1891
Clojure Numerics: Orthogonalization and Least Squares
How to solve linear systems that have many solutions, or those that have no solutions at all? That's the theme for a thick math textbook, of course, but from...
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
1892
Defining Statistical Models in Jax?
This is Bob. And I’d like to know the best way for us to code a bunch of models in JAX to use to evaluate parallel algorithms including normalizing flows. I’m going to dump out my current thinking, but I’m really hoping to get feedback from experts on the best way to do this without starting a flame war in the…
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Nibble Sort
A while back, John Regehr posted the Nibble Sort Programming Contest on his blog. The objective was to write a program that sorts the 4-bit components (nibbles) of 64-bit words as fast as possible. For example, 0x42badc0ffeed00d5 should result in 0xffeedddcba542000 after sorting.
1896
What Are Diffusion Models?
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1897
Dungeon Generation in Enter The Gungeon
I’ve been playing a lot of Enter The Gungeon recently. It’s a great, brutally hard, twin stick bullet hell that reminded me a lot of Binding of Isaac. But as I’ve been playing it …
1898
The Dome: A simple violation of determinism in Newtonian mechanics (2005)
John D. Norton Department of History and Philosophy of Science, University of Pittsburgh Pittsburgh PA 15260. Homepage: www.pitt.edu/~jdnorton This page is available at www.pitt.edu/~jdnorton/goodies
1899
Why I decided not to enter the $100k global warming time-series challenge
Interesting applied project for your students , or as a warning for decisions under uncertainty / statistical significance. Real money on the line so the length of time and number of entries required to get a winner may be an interesting dataset after this is all done.
1900
Breaking 256-Bit Elliptic Curve Encryption with a Quantum Computer
Researchers have calculated the quantum computer size necessary to break 256-bit elliptic curve public-key cryptography: Finally, we calculate the number of physical qubits required to break the 256-bit elliptic curve encryption of keys in the Bitcoin network within the small available time frame in which it would…
1901
Not all graphs are trees
It's pretty easy to imagine how to represent relational algebra expressions as a tree—they are already structurally rooted trees where each operator has its...
1902
Reinventing the Wheel: Discovering the Optimal Rolling Shape with PyTorch (2019)
It is thought that the wheel was invented more than five thousand years ago, yet modern machine learning tools were only developed in the past few decade...
1903
Embeddings, vectors, and arithmetic
An embedding is the representation of a piece of text like a word, sentence, or paragraph. Traditionally this value is in the form of a mathematical vector - a point in space. You can think of it as analogous to coordinates on a map that just happens to have many, many dimensions.
1904
DARPA’s 23 Challenge Questions
Research in Scientific Computing in Undergraduate Education2020117 points30 commentsMath & Algorithms details
DARPA challenges The Defense Advanced Research Projects Agency (DARPA) has issued 23 mathematical challenges. DARPA says the solution of any one of these challenges would have the effect of “…
1905
One night in Uzbekistan: Why was this one data point so influential?
We have a comment coming out in Nature next week that is going to cause the retraction of a high-profile paper by Kotz et al. from last year (the second most cited climate paper in the news in 2024).
1906
Category Theory Illustrated – Types
In this chapter we will talk about types. This might be disappointing for you, if you expected to learn about as many new categories as possible (which you don’t even suspect are really categories till the unexpected reveal)—we’ve been talking about the category of types in a given programming language ever since the…
1907
Notes on Weight Initialization for Deep Neural Networks
Neural networks involve long sequence of multiplications, usually between a matrix and a vector, say \(a*x\). The result of this sequence of multiplications will either have a huge magnitude or be reduced to 0. We can divide \(a\) by a number ( scaling_factor ) to scale down its magnitude to the right level. Proper…
1908
Fast, Constant-Time Sphere Indexing
Map any 3D point on or above a triangle-subdivided sphere to a triangle index in constant time, without recursion, table lookups or complicated branching logic.
1909
1910
Difficult math is about recognizing patterns
Jeff Bezos tells a great story about the smartest guy he knew at Princeton. He and a classmate were working on a really tough partial differential equation and getting nowhere. They spent 3 hours on the problem and gave up.
1911
Romeo and Julia, Where Romeo Is Basic Statistics
Hello there. This is an open access book entitled: “Romeo and Julia, where Romeo is Basic Statistics”. So I guess it’s gonna be about a programming language named Julia and its usage for basic statistics.
1912
Legible Mathematics: Sketches of interactive arithmetic for programming (2014)
Sketches of an interactive arithmetic for programming by Glen Chiacchieri.
1913
Spikey Spheres
A word of warning ... I'm presenting here something called an analogy. It's not perfect, it has problems, it's not exact, but there are ways in which it can aid your thinking. I'm giving a way of visualising high-dimensional spheres, a way that has its limitations, but which can help avoid making mistakes based on…
1914
Higher quality random floats
Much has been written about how to generate random 64-bit integers; people might argue over which particular (CS)PRNG is best suited for a given task, but there is agreement on the general shape of the solution: keep some state around, and then extract 64 bits of randomness at a time, where each bit is equally likely…
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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…
1918
1919
Probably Approximately Correct – A Formal Theory of Learning (2014)
In tackling machine learning (and computer science in general) we face some deep philosophical questions. Questions like, “What does it mean to learn?” and, “Can a computer learn?” and, “How do you define simplicity?” and, “Why does Occam’s Razor work? (Why do simple hypotheses do well at modelling reality?)” In a…
1920
Prospecting for Hash Functions
Update 2022 : TheIronBorn has found even better permutations using a smarter technique. That thread completely eclipses my efforts in this article.