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Data diffs: Algorithms for explaining what changed in a dataset (2022)
tl;dr: part 1 explains what an explanation algorithm is, and part 2 describes an open source SQL data differ.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Building a constraint programming solver in Julia
How to build a constraint programming solver in Julia. Part 1: Solving Sudoku using backtracking
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Generating Voronoi diagrams using Fortune's algorithm
This article is about using Fortune’s Algorithm to generate Voronoi Diagrams in O(nlogn) time. If I’d known how hard it would be I wouldn’t have started it. If you are intending to implement it with the intent to actually use it, rather than as an exercise, I would recommend not using Fortune’s. Unless you are doing a…
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How Slide Rules Work
The survival of our species owes much to our brain, specifically, its ability to observe, analyse, and plan. Planting crops and storing grains for the winter were some of the earliest uses of these abilities. Measuring and calculating are foundational elements of observation, analysis, and planning. Computation, upon…
997
Sampling at negative temperature
Summary : Inspired by the definition of temperature in statistical mechanics and the possibility for it to be below zero, we try sampling LLaMA at T = − 0.001 T=-0.001 T = − 0.001 . The results are maximally weird.
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If 1+x is 1, how much is 1-x?
► Versión en Español (The title should be "if (= (+ 1 x) 1), how much is (- 1 x)?", but ...) Toy floating point Mathematically, if we...
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How SHA-2 works step-by-step (SHA-256)
Learn to code from scratch with hands-on lessons, a structured curriculum, and real projects. Stop watching tutorials, start writing code for free now.
1001
Solving some formal math olympiad problems
We built a neural theorem prover for Lean that learned to solve a variety of challenging high-school olympiad problems, including problems from the AMC12 and AIME competitions, as well as two problems adapted from the IMO.
1002
Game theory as an engine for large-scale data analysis
Modern AI systems approach tasks like recognising objects in images and predicting the 3D structure of proteins as a diligent student would prepare for an exam. By training on many example problems, they minimise their mistakes over time until they achieve success. But this is a solitary endeavour and only one of the…
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Solving Every Sudoku Puzzle (2006)
Every square has exactly 3 units and 20 peers. For example, here are the units and peers for the square C2 :
1004
A proof that Unix utility sed is Turing complete
Many people are surprised to learn that `sed`, a seemingly simple text filtering program, is actually Turing complete. This realization prompts the question: how can a text processing utility achieve such computational power? The answer lies in sed's fundamental operations. Essentially, sed functions as a miniature...
1005
What’s the difference between statistics and machine learning?
I had an interesting discussion at work today (among people I think would all call themselves statisticians!) about the distinction(s) between statistics and machine learning. It is something I am …
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LaTeX Math in MS Office
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1007
A Mechanistic Interpretability Analysis of Grokking
Neel Nanda reverse engineers neural networks that have "grokked" modular addition, showing that they operate using Discrete Fourier Transforms and tr…
1008
Sphere Eversion
Topology is the study of the properties of geometric objects which aren’t changed by continuous deformation. A standard low-grade math joke is that toplogists consider a coffee mug and a doughnut equivalent because they’re both torii—(pauses for laughter)—one can be continuously deformed into the other, called a…
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Gaussian integration is cool
Brief discussion on gaussian quadrature and chebyshev-gauss quadrature
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The Irish Logarithm
From the highly eclectic blog of Mark Dominus
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So you still don't understand Hindley-Milner? (2013)
I was out for drinks with Josh Long and some other friends from work, when he found out I "speak math." He had come across this …
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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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ProtonMail now offers elliptic curve cryptography
Proton Mail has become the first and only encrypted email provider to support elliptic curve cryptography (ECC), providing more security and performance.
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Finally getting two's complement
A different view on two's complement math.
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Computer scientists prove that a 40-year-old algorithm is optimal
Computer scientists from MIT find that a 40-year-old algorithm for determining the “edit distance” between symbols cannot be optimized any further.
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What the Four Color Theorem Can Teach Us About Writing Software
A visual exploration of what The Four Color Theorem can say about software complexity.
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Overkilling the 8-queens Problem
Last night, a fellow Hacker Schooler challenged me to a running-time contest on the classic eight queens puzzle. Naturally, I pulled up my trusty …