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New
The latest blog posts to take off on Hacker News. 2,851 posts.
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Basic math related to computation and memory usage for transformers
We present basic math related to computation and memory usage for transformers
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The New XOR Problem
In 1969, Marvin Minsky and Seymour Papert published Perceptrons: An Introduction to Computational Geometry. In it, they showed that a single-layer perceptron cannot compute the XOR function. The main argument relies on linear separability: Perceptrons are linear classifiers, which essentially means drawing a line to…
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Tag Systems
I've tried to write a blog post on tag systems for years now. Literally years, I think I first started drafting it out in 2018 or so? The problem is that...
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I liked this simple calculus exercise
From the highly eclectic blog of Mark Dominus
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Constraint Programming (2020)
A brief introduction tutorial to Constraint Programming with Python, we introduce some relevant definitions and solve our old Pokémon Centers and Pokémon Gyms problem this time with CP!
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Algebraic graph calculus (2021)
We describe a graph-theoretic analogue of vector calculus. The linear operators of vector calculus (gradient, divergence, laplacian) correspond to the matrices naturally associated to graphs (incidence matrix, adjacency matrix). This analogy is useful for formalizing the discretization of some problems in image and…
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Generalizations of Fourier analysis (2021)
When I first learned about Fourier series and integrals, I hated it because it seemed like a collection of many ad-hoc definitions, formally related but very different.
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Beyond automatic differentiation
Posted by Matthew Streeter, Software Engineer, Google Research Derivatives play a central role in optimization and machine learning. By locally app...
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GPT-4 gets a B on my quantum computing final exam
Update (April 14): On the suggestion of my TA Justin Yirka, I gave GPT-4 problem 2 from the final exam, along with its own answers and my and Justin’s grading comments, and asked it whether i…
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P < 0.05 Considered Harmful
The unreasonable persistence of an old standard
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Two algorithms for randomly generating aperiodic tilings
[Part of a series: Penrose and hats | Spectres | finite-state transducers | more transducers | refining tilings ]
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Lerp
Lerp is the nickname for Linear Interpolation between two points. It's a fairly simple effect to implement but can really improve the look of your animations if you're moving an object from a point A to point B.
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We're Knot Friends
It’s April Cools again. For a few summers in high school and undergrad, I was a day camp counselor. I’ve written before about how it helped me develop storytelling skills, but recently I thought of it again because, while I was cleaning out a closet full of old junk, I happened upon a bag of embroidery thread. While…
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Bicycle
Interactive article explaining the physics of a bicycle.
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Introduction to P vs. NP
Series Introduction In this series of articles I would like to share with you a set of ideas that are meant to help non-technical people build a better intuition as to what the current software and…
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Every possible Wordle solution visualized
Every Wordle solution laid out at once. Filter all 2,309 by letter, position, and gray/yellow/green clues to narrow down today's answer.
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Avoiding visible texture repetition (2015)
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
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Dividing a Square into 7 Similar Rectangles
This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectan…
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The Smallest Hash Table
This December I once again did the Advent of Code , in Rust. If you are interested, my solutions are on Github. I wanted to highlight one particular solution to the day 2 problem as it is both optimized completely beyond the point of reason yet contains a useful technique. For simplicity we’re only going to do part 1…
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Bitwise Division
Integer division is expensive. Much more expensive than multiplication. Much, much more expensive than addition. If you’re trying to make some integer operations really fast it’s bad news if you need to do division.
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SymPy makes math fun again
An introduction into symbolic computations in Python. Don't worry, it's much simpler than it sounds. It's about making Python do your math for you with very little investment in the technology.
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The unreasonable effectiveness of conditional probabilities
I have been steeping myself in probabilistic exercises recently, because it’s an area where I feel like I could benefit from building better intuition. I have found a recurring key to solving many of them: conditioning on an intermediary state, and then computing the value of that intermediary state separately. This…
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NP-complete isn't always hard
A common assumption I see on the ‘net is that NP-complete problems are impossible to solve. I recently read that dependency management in Python is hard because package resolution is NP-complete. This is true in principle, but the reality is more complicated. When we say “NP-complete is hard” we’re talking about…
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An interactive explanation of quadtrees (2014)
The space is divided into four rectangles . Each of those rectangles is divided such that it contains a maximum of four children . Each child is either a point or a smaller rectangle.
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Google’s fully homomorphic encryption compiler – a primer
Back in May of 2022 I transferred teams at Google to work on Fully Homomorphic Encryption (newsletter announcement). Since then I’ve been working on a variety of projects in the space, including being the primary maintainer on github.com/google/fully-homomorphic-encryption, which is an open source FHE compiler for…