2191
The inefficiency of RL, and implications for RLVR progress
And implications for RLVR progress
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
2192
What is the roundest country?
We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem…
2193
Algorithms Every Data Scientist Should Know: Reservoir Sampling
Cloudera Blog is your source for expert guidance on the latest data and AI trends, technology innovation, best practices, success stories, and more.
2194
The 17x17 problem solved
THE 17x17 PROBLEM HAS BEEN SOLVED!!!!! On Nov 30, 2009 I posted here the following challenge: If someone emails me a 4-coloring of...
2195
Why Deep Learning Works II: the Renormalization Group
Deep Learning is amazing. But why is Deep Learning so successful? Is Deep Learning just old-school Neural Networks on modern hardware? Is it just that we have so much data now the methods work b…
2196
An interactive review of the Oklab perceptual color space
Blog of Raph Levien.
2197
Magic: The Gathering Is Turing Complete (v5)
I'm assuming you're familiar with the basic idea of what a Turing machine is . There are a few parts to building one in Magic: a tape extending in two directions storing cells of a few different "colours"; a processing head that can read the current cell's colour, write a new colour and change its state if necessary…
2198
Introduction to Mean Shift Algorithm
Its been quite some time since I wrote a Data Mining post . Today, I intend to post on Mean Shift – a really cool but not very well known algorithm. The basic idea is quite simple but the results a…
2199
Random Points on a Sphere
John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances $latex |xy R…
2200
Inspecting C's qsort Through Animation
The C standard library includes a qsort() function for sorting arbitrary buffers given a comparator function. The name comes from its original Unix implementation, “quicker sort,” a variation of the well-known quicksort algorithm. The C standard doesn’t specify an algorithm, except to say that it may be unstable (C99…
2201
Algebraic graph calculus (2021)
We describe a graph-theoretic analogue of vector calculus. The linear operators of vector calculus (gradient, divergence, laplacian) correspond to the matrices naturally associated to graphs (incidence matrix, adjacency matrix). This analogy is useful for formalizing the discretization of some problems in image and…
2202
2203
Sparse Matrices (2019)
A sparse matrix is a matrix that has a value of 0 for most elements. If the ratio of N umber of N on- Z ero ( NNZ ) elements to the size is less than 0.5, the matrix is sparse. While this is the mathematical definition, I will be using the term sparse for matrices with only NNZ elements and dense for matrices with all…
2204
Andrew Wiles on the struggle and beauty of mathematics
Roger Highfield explores the beauty of mathematics at a recent event at the Science Museum
2205
Fine, I'll Play With Skiplists
Follow me on Bluesky! A Log-Structured Merge tree, or LSM, is a popular data structure for storage engines. It’s what is used by RocksDB, which is sort of...
2206
2207
An Introduction to Lagrange Multipliers
Lagrange multipliers are used in multivariable calculus to find maxima and minima of a function subject to constraints (like "find the highest elevation along the given path" or "minimize the cost of materials for a box enclosing a given volume"). It's a useful technique, but all too often it is poorly taught and…
2208
Summary of all the MIT Introduction to Algorithms lectures
As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an...
2209
1 kilobyte is precisely 1000 bytes?
We usually learn that 1 kilobyte is 1024 bytes, 1 MB is 1024 kilobytes, etc. But is this true or a kilobyte is precisely 1000 bytes?
2210
2211
EU proposing to regulate the use of Bayesian estimation
The European Commission just released their Proposal for a Regulation on a European approach for Artificial Intelligence . They finally get around to a definition of “AI” on page 60 of the report (link above):
2212
Implementing the Elo Rating System (2020)
In this article we’ll look at how to implement the Elo rating system in code.
2213
Time Travel (2006)
Last time we talked about free will, superintelligent predictors, and Dr. Evil planning to destroy the earth from his moon base. Today I'd like to talk about a more down-to-earth topic: time travel. The first point I have to make is one that Carl Sagan made: we're all time travelers—at the rate of one second per…
2214
Can a person be identified by just the way they type?
Do a detailed analysis of your own typing style, just using Mathematica. Can a person be identified just by the way they type? See group data analysis.
2215
2216
2217
Computational Category Theory in Python III: Monoids, Groups, and Preorders
Parts 1 and 2 are found here and here
2218
Insert D-Wave Post Here
In the two months since I last blogged, the US has continued its descent into madness. Yet even while so many certainties have proven ephemeral as the morning dew—the US’…
2219
How to create a game using hyperbolic geometry? (2020)
puzzle roguelike on a hyperbolic plane
2220
How medieval astronomers made trig tables
Clever tricks used by medieval astronomers to tabulate sines at every degree, before calculators and before calculus.