The latest blog posts to take off on Hacker News. 171 posts.
Background Backpropagation is a common method for training a neural network. There is no shortage of papers online that attempt to explain how backpropagation works, but few that include an example…
This post describes the implementation of pysmtgcc. See “GCC Translation Validation” for background information.
In 1986, Eugene Myers published An O(ND) Difference Algorithm and Its Variations , which unified the problems of finding the longest common subsequence of two sequences (the LCS of "driftwood" and "artwork" is "two") and finding the shortest edit script for transforming one sequence into another. Myers showed that…
I have a little secret: I don’t like the terminology, notation, and style of writing in statistics. I find it unnecessarily complicated. This shows up when trying to read about Markov Chain Monte Carlo methods. Take, for example, the abstract to the Markov Chain Monte Carlo article in the Encyclopedia of…
Shamir's Secret Sharing Scheme
Update: This result appeared in the proceedings of CT-RSA 2023. A preprint is available.
Today's date is a good excuse to memorize a few more digits of 3.1415926 53589793 23846264 33832795....
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.
Now available for preorder.
In numerical linear algebra we are concerned with solving linear algebra problems accurately and efficiently and understanding the sensitivity of the problems to perturbations. We describe seven si…
Note: The full source code for this article can be found here (summarized version). Individual sections contain references to specific code snippets below.
Two acquaintances independently asked about this today, so it seems worth a write-up: recently (as of this writing), DeepMind published a new paper about a new practical fast matrix multiplication …
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…
(I'm still looking for the catchiest way to appreciate the number MMXXVI. Exercise 7.2.1.6–122 gives 1234+.5*6+789 and -1+2345*6/7+8+9 and 1+(2/3)*45*67.8-9 ; other suggestions are welcome. The most elegant that I've seen so far is a beauty that was suggested independently by Arnaud Lefebvre and by Evangelos…
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…
In this post we'll work our way towards an algorithm that can compute convex polygon intersections. We'll also explore a method for intersections between axis-aligned rectangles, a function that can determine the intersection of two line segments, as well as a point in polygon test.
This is a from-scratch explanation of private information retrieval built using homomorphic encryption. I try to assume only a general math / computer science background. To simplify things, my explanations may not always match academic definitions. You can check out this paper or code for more.
Switching away from radians makes code simpler, faster, and more precise.
I wondered how GPT-3 might do on the following problem: given a partially-connected graph, find a path between two nodes, or determine that no path exists. I wrote some code to automate generating …
A lot of modern cryptography builds on insights from number theory, which has been studied for centuries.
The Latest News from Research at Kudelski Security
You may be familiar with the term “hockey stick curve,” used describe a trend that has been flat/stable for a very long time, but shoots up at the end of the series in dramatic fashion, resembling the shape of a hockey stick. Hockey can be a violent sport, and it’s easy to get hurt by even one well-aimed swing…
[Thanks to Jacob Falkovich, Eric Neyman, and my LessWrong reviewer, among others, for their feedback on earlier drafts.] …
Blog of Raph Levien.
Ramanujan came up with an approximation for factorial that resembles Stirling's famous approximation but is much more accurate. As with Stirling's approximation, the relative error in Ramanujan's approximation decreases as n gets larger. Typically these approximations are not useful for small values of n. For n = 5…
TL;DR: After noticing an annoying warning, I went on an absurd yak shave, and discovered that because of a tiny handful of Python packages b...
Way back in the covid-filled summer of 2020, I wrote a survey article about the ridiculously-rapidly-growing Busy Beaver function. My survey then expanded to nearly twice its original length, with …
