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Automatic differentiation can be incorrect

ISCL Seminar Series The Numerical Analysis of Differentiable Simulation: How Automatic Differentiation of Physics Can Give Incorrect Derivatives Scientific machine learning (SciML) relies heavily on automatic differentiation (AD), the process of constructing gradients which include machine learning integrated into mechanistic models for the purpose of gradient-based optimization. While these differentiable programming approaches pitch an idea of “simply put the simulator into a loss function a

Automatic Differentiation Can Be Incorrect

ISCL Seminar Series The Numerical Analysis of Differentiable Simulation: How Automatic Differentiation of Physics Can Give Incorrect Derivatives Scientific machine learning (SciML) relies heavily on automatic differentiation (AD), the process of constructing gradients which include machine learning integrated into mechanistic models for the purpose of gradient-based optimization. While these differentiable programming approaches pitch an idea of “simply put the simulator into a loss function a

Trump admin says Social Security database wasn’t “leaked, hacked, or shared”

The Trump administration yesterday issued a lengthier denial of a whistleblower's allegation that DOGE officials at the Social Security Administration (SSA) copied the agency's database to an insecure cloud system. The allegation centers on the Numerical Identification System (NUMIDENT) database containing Americans' personally identifiable information. The cloud location described by the whistleblower report "is actually a secured server in the agency's cloud infrastructure which historically

Word numbers: Billion approaches (2008)

Word numbers, Part 1: Billion approaches ITA Software recruits computer scientists using puzzles such as the following. If the integers from 1 to 999,999,999 are written as words, sorted alphabetically, and concatenated, what is the 51 billionth letter? In a series of posts, Dylan Thurston and I will solve this problem step by step, introducing concepts such as monoids and differentiation along the way. We will use the programming language Haskell: every post will be a literate program that y

WordNumbers: Counting letters of number names, alphabetized and concatenated

Word numbers, Part 1: Billion approaches ITA Software recruits computer scientists using puzzles such as the following. If the integers from 1 to 999,999,999 are written as words, sorted alphabetically, and concatenated, what is the 51 billionth letter? In a series of posts, Dylan Thurston and I will solve this problem step by step, introducing concepts such as monoids and differentiation along the way. We will use the programming language Haskell: every post will be a literate program that y

Basics of Equality Saturation

01 - Basics of Equality Saturation# This tutorial is translated from egglog. In this tutorial, we will build an optimizer for a subset of linear algebra using egglog. We will start by optimizing simple integer arithmetic expressions. Our initial DSL supports constants, variables, addition, and multiplication. # mypy: disable-error-code="empty-body" from __future__ import annotations from typing import TypeAlias from collections.abc import Iterable from egglog import * class Num ( Expr ): def

Topics: _x _y egraph num rewrite

Locking Your Social Security Number Can Protect You From Identity Theft – Here's How It Works

Credit freezes are your free shield against thieves. fstop123/Getty Images Your Social Security number is a crucial piece of personal information. It's used for everything from getting a new job to securing lines of credit, making it a prime target for identity thieves. This nine-digit number is linked to health benefits, taxes and more. As we see major breaches happen more and more often, protecting your SSN is more important than ever. You can pay for monitoring, but there is a tougher, free

Which NPM package has the largest version number?

Which npm package has the largest version number? I spent way too much time on this I was recently working on a project that uses the AWS SDK for JavaScript. When updating the dependencies in said project, I noticed that the version of that dependency was v3.888.0 . Eight hundred eighty eight. That’s a big number as far as versions go. That got me thinking: I wonder what package in the npm registry has the largest number in its version. It could be a major, minor, or patch version, and it doe

The Quest to Find the Longest-Running Simple Computer Program

The original version of this story appeared in Quanta Magazine. Imagine that someone gives you a list of five numbers: 1, 6, 21, 107 and—wait for it—47,176,870. Can you guess what comes next? If you’re stumped, you’re not alone. These are the first five busy beaver numbers. They form a sequence that’s intimately tied to one of the most notoriously difficult questions in theoretical computer science. Determining the values of busy beaver numbers is a daunting challenge that has attracted a cult

Senator demands to know status of 'duplicate' SSA database 'immediately'

A US Senator is demanding answers after a Social Security Administration (SSA) employee who blew the whistle on Department of Government Efficiency (DOGE) dealings involuntarily resigned last month, citing workplace hostility in response to his concerns. Republican Senator Mike Crapo (it's pronounced Cray-poe), chairman of the Senate Finance Committee, sent a letter to the SSA's commissioner, Frank Bisignano, giving him just two weeks to provide answers to concerns raised last month by now-form

