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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 latest blog posts to take off on Hacker News. 460 posts.
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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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Fundamental Math for Game Developers
Let's review the most important math topics used by game devs, reflect about math education, and discuss techniques that can be used to improve the way we learn new math topics.
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PageRank algorithm for graph databases
What is PageRank algorithm? How can it be used in various graph database use cases? How to use it in Memgraph? If these questions are keeping you up at night, here is a blog post that will finally put your mind at ease.
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A Curious Integral
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Nearly all binary searches and mergesorts are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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Emulating double precision on the GPU to render large worlds
One of the problems with developing games with large game worlds is that objects start to jitter and teleport around as you move away from the world origin. This post is about how we overcame one challenge in particular and what we did.
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Discovering Novel Algorithms with AlphaTensor
In our paper, published today in Nature, we introduce AlphaTensor, the first artificial intelligence (AI) system for discovering novel, efficient, and provably correct algorithms for fundamental tasks such as matrix multiplication. This sheds light on a 50-year-old open question in mathematics about finding the…
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The definitive guide to “modulo bias” and how to avoid it (2020)
The Latest News from Research at Kudelski Security
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Gödel, Escher, Bach: an in-depth explainer
[Thanks to Jacob Falkovich, Eric Neyman, and my LessWrong reviewer, among others, for their feedback on earlier drafts.] …
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Quaternions: A Practical Guide
AnyLeaf Articles: Quaternions: A practical guide
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Algorithms you should know before you take system design interviews
I put together a list and explained why they are important.
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New method identifies the root causes of statistical outliers
Amazon ICML paper proposes information-theoretic measurement of quantitative causal contribution.
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Hinge and Its Implementation of the Gale–Shapley algorithm
https://thetab.com/uk/2020/05/20/this-is-how-the-nobel-prize-winning-hinge-algorithm-actually-works-157740
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Render mathematical expressions in Markdown On GitHub
You can now use LaTeX style syntax to render math expressions within Markdown inline (using $ delimiters) or in blocks (using $$ delimiters). Writing expressions as blocks To add math…
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Time-Series Compression Algorithms
These algorithms aren't magic – but combined they can save over 90% of storage costs and speed up queries. Here’s how 5 common ones work.
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A 9-line summary of textbook physics
All their wonders in one table
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The Kalman filter: helping chickens cross the road
The Kalman Filter. Helping Chickens Cross the Road. David Austin Grand Valley State University I was running some errands recently when I spied the Chicken Robot ambling down the sidewalk, then vee…
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A gentle introduction to automated reasoning
Meet Amazon Science’s newest research area.
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Some neurons are active when adding, others when subtracting
Most elementary school children probably already know that three apples plus two apples add up to five apples. However, what happens in the brain during such calculations is still largely unknown. The current study by the Universities of Bonn and Tübingen now sheds light on this issue.
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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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Finding the average of two unsigned integers without overflow
Another code golfing adventure.
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The Stacks Project, a new model for organizing and visualizing mathematics
Columbia professor Johan de Jong has spent the last 15 years gathering the foundational theorems of algebraic geometry in one place. His creation, the Stacks Project, offers a new model for organizing and visualizing mathematical information.
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Protons are probably smaller than long thought
Our office chair, the air we breathe, the stars in the night sky: they are all made of atoms, which in turn are composed of electrons, protons and neutrons. Electrons are negatively charged; according to current knowledge, they have no expansion, but are point-like. The positively charged protons are different …
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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.
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Provably space-efficient parallel functional programming
You have heard your grandmother tell you many times: parallel programming is hard. In 2022, does it still have to be? Back in grandma’s heyday, they knew a cool and breezy way to do paralleli…
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Penrose: From mathematical notation to beautiful diagrams
Materials from our SIGGRAPH '20 paper.