
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The economics behind "Basic Economy" – A masterclass in price discrimination
Basic Economy fares are ultra-restricted airline tickets that offer a lower base price in exchange for fewer benefits than standard economy class. Introduced by major U.S. carriers in the 2010s, these fares have become a widespread strategy for market segmentation - a textbook example of price discrimination in…
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Reinforcement learning, explained with a minimum of math and jargon
To create reliable agents, AI companies had to go beyond predicting the next token.
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Solving LinkedIn Queens Using Haskell
Solving LinkedIn Queens in the LogicT monad
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Modeling the World in 280 Characters
An exploration of the mindset, methods, and motivations behind crafting tiny, expressive shaders that combine code, art, and constraint.
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The probability of a hash collision (2022)
Exploring the math behind hash collisions.
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Learn you Galois fields for great good (2023)
This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science. This is a project I've been excited about for many years now, but have been too busy to dedicate the adequate effort to meet my…