Adjacency Matrix and std:mdspan, C++23

In graph theory, an adjacency matrix is a square matrix used to represent a finite (and usually dense) graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not, and in weighted graphs, they store the edge weights. In many beginner-level tutorials, adjacency matrices are implemented using vector of vectors (nested dynamic arrays), but this approach has inefficiencies due to multiple memory allocations. C++23 introduces std::mdspan , which provides a more efficient

Three big things we still don’t know about AI’s energy burden

The problem with finding that number, as we explain in our piece published in May, was that AI companies are the only ones who have it. We pestered Google, OpenAI, and Microsoft, but each company refused to provide its figure. Researchers we spoke to who study AI’s impact on energy grids compared it to trying to measure the fuel efficiency of a car without ever being able to drive it, making guesses based on rumors of its engine size and what it sounds like going down the highway. But then this

I only give my real number to people, not companies

Ryan Haines / Android Authority I shudder every time I get a phone call from an unknown number. I dread looking at the hundreds of unread text messages in my inbox. No, I’m not being melodramatic. I don’t know about you, but I’ve been very lax with securing my phone number. Every app, every food delivery service, every shopping website that I’ve logged into has my phone number. At the time of signing up for these services, it seemed like the obvious thing to do. After all, if the delivery guy n

The Polestar 5 electric sedan makes its world debut

Today, Polestar debuted its newest model. Just as three is followed by four, next in the series comes five—in this case the Polestar 5. And the new EV is a little departure from the products we've seen so far from this Swedish/Chinese startup. It's a handsome if angular sedan that, like the Polestar 4 SUV, eschews a rear window in favor of more headroom for passengers and a rear-view camera. "Polestar 5 is bringing the future to our present. Our vision for Polestar's design, technology, and sus

The Polestar 5 is an 884hp fastback sedan that should make Porsche nervous

is transportation editor with 10+ years of experience who covers EVs, public transportation, and aviation. His work has appeared in The New York Daily News and City & State. Posts from this author will be added to your daily email digest and your homepage feed. It’s been five years since Polestar first introduced the Precept, a concept car that the electric automaker described as “a manifesto of things to come; a declaration.” Well, come they have, because today Polestar finally revealed the p

How many dimensions is this?

In the past couple of weeks, I’ve been posting about seemingly simple mathematical problems that defy intuition, and where the answers we find on the internet turn out to be shallow or hard to parse. For a taste, you might enjoy the articles on Gödel’s beavers or on infinite decimals. Today, let’s continue by asking a simple question: how many dimensions does a line have? A trained mathematician might blurt out an answer involving vector spaces or open set coverings, but there’s no fun in that.

Zuckerberg caught on hot mic telling Trump 'I wasn't sure' how much to promise to spend on AI in the US

US President Donald Trump jokes with Meta CEO Mark Zuckerberg (L) as he hosts tech leaders for a dinner in the State Dining Room of the White House in Washington, DC, on September 4, 2025. (Photo by SAUL LOEB/AFP via Getty Images) Mark Zuckerberg has certainly come a long way in his relationship with President Donald Trump. Almost exactly a year after the president threatened the Meta CEO with imprisonment, the two sat side-by-side at a White House dinner, alongside numerous other tech CEOs. T

Everything About Bitflags: How to store up to 32 booleans in one value?

When I was younger and I was involved in reverse engineering communities and systems programming, there was this concept called bit flags. They were a standard way of storing a pack of true or false values in ... actually a single value - a function parameter, local variable or entry in some configuration. I found nothing fascinating about that back then and just used it on a regular basis, as every other engineer was. Long time after that and after shifting my focus to web development I just r

iPhone 17 Pro will drop titanium for aluminum, and this might be why

Among the various rumors about Apple’s new iPhone 17 lineup, one of the most curious centers on design materials. Apple will reportedly drop titanium from the iPhone 17 Pro and Pro Max in favor of aluminum, and now we might finally know why. Aluminum iPhone 17 Pro design may provide two key benefits Mark Gurman writes at Bloomberg: One other major change to the iPhone 17 Pro and 17 Pro Max design will be a reversal: moving back to an aluminum frame after switching to titanium in 2023 with the

Love the Pixel 10? You can now wear it on your sleeve, almost literally

Google TL;DR Google has launched new Pixel 10-themed merchandise. The T-Shirt, ceramic mug, and a roll of washi tape, all come with a coded message. Besides online, Google will also sell these items in its physical stores across the US. Google has just dropped a new set of merchandise in succession of the Pixel 10 series phones announced last month. The newly added products include a coffee mug, a full-sleeve T-shirt, and a roll of washi tape. All of these products are available in black an

