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Gradients Are the New Intervals
At the New England Symposium on Graphics , James Tompkin compared graphics researchers to magpies: they're easily distracted by shiny objects and pretty renderings.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Demystifying Floating Point Precision
Floating point numbers have limited precision. If you are a game programmer, you have likely encountered bugs where things start breaking after too much time has elapsed, or after something has mov…
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Einsum Is All You Need – Einstein Summation in Deep Learning (2018)
Tim Rocktäschel — Co-Founder and Chief Scientist of Recursive; Professor of AI at UCL. Artificial General Intelligence, Open-Endedness, and Recursive Self-Improvement.
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Predict the future with Machine Learning
Learn Machine Learning (ML) and be ahead of the pack in the Software industry. Machine Learning is a sub-field of Artificial Intelligence (A.I), which is heavily used in modern software systems. Machine Learning algorithms can improve software (a robot) and it's ability to solve problems through gaining experience and…
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Does having prime neighbors make you more composite?
Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal numbers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and…
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Random Solutions are Often Good Enough
Sometimes taking the easy way out isn’t nearly as bad as it might seem! posted Thursday February 13th, 2014 Tagged: Math
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The quadratic formula and low-precision arithmetic
The familiar quadratic formula can give the wrong answer in a program due to numerical precision issues. This post shows what can go wrong and how to fix it. Especially important in low-precision arithmetic.
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Math library functions that seem unnecessary
Functions include in the standard C math library that seem unnecessary at first glance and why they are necessary.
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Principal Component Analysis for Dummies
(I recently wrote a new post that you may also find interesting called Principal Component Analysis 4 Philosophers) Having been in the social sciences for a couple of weeks it seems like a large am…
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Subatomic particle seen changing to antiparticle and back for the first time
Physicists have proved that a subatomic particle can switch into its antiparticle alter-ego and back again, in a new discovery revealed today. An extraordinarily precise measurement made by Oxford researchers using the LHCb experiment at CERN has provided the first evidence that charm mesons can change into their…
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The quadratic sandwich
If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your…
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A Long Peek into Reinforcement Learning
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Peter Montgomery Has Died
Peter was born in San Francisco, California, on September 25, 1947. He went to UC Berkeley in 1967 and received a BA in Mathematics in 1969 and an MA in 1971. Peter’s undergraduate advisor was Derrick H. Lehmer, an excellent match given Peter’s research interests since high school: integer factorization.
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The game theory of seduction and marriage with Jane Austen
The enduring success of her early 19th century novels are in large part due to their persistent relevance
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Not all elementary functions can be expressed with exp-minus-log
a personal blog
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A Brutal Look at Balanced Parentheses, Computing Machines, and Pushdown Automata
As discussed in Pattern Matching and Recursion , a well-known programming puzzle is to write a function that determines whether a string of parentheses is “balanced,” i.e. each opening parenthesis has a corresponding closing parenthesis, and the parentheses are properly nested.
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Solver Performance: 1989 vs. 2024
We estimate the magnitude of speed improvement for optimization solvers and computer hardware in the 35 years from 1989 to 2024.
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Revisiting the algorithm that changed horse race betting (2023)
Explore Bill Benter’s iconic horse betting strategy, enhanced with modern code and contrasted against three decades of evolving data.
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Corrected identification of object about to hit the moon
Note : I keep getting questions that cause me to realize I should explain something else, or that I explained something poorly. Click here for a list of recent changes. Last modified 2015 Mar 05 16:00 UTC. Here's the original story about this object .
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Trying Kolmogorov-Arnold Networks in Practice
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
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Markov Chain Monte Carlo (MCMC) Sampling, Part 1: The Basics (2019)
In this first post of Tweag’s four-part series on Markov chain Monte Carlo sampling algorithms, you will learn about why and when to use them and the theoretical underpinnings of this powerful class of sampling methods. We discuss the famous Metropolis-Hastings algorithm and give an intuition on the choice of its free…
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The Entropy of a Markov Chain
A more explicit example
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The Point of the Banach-Tarski Theorem
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
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What Are the Odds?
An unusual lottery result made the news recently: on October 1, 2022, the PCSO Grand Lotto in the Philippines, which draws six numbers from $latex {1}&fg=000000$ to $latex {55}&fg=000000$ a…
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How to average floating point numbers (2015)
When it comes to accuracy, how you add a series of arbitrary values together, and average them still matters.
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A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter?
Learn about public engagement activities from the American Physical Society