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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? 1
Classical CPU architecture is a poor choice for performing matrix-oriented computations. Developers have to spend much effort to create efficient algorithms even for the problems appearing trivial on the surface. Matrix transpose is probably the most striking representative of such problems. It exposes numerous…
[This is a guest post by Kate Stange and Edmund Harriss. This blog post was initially written in a different file format and converted using AI. — T.] In January a group of mathematicians, hi…
This article was originally published in the Russian functional programming journal http://fprog.ru/ and this translation was intended to be published in Peter Seibel’s http://codequarterly.com/ journal, but as Peter eventually decided not to proceed with the journal, I am publishing it on my personal space.
A blog about life, programming, math, logic, and physics.
Double descent is a puzzling phenomenon in machine learning where increasing model size/training time/data can initially hurt performance, but then i…
In the early 1930s, Pascual Jordan attempted to formalise the algebraic properties of Hermitian matrices. In particular: Hermitian matrices form a real vector space: we can add and subtract Hermiti…
In this post I'm going to explore how a mathematical concept can be redefined in progressively more computer-oriented terms, all the way from high level languages down to machine code, ready for direct execution by a computer. To that end, I'm going to define the same logic in several different but related formats:
Introduction In this blog post you are going to read about two things:
Redirecting to https://www.mukeshmithrakumar.com/blog/deep-learning-with-tf2-probability-and-information-theory/ .
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
Basic Economy fares are ultra-restricted airline tickets that offer a lower base price in exchange for fewer benefits than standard economy class. Introduced by major U.S. carriers in the 2010s, these fares have become a widespread strategy for market segmentation - a textbook example of price discrimination in…
The short, simple answer used in calculus courses is that a real number is a point on the number line . That's not the whole truth, but it is adequate for the needs of freshman calculus. The freshman calculus course (at most universities nowadays) follows the 17th century style of Newton and Leibniz, emphasizing…
Everyone uses math libraries. Surprisingly, mainstream math libraries do not produce correct results for several thousands of inputs. Developers are seldom aware of them, which affects reproducibil…
I'm no graphics expert, but appreciate why square roots are useful. The Pythagorean theorem computes distance between points, and dividing by distance helps…
Emergency special: The information we need to understand what Q* is was right in front of us, but the memes are more fun than reality.
3D visualization tool of spherical harmonics. Visualize and compare real, imaginary, and complex components by adjusting the degree l and order m parameters.
For several years I have been designing and implementing a functional teaching language especially for use in the context of a Discrete Mathematics course. The idea is for students to be exposed to…
Description of the film grain synthesis algorithm in AV1. This page provides information on the film grain synthesis algorithm and links for further study
We have identified a vulnerability in the Internet Public Key Infrastructure (PKI) used to issue digital certificates for secure websites. As a proof of concept we executed a practical attack scenario and successfully created a rogue Certification Authority (CA) certificate trusted by all common web browsers. This…
Amazon ICML paper proposes information-theoretic measurement of quantitative causal contribution.
Tetration -- repeated exponentiation a fractional number of times.
Once upon a time I was given the following problem for a technical programming interview:
A number of people have asked me to weigh in on this story in Quanta Magazine (based on this paper [ PDF version ] and also reported in t...
Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care about…
Using Self-Organizing Maps to solve the Traveling Salesman Problem The Traveling Salesman Problem is a well known challenge in Computer Science: it consists on finding the shortest route possible that traverses all cities in a given map only once. Although its simple explanation, this problem is, indeed, NP-Complete…
When an experimental study states "The group with treatment X had significantly less disease ( p = 1%)", many people interpret this statement as being equivalent to "there is a 99% chance that if I do treatment X it will prevent disease." This essay explains why these statements are not equivalent. For such an…