New knot theory discovery overturns long-held mathematical assumption

Scanning the crowd at a fancy soiree may reveal a wide array of neckties, each fastened with a highly complex mathematical object masquerading as fashion. An entire field of mathematics is devoted to understanding mathematical knots, which one can obtain from any traditional knot by gluing the loose ends together. Mathematicians long believed that if you attach cut ends of two different knots to each other, the new knot will be just as complex as the sum of the individual knots’ complexity. But

New Knot Theory Discovery Overturns Long-Held Mathematical Assumption

Scanning the crowd at a fancy soiree may reveal a wide array of neckties, each fastened with a highly complex mathematical object masquerading as fashion. An entire field of mathematics is devoted to understanding mathematical knots, which one can obtain from any traditional knot by gluing the loose ends together. Mathematicians long believed that if you attach cut ends of two different knots to each other, the new knot will be just as complex as the sum of the individual knots’ complexity. But

For all that's holy, can you just leverage the Web, please?

When I moved in with my wife Laura in 2005, we lived in a shared apartment in Barcelona that had an ancient washing machine that was just there already, no idea who initially bought it. I managed to break the washing machine door's closing mechanism some time in 2006, so for a few weeks, whenever we did the washing, we had to lean a chair against the door so it wouldn't open. At the time, we were both students and living on a small budget. Eventually, later in the same year, we bought an Electr

How to perform a reverse phone number lookup

In an age of constant communication, receiving phone calls or messages from unknown numbers has become increasingly common. Whether it's a missed call from an unfamiliar number, a potential scam or a wrong number, performing a reverse phone number lookup can help you identify the caller. You could start your search with free tools like Google or Whitepages, but if you’re struggling to find the person behind the number, paid services such as Spokeo or BeenVerified might give you more detail. In t

$1B Powerball Is Minting Social Media Gold

Powerball just hit a billion dollars, and people are freaking out about it. For 39 draws in a row, no ticket matched all six numbers for the Powerball jackpot. The last draw was on Saturday night. Now, for the next drawing on Labor Day, the jackpot has snowballed to $1.1 billion and will be the game’s fifth-largest prize ever, according to a statement from the lottery. The largest jackpot prize ever was cashed out in November 2022 by Edwin Castro, a California man who scored a $2.04 billion do

Nullable vs. Nullable in C#

Nullable vs nullable in C# One of the most unfortunate parts of the nullability narrative in C# is the reuse of the T? syntax to denote two completely separate concepts for value types and reference types. This leads to some odd and confusing behaviour. As you may know, nullable value types is a much older concept than nullable reference types. Nullable value types were introduced in C# 2.0, whereas nullable reference types came in C# 8.0. And they’re not the same. Nullable isn’t nullable. Fo

Miss your landline? Verizon's new Family Line lets 5 phones share one number

Elyse Betters Picaro / ZDNET Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways Verizon's new Family Line gives you a single shared mobile number. You can share the number across as many as five smartphones. Verizon Family Plus with Family Line will cost you an extra $10 a month. My wife and I got rid of our landline years ago, relying solely on our individual mobile phones to make and receive calls. One feature I miss about our home phone was the way we could shar

That boolean should probably be something else

Monday, June 30, 2025 One of the first types we learn about is the boolean. It's pretty natural to use, because boolean logic underpins much of modern computing. And yet, it's one of the types we should probably be using a lot less of. In almost every single instance when you use a boolean, it should be something else. The trick is figuring out what "something else" is. Doing this is worth the effort. It tells you a lot about your system, and it will improve your design (even if you end up usi

Crystal Dynamics announces layoffs, but says Tomb Raider will not be impacted

Crystal Dynamics, the studio behind the recent Tomb Raider games, announced an unspecified number of layoffs today. In a post on LinkedIn, the game developer kept the size of the cuts vague, only stating that "a number of our talented colleagues" would be impacted. In what's becoming an all-too-familiar refrain, the company cited "evolving business conditions" as the reason for the layoffs. "This decision was not made lightly," the post reads. "It was necessary, however, to ensure the long-term

Using information theory to solve Mastermind

How you've just played optimal Mastermind Mastermind is a game all about information. The Code Master selects one of \( 6^4 = 1\,296 \) secret codes. Each incorrect guess gives us information by eliminating some of these; the more codes that are ruled out, the more information that guess has provided. Let's quantify this insight! Suppose a guess gets some response that reduces the number of possible keys from some number \(n\) to a smaller \(n'<n\). The convention in information theory, a branc